diff --git a/geo_LHC001_AoA_4/boundary_dual_area_geo_LHC001_AoA_4.npy b/geo_LHC001_AoA_4/boundary_dual_area_geo_LHC001_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ffd4828717a2ffc37d598eb6a8d59d2a0f3e0ff4
--- /dev/null
+++ b/geo_LHC001_AoA_4/boundary_dual_area_geo_LHC001_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:54542164a2615f8f99c8e6d0bb5aa5baff36d24b4291a61ebe158528dcdd9c6e
+size 546264132
diff --git a/geo_LHC003_AoA_22/boundary_dual_area_geo_LHC003_AoA_22.npy b/geo_LHC003_AoA_22/boundary_dual_area_geo_LHC003_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2c5027d45a00ac1b8ec3abf20f2e1a84f9738c15
--- /dev/null
+++ b/geo_LHC003_AoA_22/boundary_dual_area_geo_LHC003_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:16e405937cb3a61ec6b416b8f10101cd0b251ee4c1f2196e189ccef0b84a156f
+size 592204672
diff --git a/geo_LHC004_AoA_6/boundary_dual_area_geo_LHC004_AoA_6.npy b/geo_LHC004_AoA_6/boundary_dual_area_geo_LHC004_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..55cbc47980a4298e0e21bc51eab1837690523966
--- /dev/null
+++ b/geo_LHC004_AoA_6/boundary_dual_area_geo_LHC004_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d3cdeb185fbe96172e26af88c79fb7320130216fbeb9268576f5c6caf594b9db
+size 532340656
diff --git a/geo_LHC005_AoA_12/boundary_dual_area_geo_LHC005_AoA_12.npy b/geo_LHC005_AoA_12/boundary_dual_area_geo_LHC005_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..22289e858fcb2e7994e24b5724b0c1cc11ab76fe
--- /dev/null
+++ b/geo_LHC005_AoA_12/boundary_dual_area_geo_LHC005_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:538bbaa1ac822d63541af173102bd0441efdfb0b89b0d7b4f915dce2de80819a
+size 566666508
diff --git a/geo_LHC005_AoA_4/boundary_dual_area_geo_LHC005_AoA_4.npy b/geo_LHC005_AoA_4/boundary_dual_area_geo_LHC005_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0a164352f4487e8f6ebe409ff99d36b7b77ccfce
--- /dev/null
+++ b/geo_LHC005_AoA_4/boundary_dual_area_geo_LHC005_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:724f9ebef02f894e52c428d5e1050bb29a8736cd5b8c4ba65c50f1f431a06c36
+size 536923164
diff --git a/geo_LHC005_AoA_6/boundary_dual_area_geo_LHC005_AoA_6.npy b/geo_LHC005_AoA_6/boundary_dual_area_geo_LHC005_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..00fa3bf198e7d31fb7d99c2fefb323ec8d247145
--- /dev/null
+++ b/geo_LHC005_AoA_6/boundary_dual_area_geo_LHC005_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6910c7bd749a768bfe4bc0bcf735d997d839a5f270302b63cd12641554eb7dd6
+size 552763036
diff --git a/geo_LHC006_AoA_12/boundary_dual_area_geo_LHC006_AoA_12.npy b/geo_LHC006_AoA_12/boundary_dual_area_geo_LHC006_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1562d3b638760dc7748187018a0f8f943030bc91
--- /dev/null
+++ b/geo_LHC006_AoA_12/boundary_dual_area_geo_LHC006_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dd1f25980e470a47242a4ae871afe4e06c296e35a647b9fea5fb50a3298a805e
+size 586430508
diff --git a/geo_LHC007_AoA_14/boundary_dual_area_geo_LHC007_AoA_14.npy b/geo_LHC007_AoA_14/boundary_dual_area_geo_LHC007_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..be6e3d5479f1ce2845934b3dafc427f2df241819
--- /dev/null
+++ b/geo_LHC007_AoA_14/boundary_dual_area_geo_LHC007_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c04693362385a4747eb02fbe8b3be620abea39db177e8aaa992b048b0e0a6e1
+size 566528424
diff --git a/geo_LHC009_AoA_12/boundary_dual_area_geo_LHC009_AoA_12.npy b/geo_LHC009_AoA_12/boundary_dual_area_geo_LHC009_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4162fca9730cd0f549cf830ef96c831e99b8bc1f
--- /dev/null
+++ b/geo_LHC009_AoA_12/boundary_dual_area_geo_LHC009_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1fea9d3f5fa9bcda6195402c10600786ab7c46258efefe06a1e302e61ab12d0d
+size 548162212
diff --git a/geo_LHC010_AoA_10/boundary_dual_area_geo_LHC010_AoA_10.npy b/geo_LHC010_AoA_10/boundary_dual_area_geo_LHC010_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..be3c5f736ecc9bf6d7fe8d3c30d156138353d9fd
--- /dev/null
+++ b/geo_LHC010_AoA_10/boundary_dual_area_geo_LHC010_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b3e5b87201f3ba351ad1eae479d13242d4697b8ab164add369b28c53b23470a1
+size 551457572
diff --git a/geo_LHC010_AoA_22/boundary_dual_area_geo_LHC010_AoA_22.npy b/geo_LHC010_AoA_22/boundary_dual_area_geo_LHC010_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b24bc5a27f40e2a46a8eb5c4bd10a718c1459f7f
--- /dev/null
+++ b/geo_LHC010_AoA_22/boundary_dual_area_geo_LHC010_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e644ac0ad082d6d1b2297939f39eaed5da8dd1428b933a5687288b5bf3edb1f0
+size 565460460
diff --git a/geo_LHC010_AoA_6/boundary_dual_area_geo_LHC010_AoA_6.npy b/geo_LHC010_AoA_6/boundary_dual_area_geo_LHC010_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d3d221a183f6301c43ac42445b913e6918179d85
--- /dev/null
+++ b/geo_LHC010_AoA_6/boundary_dual_area_geo_LHC010_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dbb8a8f962993a44749ad50c5e901b48f0d7d9ed6cea7e5130e1f93a2076e7bf
+size 518486992
diff --git a/geo_LHC011_AoA_10/boundary_dual_area_geo_LHC011_AoA_10.npy b/geo_LHC011_AoA_10/boundary_dual_area_geo_LHC011_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2a68f5ca2c66514d923214f0f35ec2f62c285554
--- /dev/null
+++ b/geo_LHC011_AoA_10/boundary_dual_area_geo_LHC011_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bab933464beee5e57cc2e32e5c00dd10940f7b521a2add588e385d1b48438040
+size 575407508
diff --git a/geo_LHC012_AoA_4/boundary_dual_area_geo_LHC012_AoA_4.npy b/geo_LHC012_AoA_4/boundary_dual_area_geo_LHC012_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..261dd2ebd3a9bdb1e2c8d970e7abd524fe281f88
--- /dev/null
+++ b/geo_LHC012_AoA_4/boundary_dual_area_geo_LHC012_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f8b04e2e71b449b58e907789a7271b3d0d7fe7873664b282497633ea9912c1c7
+size 516973420
diff --git a/geo_LHC012_AoA_8/boundary_dual_area_geo_LHC012_AoA_8.npy b/geo_LHC012_AoA_8/boundary_dual_area_geo_LHC012_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7818afba2022e5a78889170bd213ac3ce098f61a
--- /dev/null
+++ b/geo_LHC012_AoA_8/boundary_dual_area_geo_LHC012_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b54bd154204820ab4c75395121101ad985be13c1d8d071da19cc5b149cbeccbf
+size 550332000
diff --git a/geo_LHC013_AoA_20/boundary_dual_area_geo_LHC013_AoA_20.npy b/geo_LHC013_AoA_20/boundary_dual_area_geo_LHC013_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6d74e5105fdbcc22d92192184676fad246bc538b
--- /dev/null
+++ b/geo_LHC013_AoA_20/boundary_dual_area_geo_LHC013_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:12ef5ca4badeafa11e930a7a6d61877f5df56ab79c5a220a76507c7461272e8f
+size 548358300
diff --git a/geo_LHC013_AoA_6/boundary_dual_area_geo_LHC013_AoA_6.npy b/geo_LHC013_AoA_6/boundary_dual_area_geo_LHC013_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..024b17dbd2c1fe038b9f0bca3bfc5fc67dca7470
--- /dev/null
+++ b/geo_LHC013_AoA_6/boundary_dual_area_geo_LHC013_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fd21ba457e24d9981dfea19483a4d20f3383fbf4e3c961ecaf1c3920d9374ec6
+size 532687460
diff --git a/geo_LHC014_AoA_12/boundary_dual_area_geo_LHC014_AoA_12.npy b/geo_LHC014_AoA_12/boundary_dual_area_geo_LHC014_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8a2b017ee022964394dc2b1401885fe32ed52878
--- /dev/null
+++ b/geo_LHC014_AoA_12/boundary_dual_area_geo_LHC014_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:85e33de5a06b9d47b632616deee9293280fabc602dae41cd5e73d4bebc40256a
+size 568723856
diff --git a/geo_LHC015_AoA_14/boundary_dual_area_geo_LHC015_AoA_14.npy b/geo_LHC015_AoA_14/boundary_dual_area_geo_LHC015_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..eb1c8a00a63c7536f2797c73e75e0b4001a81144
--- /dev/null
+++ b/geo_LHC015_AoA_14/boundary_dual_area_geo_LHC015_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1e28a904e32c95f8268e85847e376cf1c955265c74373d90cb3c827a81792994
+size 588638004
diff --git a/geo_LHC015_AoA_22/boundary_dual_area_geo_LHC015_AoA_22.npy b/geo_LHC015_AoA_22/boundary_dual_area_geo_LHC015_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fa781176870fa692280336573809932512c4c1f1
--- /dev/null
+++ b/geo_LHC015_AoA_22/boundary_dual_area_geo_LHC015_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:540ba5885995ff06e2df07a0270dd7a0058c5cb6bae0ccb273f5af5377bf827f
+size 591679860
diff --git a/geo_LHC016_AoA_6/boundary_dual_area_geo_LHC016_AoA_6.npy b/geo_LHC016_AoA_6/boundary_dual_area_geo_LHC016_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..eadaeeb6ac202c69bd5e1f2e2794b0e4b17316c8
--- /dev/null
+++ b/geo_LHC016_AoA_6/boundary_dual_area_geo_LHC016_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8fa120fc5e89965f913f99139b5934420c697e10d86f67795ea2fb8c575ec26c
+size 511980504
diff --git a/geo_LHC017_AoA_22/boundary_dual_area_geo_LHC017_AoA_22.npy b/geo_LHC017_AoA_22/boundary_dual_area_geo_LHC017_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..070594870b5f9ee7ff6fd808f9a65c898534e235
--- /dev/null
+++ b/geo_LHC017_AoA_22/boundary_dual_area_geo_LHC017_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b32eb15c67a433d14c73deb5e8128f014c959b21fada48327f360eccafab3d3a
+size 560256524
diff --git a/geo_LHC017_AoA_8/boundary_dual_area_geo_LHC017_AoA_8.npy b/geo_LHC017_AoA_8/boundary_dual_area_geo_LHC017_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..371fb784d8ce4447faedb56be4550d56e457bc9d
--- /dev/null
+++ b/geo_LHC017_AoA_8/boundary_dual_area_geo_LHC017_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2ca1733cc7476cb9917c86945224d15ea9239d347b9d905476522dfdf32b3d87
+size 569063896
diff --git a/geo_LHC018_AoA_10/boundary_dual_area_geo_LHC018_AoA_10.npy b/geo_LHC018_AoA_10/boundary_dual_area_geo_LHC018_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c3e55f238f407339cc79841eaf7c4f3a5df68e2f
--- /dev/null
+++ b/geo_LHC018_AoA_10/boundary_dual_area_geo_LHC018_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:770389ea9031f6f0ffd895e99f1c7a202d0cea6a86b51cc23bfba95c4fc95bfa
+size 554258684
diff --git a/geo_LHC018_AoA_4/boundary_dual_area_geo_LHC018_AoA_4.npy b/geo_LHC018_AoA_4/boundary_dual_area_geo_LHC018_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4174b0b17389bd104e1e71012acc18b083db3c88
--- /dev/null
+++ b/geo_LHC018_AoA_4/boundary_dual_area_geo_LHC018_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eb305c38a7bd43edcdb0a25919f1806761680f341453f6832c71760bfed58409
+size 515517772
diff --git a/geo_LHC018_AoA_8/boundary_dual_area_geo_LHC018_AoA_8.npy b/geo_LHC018_AoA_8/boundary_dual_area_geo_LHC018_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2c019149aac4dc845a261e9ee56e7a5e7abbaa08
--- /dev/null
+++ b/geo_LHC018_AoA_8/boundary_dual_area_geo_LHC018_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a2a7f3ec2ec655ee57ecb2a9ca4114c5157fb4b18ba8b86e9f6acbc3788a029a
+size 550216988
diff --git a/geo_LHC019_AoA_22/boundary_dual_area_geo_LHC019_AoA_22.npy b/geo_LHC019_AoA_22/boundary_dual_area_geo_LHC019_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4dc159dcd104b3352ca2849090ff2eaa0df649f5
--- /dev/null
+++ b/geo_LHC019_AoA_22/boundary_dual_area_geo_LHC019_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4981f8cc2629bb899dc6f732fa24539f5351464117323698f2248b66d41b591a
+size 545409112
diff --git a/geo_LHC020_AoA_18/boundary_dual_area_geo_LHC020_AoA_18.npy b/geo_LHC020_AoA_18/boundary_dual_area_geo_LHC020_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..09fe7ec0e4a69dc6a3defc180b9451702f7cdc07
--- /dev/null
+++ b/geo_LHC020_AoA_18/boundary_dual_area_geo_LHC020_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd98270bb842d085d8d4ac6056a4d557dcc71b355510257b8e76ba83596bf024
+size 593201504
diff --git a/geo_LHC020_AoA_22/boundary_dual_area_geo_LHC020_AoA_22.npy b/geo_LHC020_AoA_22/boundary_dual_area_geo_LHC020_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..293bcb9a1cea79ad715ba74576068c06186640aa
--- /dev/null
+++ b/geo_LHC020_AoA_22/boundary_dual_area_geo_LHC020_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8e05a2a1ce1ef5a45e0d8628e33af15f7091211c445f1bb0034ff313df1e1d1d
+size 588720632
diff --git a/geo_LHC021_AoA_10/boundary_dual_area_geo_LHC021_AoA_10.npy b/geo_LHC021_AoA_10/boundary_dual_area_geo_LHC021_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..335e221ddfd59a3c7b3782494fecc42f9d720dbe
--- /dev/null
+++ b/geo_LHC021_AoA_10/boundary_dual_area_geo_LHC021_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:73199c162c67669bfd019b34eab4f8f19c93bd4fd0f1e8ca250c79350dd8efad
+size 569175768
diff --git a/geo_LHC022_AoA_16/boundary_dual_area_geo_LHC022_AoA_16.npy b/geo_LHC022_AoA_16/boundary_dual_area_geo_LHC022_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7e8e161f0d48a4c6872b03fc09cc131cf1dd3f84
--- /dev/null
+++ b/geo_LHC022_AoA_16/boundary_dual_area_geo_LHC022_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:62336d15199e36c81b14f1a5f7b043b0e276f09159c63528701035ee73c0dd6f
+size 558736492
diff --git a/geo_LHC022_AoA_20/boundary_dual_area_geo_LHC022_AoA_20.npy b/geo_LHC022_AoA_20/boundary_dual_area_geo_LHC022_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3e446d3bb8f19e46829b4bdd70b6ffa6394dcee8
--- /dev/null
+++ b/geo_LHC022_AoA_20/boundary_dual_area_geo_LHC022_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0b0cfd39c3fc08e54a62d9d563ea1df17a1ecf6cc7261f0b9a82be2f64cfa598
+size 561676592
diff --git a/geo_LHC022_AoA_4/boundary_dual_area_geo_LHC022_AoA_4.npy b/geo_LHC022_AoA_4/boundary_dual_area_geo_LHC022_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..48e77a4c2dcda961709eb881c39fc188f1d65064
--- /dev/null
+++ b/geo_LHC022_AoA_4/boundary_dual_area_geo_LHC022_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4b5cf6e7b8a0d2d1b88f353980384d556b8a80f9010ba5312ab64c8e6a7f77ba
+size 513204812
diff --git a/geo_LHC023_AoA_14/boundary_dual_area_geo_LHC023_AoA_14.npy b/geo_LHC023_AoA_14/boundary_dual_area_geo_LHC023_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..804440cbe64dd6a1a9004b6cf564d166d6838162
--- /dev/null
+++ b/geo_LHC023_AoA_14/boundary_dual_area_geo_LHC023_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e5b8f6e3136ff6a97a7d9b13775e3659db36d969971d2459d0ad96df1fdc4fd7
+size 580733664
diff --git a/geo_LHC023_AoA_16/boundary_dual_area_geo_LHC023_AoA_16.npy b/geo_LHC023_AoA_16/boundary_dual_area_geo_LHC023_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..23264c5eb300f5898af97f2df8688456e2c04a1d
--- /dev/null
+++ b/geo_LHC023_AoA_16/boundary_dual_area_geo_LHC023_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7b24d6b620eefbbd043f815b18c840fdecc6e4b5d59bd7a3efa7bb7c31ec7425
+size 586354156
diff --git a/geo_LHC023_AoA_20/boundary_dual_area_geo_LHC023_AoA_20.npy b/geo_LHC023_AoA_20/boundary_dual_area_geo_LHC023_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..95a2a52844db3ec9c87a8d74d2cb526da7b530cc
--- /dev/null
+++ b/geo_LHC023_AoA_20/boundary_dual_area_geo_LHC023_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:96583a38f428cc38f6f2a326dc8d06800c9f1969ea690a3637a4ff0a60a04adc
+size 592550544
diff --git a/geo_LHC024_AoA_18/boundary_dual_area_geo_LHC024_AoA_18.npy b/geo_LHC024_AoA_18/boundary_dual_area_geo_LHC024_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..41652f39aafcee965ff753610a5ec64a39c18b54
--- /dev/null
+++ b/geo_LHC024_AoA_18/boundary_dual_area_geo_LHC024_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6e937839d5b9738889579a7d5aed7dee69d538b2b9ec2f1fb18bad1f6d6ac515
+size 597923644
diff --git a/geo_LHC024_AoA_20/boundary_dual_area_geo_LHC024_AoA_20.npy b/geo_LHC024_AoA_20/boundary_dual_area_geo_LHC024_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cb7a0146d74e5f02ee13c9c88a3963dff1c0fc3e
--- /dev/null
+++ b/geo_LHC024_AoA_20/boundary_dual_area_geo_LHC024_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d51238f1a20aefc80f66e884408da2a10b92cb248a855a36f52ca31014ff4e6b
+size 592566036
diff --git a/geo_LHC024_AoA_22/boundary_dual_area_geo_LHC024_AoA_22.npy b/geo_LHC024_AoA_22/boundary_dual_area_geo_LHC024_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c770efa95102252b820ca9f89830fad33593c204
--- /dev/null
+++ b/geo_LHC024_AoA_22/boundary_dual_area_geo_LHC024_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:70c992f9c60fbdd9b6717c3e5809f5876b5cb91e48b18c7a471a7f3017f9ab69
+size 591857280
diff --git a/geo_LHC024_AoA_4/boundary_dual_area_geo_LHC024_AoA_4.npy b/geo_LHC024_AoA_4/boundary_dual_area_geo_LHC024_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2e795532702b4be82ea9334e21d32205acc08727
--- /dev/null
+++ b/geo_LHC024_AoA_4/boundary_dual_area_geo_LHC024_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:06687bead9909fbb18f01896dac0050779e09e9a58e20347661e701d0378d62e
+size 557669800
diff --git a/geo_LHC024_AoA_8/boundary_dual_area_geo_LHC024_AoA_8.npy b/geo_LHC024_AoA_8/boundary_dual_area_geo_LHC024_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3106f2b97b6bc22bc18f160e1738121d3babc355
--- /dev/null
+++ b/geo_LHC024_AoA_8/boundary_dual_area_geo_LHC024_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:17f0ed09e8f1c9a5386edc2d321bd56df57c92bb1c7568026970869b22bb1b77
+size 573824564
diff --git a/geo_LHC025_AoA_10/boundary_dual_area_geo_LHC025_AoA_10.npy b/geo_LHC025_AoA_10/boundary_dual_area_geo_LHC025_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9304d9484d8934e0963fac3a4cbb897c440894c1
--- /dev/null
+++ b/geo_LHC025_AoA_10/boundary_dual_area_geo_LHC025_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:edead1e697c804c4ca70c0e18d18b3d31008153030da8c1aa2c9a7873bd90e75
+size 545562616
diff --git a/geo_LHC025_AoA_12/boundary_dual_area_geo_LHC025_AoA_12.npy b/geo_LHC025_AoA_12/boundary_dual_area_geo_LHC025_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..77236fc81dd90c3126059f3c1f8eb09aa75ff3f9
--- /dev/null
+++ b/geo_LHC025_AoA_12/boundary_dual_area_geo_LHC025_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2733efd69e0c75c4637ffff465be140ed5eeba89cdf7d279caf2d76e74c513c1
+size 549470352
diff --git a/geo_LHC025_AoA_16/boundary_dual_area_geo_LHC025_AoA_16.npy b/geo_LHC025_AoA_16/boundary_dual_area_geo_LHC025_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1ddeb1e95f8e7b60b56667a9e4e195e73a38ff8e
--- /dev/null
+++ b/geo_LHC025_AoA_16/boundary_dual_area_geo_LHC025_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6afe5ad78afde8e3d56a1153b74ab34b325f255a815e56c85f0f4f42e52f9196
+size 551118024
diff --git a/geo_LHC025_AoA_20/boundary_dual_area_geo_LHC025_AoA_20.npy b/geo_LHC025_AoA_20/boundary_dual_area_geo_LHC025_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a34e5731dc97af4415df68fa547fffc3d0a2155b
--- /dev/null
+++ b/geo_LHC025_AoA_20/boundary_dual_area_geo_LHC025_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1bb703be0c79622157c47ddd652280ef42e3255cac68864cbc75e07963af1f31
+size 554694832
diff --git a/geo_LHC025_AoA_4/boundary_dual_area_geo_LHC025_AoA_4.npy b/geo_LHC025_AoA_4/boundary_dual_area_geo_LHC025_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5b0958f06d4e7a0e13f3cadb023f9b3b066342e0
--- /dev/null
+++ b/geo_LHC025_AoA_4/boundary_dual_area_geo_LHC025_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2dccd1b819f2aa7ee6d03ad77b5506da999a137ad44a4a34b54e9afa5df30b2b
+size 506744384
diff --git a/geo_LHC026_AoA_10/boundary_dual_area_geo_LHC026_AoA_10.npy b/geo_LHC026_AoA_10/boundary_dual_area_geo_LHC026_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2c4fbcf402f69463dfdda6ba26f470b86c6c9825
--- /dev/null
+++ b/geo_LHC026_AoA_10/boundary_dual_area_geo_LHC026_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0f01ac780e05f04e23ec097f9332f0a91f9546484bb133937b8c93a05dcfde9b
+size 563020884
diff --git a/geo_LHC026_AoA_14/boundary_dual_area_geo_LHC026_AoA_14.npy b/geo_LHC026_AoA_14/boundary_dual_area_geo_LHC026_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b9eb5477f974b4721f8bfc553147b5fb65b69d1f
--- /dev/null
+++ b/geo_LHC026_AoA_14/boundary_dual_area_geo_LHC026_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:752f3f12bcaf604f0e103dfb14386ce475367d08c2590a47e1451804a5cad125
+size 569665756
diff --git a/geo_LHC027_AoA_22/boundary_dual_area_geo_LHC027_AoA_22.npy b/geo_LHC027_AoA_22/boundary_dual_area_geo_LHC027_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a64d1a562a2062d704e863ae72d91fc8923eabc6
--- /dev/null
+++ b/geo_LHC027_AoA_22/boundary_dual_area_geo_LHC027_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a55c99b33a7a31679c1bf43e002c2f6967bf99b82504ab18faf676ee4b44cb1f
+size 550362576
diff --git a/geo_LHC027_AoA_4/boundary_dual_area_geo_LHC027_AoA_4.npy b/geo_LHC027_AoA_4/boundary_dual_area_geo_LHC027_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..30d5cc7898a68263e0c8ae203beedc05639f6b83
--- /dev/null
+++ b/geo_LHC027_AoA_4/boundary_dual_area_geo_LHC027_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fb9fe1e078fefa853a32381a589c0a4560a6614629d914a1beb5e02ec1b96651
+size 515746552
diff --git a/geo_LHC028_AoA_18/boundary_dual_area_geo_LHC028_AoA_18.npy b/geo_LHC028_AoA_18/boundary_dual_area_geo_LHC028_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f32300c41b820f4bdf79d9eef58c721bfcdaa7f5
--- /dev/null
+++ b/geo_LHC028_AoA_18/boundary_dual_area_geo_LHC028_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6c193fedfe70735a33d5d1fb461dcd9381a45024b2a961228321897a6d868960
+size 556736188
diff --git a/geo_LHC029_AoA_14/boundary_dual_area_geo_LHC029_AoA_14.npy b/geo_LHC029_AoA_14/boundary_dual_area_geo_LHC029_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..771940f6399720ab9440c118a017bc48198fdde3
--- /dev/null
+++ b/geo_LHC029_AoA_14/boundary_dual_area_geo_LHC029_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:09e71b549ee77ccb76f8c6d3f33e1e4b7325f9b8c891a21273e5b560af31619c
+size 587236808
diff --git a/geo_LHC029_AoA_22/boundary_dual_area_geo_LHC029_AoA_22.npy b/geo_LHC029_AoA_22/boundary_dual_area_geo_LHC029_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..733a6be0f119f099a2fc2b7d00f1f46ae8d1f97c
--- /dev/null
+++ b/geo_LHC029_AoA_22/boundary_dual_area_geo_LHC029_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:148769b99e31a29c133b14baec24e2a0d9220190721aaf86a6b7efb8ef294e16
+size 594708080
diff --git a/geo_LHC030_AoA_22/boundary_dual_area_geo_LHC030_AoA_22.npy b/geo_LHC030_AoA_22/boundary_dual_area_geo_LHC030_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f908f33e4cdbe5ef3e1e155aa5e8cf36cf078c8a
--- /dev/null
+++ b/geo_LHC030_AoA_22/boundary_dual_area_geo_LHC030_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c650263d7a7fec502c04400e02e4d0bf6e73b331d99223f1e37cdf089820cb08
+size 563792456
diff --git a/geo_LHC031_AoA_10/boundary_dual_area_geo_LHC031_AoA_10.npy b/geo_LHC031_AoA_10/boundary_dual_area_geo_LHC031_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..210d4635bfbc9390af5cbda72ad082173cc3832e
--- /dev/null
+++ b/geo_LHC031_AoA_10/boundary_dual_area_geo_LHC031_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7680098588f61ea816ff842a459cd90c8857f2f4d4145e4818952464b13f8549
+size 546614060
diff --git a/geo_LHC032_AoA_12/boundary_dual_area_geo_LHC032_AoA_12.npy b/geo_LHC032_AoA_12/boundary_dual_area_geo_LHC032_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..eecbcb3613df3247b8c64611ad480181c2261245
--- /dev/null
+++ b/geo_LHC032_AoA_12/boundary_dual_area_geo_LHC032_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1a4204bfbc5edc9862240a508e7b5e0661b2e1ef95e89fbbeb002c462afe63a3
+size 556824808
diff --git a/geo_LHC032_AoA_22/boundary_dual_area_geo_LHC032_AoA_22.npy b/geo_LHC032_AoA_22/boundary_dual_area_geo_LHC032_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e5139b4d456e6301658e65405140202fdcfa5c22
--- /dev/null
+++ b/geo_LHC032_AoA_22/boundary_dual_area_geo_LHC032_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1b0f4577107ba7fff57a17a69adf9fd8d752e80823be5e4cbcb96f0040d7e909
+size 545946800
diff --git a/geo_LHC032_AoA_6/boundary_dual_area_geo_LHC032_AoA_6.npy b/geo_LHC032_AoA_6/boundary_dual_area_geo_LHC032_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..739ce570297e810d2f07de58086c3f45735e2c1a
--- /dev/null
+++ b/geo_LHC032_AoA_6/boundary_dual_area_geo_LHC032_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:63f9923502af3de15ce14d69d2ec434bcdeabbd92474ea55e464eaf2bfcf18f8
+size 542667792
diff --git a/geo_LHC033_AoA_12/boundary_dual_area_geo_LHC033_AoA_12.npy b/geo_LHC033_AoA_12/boundary_dual_area_geo_LHC033_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ceb53b9ffab59dbd45a7164e39cad9f1ad1b5784
--- /dev/null
+++ b/geo_LHC033_AoA_12/boundary_dual_area_geo_LHC033_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1bbd2f5f16ecbb5cc0f004ddaba8aba0626207627d389c4ed1e8840bb9648b22
+size 574095888
diff --git a/geo_LHC033_AoA_14/boundary_dual_area_geo_LHC033_AoA_14.npy b/geo_LHC033_AoA_14/boundary_dual_area_geo_LHC033_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..dd07f0537cfc5b9c3d3facc856a665739e6b8dfd
--- /dev/null
+++ b/geo_LHC033_AoA_14/boundary_dual_area_geo_LHC033_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cf8424b661639687b2cfed08d599663ff7448df5350e6b3841b1170e6092eefa
+size 579535352
diff --git a/geo_LHC033_AoA_20/boundary_dual_area_geo_LHC033_AoA_20.npy b/geo_LHC033_AoA_20/boundary_dual_area_geo_LHC033_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6484df312e50ce4f319005f3d1588fc62c1141e6
--- /dev/null
+++ b/geo_LHC033_AoA_20/boundary_dual_area_geo_LHC033_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4426a23588d38545fd1e5f0ff41870a7f15711b16a84dbfb1a9d557e001c6739
+size 582431588
diff --git a/geo_LHC034_AoA_20/boundary_dual_area_geo_LHC034_AoA_20.npy b/geo_LHC034_AoA_20/boundary_dual_area_geo_LHC034_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..141caa4dfdf3f5c1fe0975245d3865cc2773b672
--- /dev/null
+++ b/geo_LHC034_AoA_20/boundary_dual_area_geo_LHC034_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2c67073508605907d6ab348c94fd2538464d2f424967bb8cdaabff3a0b810c30
+size 596332820
diff --git a/geo_LHC035_AoA_16/boundary_dual_area_geo_LHC035_AoA_16.npy b/geo_LHC035_AoA_16/boundary_dual_area_geo_LHC035_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..17cbac1d763ccd913c328da26f463095aea595cb
--- /dev/null
+++ b/geo_LHC035_AoA_16/boundary_dual_area_geo_LHC035_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fe4387dff10b31667fd94144b6ebfc6a14f3eadd6c895585c1722f3642f87479
+size 554239600
diff --git a/geo_LHC035_AoA_20/boundary_dual_area_geo_LHC035_AoA_20.npy b/geo_LHC035_AoA_20/boundary_dual_area_geo_LHC035_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ded42f8074914cff5d452ace7c5f0fe10edc836f
--- /dev/null
+++ b/geo_LHC035_AoA_20/boundary_dual_area_geo_LHC035_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d4de16fa6c714459315b8c87340a19fd4947d70eee4b8dbd7b9fd3c58893beb3
+size 555643224
diff --git a/geo_LHC036_AoA_10/boundary_dual_area_geo_LHC036_AoA_10.npy b/geo_LHC036_AoA_10/boundary_dual_area_geo_LHC036_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2df0fcb46ea443734ab6c4d52b69eb5c539dc36a
--- /dev/null
+++ b/geo_LHC036_AoA_10/boundary_dual_area_geo_LHC036_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f264bc4ad7199581f8c458eb3769e24acf033e0a3c3a56083ec1d84c033357b7
+size 591967764
diff --git a/geo_LHC036_AoA_22/boundary_dual_area_geo_LHC036_AoA_22.npy b/geo_LHC036_AoA_22/boundary_dual_area_geo_LHC036_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..49ebec79f8843ec9c932cb5017bbca0fc7ca43f0
--- /dev/null
+++ b/geo_LHC036_AoA_22/boundary_dual_area_geo_LHC036_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d2e1cdc9cdd1a4c3199d8507395c70cab4187cefecb35ab765eb7e89d1f9f3d2
+size 604568052
diff --git a/geo_LHC037_AoA_12/boundary_dual_area_geo_LHC037_AoA_12.npy b/geo_LHC037_AoA_12/boundary_dual_area_geo_LHC037_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ecefa2d718b39506955aa11329415a324bb2b77a
--- /dev/null
+++ b/geo_LHC037_AoA_12/boundary_dual_area_geo_LHC037_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5beddea4c68ae98156418014db6916faef763c4238c9d3001e0f9ed4e4bb8b96
+size 560351416
diff --git a/geo_LHC037_AoA_18/boundary_dual_area_geo_LHC037_AoA_18.npy b/geo_LHC037_AoA_18/boundary_dual_area_geo_LHC037_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..38675581c7b4e232628e0e5523db449d29f22cfc
--- /dev/null
+++ b/geo_LHC037_AoA_18/boundary_dual_area_geo_LHC037_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e89bc39e8f060c476fd711f659fde42e3a59d2f97aa4bf65ff166be0bb33ec8e
+size 556406412
diff --git a/geo_LHC039_AoA_10/boundary_dual_area_geo_LHC039_AoA_10.npy b/geo_LHC039_AoA_10/boundary_dual_area_geo_LHC039_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b13170f41627a306d5c4011aa4be53d4a4c26cca
--- /dev/null
+++ b/geo_LHC039_AoA_10/boundary_dual_area_geo_LHC039_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:70261ee44107aebae0bef8b6553bdc8a67c7114bcd03c2bdb66073ea548a8161
+size 544602472
diff --git a/geo_LHC039_AoA_18/boundary_dual_area_geo_LHC039_AoA_18.npy b/geo_LHC039_AoA_18/boundary_dual_area_geo_LHC039_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0cfd1f0810761d838fce331e928ae6e1bcf13b14
--- /dev/null
+++ b/geo_LHC039_AoA_18/boundary_dual_area_geo_LHC039_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b3c852ff1c8a4d60324d433ed54f06b7d338d56b30faae6046174af10a3f4cb6
+size 555423484
diff --git a/geo_LHC039_AoA_4/boundary_dual_area_geo_LHC039_AoA_4.npy b/geo_LHC039_AoA_4/boundary_dual_area_geo_LHC039_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a75c7006747f6a28faefead2abe5b3eec1392b2a
--- /dev/null
+++ b/geo_LHC039_AoA_4/boundary_dual_area_geo_LHC039_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ac885ba0f1c8a9688e585426c5ab009897b147d0c033e36793d9960fce0f8654
+size 505115176
diff --git a/geo_LHC041_AoA_14/boundary_dual_area_geo_LHC041_AoA_14.npy b/geo_LHC041_AoA_14/boundary_dual_area_geo_LHC041_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..86230142775af5ba7516f950f4107c4b23cf2ab2
--- /dev/null
+++ b/geo_LHC041_AoA_14/boundary_dual_area_geo_LHC041_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fb3dd4cb60c141655be53bf89922506eada1b9b3be4ff08e199e2eda5a23e539
+size 564600932
diff --git a/geo_LHC041_AoA_4/boundary_dual_area_geo_LHC041_AoA_4.npy b/geo_LHC041_AoA_4/boundary_dual_area_geo_LHC041_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..796a36f3571e89fed169d6bd10cba938db3ed815
--- /dev/null
+++ b/geo_LHC041_AoA_4/boundary_dual_area_geo_LHC041_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6631c3afc4f7b4806f321500e1e1fe1ba4eb8dc453a20a0c99cbe42241e9882b
+size 538506728
diff --git a/geo_LHC041_AoA_6/boundary_dual_area_geo_LHC041_AoA_6.npy b/geo_LHC041_AoA_6/boundary_dual_area_geo_LHC041_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a71ea79b9a306fb1213d35538c61557aac237ad2
--- /dev/null
+++ b/geo_LHC041_AoA_6/boundary_dual_area_geo_LHC041_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3267ac3fe8790b3e9dd9dc4d8782f4c35fac0fa5efdd14c37a7c883910ea0a0a
+size 549089832
diff --git a/geo_LHC042_AoA_18/boundary_dual_area_geo_LHC042_AoA_18.npy b/geo_LHC042_AoA_18/boundary_dual_area_geo_LHC042_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6866cc746a7fa9b2f8f3cba558d6d3175c348e29
--- /dev/null
+++ b/geo_LHC042_AoA_18/boundary_dual_area_geo_LHC042_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:844948d475c9cf85c0d69dcbd4bd2ea041027273a8cf225877ffd8e0a632568e
+size 585754800
diff --git a/geo_LHC042_AoA_20/boundary_dual_area_geo_LHC042_AoA_20.npy b/geo_LHC042_AoA_20/boundary_dual_area_geo_LHC042_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..edae47f58f828fe21dc2f6af18e1d0b23abd6e3e
--- /dev/null
+++ b/geo_LHC042_AoA_20/boundary_dual_area_geo_LHC042_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b07e2c10bb66a9a3ee8af60bc40aa5cd59b54167c273e7efbb00cc2f07e77c7d
+size 586290724
diff --git a/geo_LHC043_AoA_12/boundary_dual_area_geo_LHC043_AoA_12.npy b/geo_LHC043_AoA_12/boundary_dual_area_geo_LHC043_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0bd55c5eb22517a07b3e1d55b06aa3939aa05d16
--- /dev/null
+++ b/geo_LHC043_AoA_12/boundary_dual_area_geo_LHC043_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:08a06e194b11e7d9a7e7385306cc890ca4ebb6b58f59b9753cc58f3f171c8d4b
+size 571060280
diff --git a/geo_LHC043_AoA_14/boundary_dual_area_geo_LHC043_AoA_14.npy b/geo_LHC043_AoA_14/boundary_dual_area_geo_LHC043_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..796f8decf22b5fad3c65be278565cc4312a21f0b
--- /dev/null
+++ b/geo_LHC043_AoA_14/boundary_dual_area_geo_LHC043_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a03be2fa2dc424fd45b80a53ddf58d8f82abfe54417ebb9d78c6d23a72bea0a7
+size 580193196
diff --git a/geo_LHC044_AoA_12/boundary_dual_area_geo_LHC044_AoA_12.npy b/geo_LHC044_AoA_12/boundary_dual_area_geo_LHC044_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9734ad8ab676e1774ebab0349e3d06e4184c640a
--- /dev/null
+++ b/geo_LHC044_AoA_12/boundary_dual_area_geo_LHC044_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4713abaa99e6457af18cb182e4a88020f3016f734e43725a13cac3ee3e27041f
+size 596730128
diff --git a/geo_LHC044_AoA_18/boundary_dual_area_geo_LHC044_AoA_18.npy b/geo_LHC044_AoA_18/boundary_dual_area_geo_LHC044_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..df891ba7786852a5e9c063a80b227273a86fa4d6
--- /dev/null
+++ b/geo_LHC044_AoA_18/boundary_dual_area_geo_LHC044_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b78174a60632a456613fbce77abf9f626efa2502ee0bee2a75804b3a4b240ac5
+size 590823188
diff --git a/geo_LHC044_AoA_22/boundary_dual_area_geo_LHC044_AoA_22.npy b/geo_LHC044_AoA_22/boundary_dual_area_geo_LHC044_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..280f796b37e3596a8048ed90f8c48d928ef932f5
--- /dev/null
+++ b/geo_LHC044_AoA_22/boundary_dual_area_geo_LHC044_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:68ce46218f0bee662c153f39a80c38ad8f2b594da75083fb6fdfd01d6971d363
+size 586569660
diff --git a/geo_LHC045_AoA_16/boundary_dual_area_geo_LHC045_AoA_16.npy b/geo_LHC045_AoA_16/boundary_dual_area_geo_LHC045_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..29d15911b94a13ca77bd3035d241d70410790024
--- /dev/null
+++ b/geo_LHC045_AoA_16/boundary_dual_area_geo_LHC045_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:18f26b2dd0e2e977cd190ab6b27d83a8861348e9add2e3268f16bf5f179ecbef
+size 567334104
diff --git a/geo_LHC045_AoA_18/boundary_dual_area_geo_LHC045_AoA_18.npy b/geo_LHC045_AoA_18/boundary_dual_area_geo_LHC045_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..23436900f832af560f7d0ab8892c41a739e62a46
--- /dev/null
+++ b/geo_LHC045_AoA_18/boundary_dual_area_geo_LHC045_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:90ee6b95e18ac8d6ada84707d8e50a99b36fed0de68b12ef0f98f237fef09906
+size 557077992
diff --git a/geo_LHC045_AoA_20/boundary_dual_area_geo_LHC045_AoA_20.npy b/geo_LHC045_AoA_20/boundary_dual_area_geo_LHC045_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e5bdfff3e2dab4382ef12cbb7e6a29041cbf6190
--- /dev/null
+++ b/geo_LHC045_AoA_20/boundary_dual_area_geo_LHC045_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:872039a4ea187d2bf8385e222c0b1efc889457b01a47d3a12cbf67369e32b021
+size 555812820
diff --git a/geo_LHC046_AoA_16/boundary_dual_area_geo_LHC046_AoA_16.npy b/geo_LHC046_AoA_16/boundary_dual_area_geo_LHC046_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5b1058a2501e4b6fd4616587fb255da9e2199eae
--- /dev/null
+++ b/geo_LHC046_AoA_16/boundary_dual_area_geo_LHC046_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cb938c5b98b60d891cfd90888d58d3487f00fa0a2be2ffcdcd60added3e6402d
+size 594614640
diff --git a/geo_LHC048_AoA_12/boundary_dual_area_geo_LHC048_AoA_12.npy b/geo_LHC048_AoA_12/boundary_dual_area_geo_LHC048_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a36a9cbfb4d5ebf32a50aa0a820365fdaa434ca1
--- /dev/null
+++ b/geo_LHC048_AoA_12/boundary_dual_area_geo_LHC048_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e550616d0a45ded4b33f73f9cbb381864f375f3a6e3cda14d85c8562af8fc8e2
+size 566914248
diff --git a/geo_LHC049_AoA_20/boundary_dual_area_geo_LHC049_AoA_20.npy b/geo_LHC049_AoA_20/boundary_dual_area_geo_LHC049_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c889195b9c3867bdbae3bb7ec6ef9db44da8664b
--- /dev/null
+++ b/geo_LHC049_AoA_20/boundary_dual_area_geo_LHC049_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bbb37c2ddde34ceee554378270267be46d173bc565fcc6da8c6ae2f6f4cae022
+size 559053952
diff --git a/geo_LHC050_AoA_12/boundary_dual_area_geo_LHC050_AoA_12.npy b/geo_LHC050_AoA_12/boundary_dual_area_geo_LHC050_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5fc12c37c7f01f719cd3b72a69ebf9b5c829c7af
--- /dev/null
+++ b/geo_LHC050_AoA_12/boundary_dual_area_geo_LHC050_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aff62a1e68cf2953f2236ca74f932d383c49fc88e34bff98edc40bc245a8d283
+size 558510368
diff --git a/geo_LHC050_AoA_22/boundary_dual_area_geo_LHC050_AoA_22.npy b/geo_LHC050_AoA_22/boundary_dual_area_geo_LHC050_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b207ce333bda2b6a881336f93c053ee52868cc3f
--- /dev/null
+++ b/geo_LHC050_AoA_22/boundary_dual_area_geo_LHC050_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3367cd3c7534bfa26022ecf1da0fe9006acad5218ba54be031a6294f42425abb
+size 559441512
diff --git a/geo_LHC050_AoA_6/boundary_dual_area_geo_LHC050_AoA_6.npy b/geo_LHC050_AoA_6/boundary_dual_area_geo_LHC050_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..13e2d1af695a9638232de0b5433eff75779e330d
--- /dev/null
+++ b/geo_LHC050_AoA_6/boundary_dual_area_geo_LHC050_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0bda501c765ee7c2e2ca5cc2b2e6f5a440b710aac3cc7dce79c951db656ad379
+size 540662688
diff --git a/geo_LHC051_AoA_18/boundary_dual_area_geo_LHC051_AoA_18.npy b/geo_LHC051_AoA_18/boundary_dual_area_geo_LHC051_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..726552a45f5769e32679ca724d2bdb24babcd99e
--- /dev/null
+++ b/geo_LHC051_AoA_18/boundary_dual_area_geo_LHC051_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:811ffcbb4f9a6651ef9ce624db578b046bc33f3fa604680ae6274ef844f9969e
+size 555147580
diff --git a/geo_LHC051_AoA_22/boundary_dual_area_geo_LHC051_AoA_22.npy b/geo_LHC051_AoA_22/boundary_dual_area_geo_LHC051_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c91514801ff506e5576e98e7f7d60384ff6d6494
--- /dev/null
+++ b/geo_LHC051_AoA_22/boundary_dual_area_geo_LHC051_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4068b6da8a0aab2392728c3c2b66a1eb57ec6c795faf868a45fc98b285f01fe7
+size 545583548
diff --git a/geo_LHC052_AoA_16/boundary_dual_area_geo_LHC052_AoA_16.npy b/geo_LHC052_AoA_16/boundary_dual_area_geo_LHC052_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..134c90b2468fd1156f6c706d6dde46c6ea0586e3
--- /dev/null
+++ b/geo_LHC052_AoA_16/boundary_dual_area_geo_LHC052_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9e7a1bdf3817e9b529f4c9e2c4dcfe6a870e6fd7483dea8aede4a88efa03b427
+size 557507564
diff --git a/geo_LHC052_AoA_20/boundary_dual_area_geo_LHC052_AoA_20.npy b/geo_LHC052_AoA_20/boundary_dual_area_geo_LHC052_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1c05dd06ef3632a2676d3cc91bf808dd5bc4e1e2
--- /dev/null
+++ b/geo_LHC052_AoA_20/boundary_dual_area_geo_LHC052_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:709c39efcb99e546d39fa14d800eea6a2fb554652e935ed42cdb81a1f59ab54f
+size 562705820
diff --git a/geo_LHC053_AoA_18/boundary_dual_area_geo_LHC053_AoA_18.npy b/geo_LHC053_AoA_18/boundary_dual_area_geo_LHC053_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b25d5026a7060cecd8326f6ecbd9ce32fa39b196
--- /dev/null
+++ b/geo_LHC053_AoA_18/boundary_dual_area_geo_LHC053_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2e3675ac7a2930fe46b0a4cf3c18482a98484b1bd4064e47c3909bb929c46ffe
+size 563789240
diff --git a/geo_LHC053_AoA_22/boundary_dual_area_geo_LHC053_AoA_22.npy b/geo_LHC053_AoA_22/boundary_dual_area_geo_LHC053_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..306b6476624d0d3581cdbb0c8594a5ea230ea0da
--- /dev/null
+++ b/geo_LHC053_AoA_22/boundary_dual_area_geo_LHC053_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d2b2ade98a067cc86e18bef1b5ac73863492d15e076d296fdf6e4380f83ff4b7
+size 565776340
diff --git a/geo_LHC054_AoA_12/boundary_dual_area_geo_LHC054_AoA_12.npy b/geo_LHC054_AoA_12/boundary_dual_area_geo_LHC054_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b8288574e5bc0fe26061e328a9811537ee231ee7
--- /dev/null
+++ b/geo_LHC054_AoA_12/boundary_dual_area_geo_LHC054_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dd679eaf800a8d754ad55a9d01018fed151999368f02a6a414eef043d349cf44
+size 566680936
diff --git a/geo_LHC054_AoA_14/boundary_dual_area_geo_LHC054_AoA_14.npy b/geo_LHC054_AoA_14/boundary_dual_area_geo_LHC054_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c9e013935ef4ba7efb3bc68b260010c9793e5136
--- /dev/null
+++ b/geo_LHC054_AoA_14/boundary_dual_area_geo_LHC054_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ee6102ffd6120c2f201f3a8cd2bfcf77e670b97a800c5a55b8a3247ad57f1307
+size 566361236
diff --git a/geo_LHC055_AoA_14/boundary_dual_area_geo_LHC055_AoA_14.npy b/geo_LHC055_AoA_14/boundary_dual_area_geo_LHC055_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..722d2959d058f06c6e81ce28ad4a8e68a03a90ce
--- /dev/null
+++ b/geo_LHC055_AoA_14/boundary_dual_area_geo_LHC055_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c034bbdf7d853722e6cfc6115b674fc7aebe5ae795edfa04c9fa6cf7afbf7c35
+size 567364636
diff --git a/geo_LHC055_AoA_20/boundary_dual_area_geo_LHC055_AoA_20.npy b/geo_LHC055_AoA_20/boundary_dual_area_geo_LHC055_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b8c1c2de2be56f7146ad1742fb4bcaf58f76147c
--- /dev/null
+++ b/geo_LHC055_AoA_20/boundary_dual_area_geo_LHC055_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:578c96f5e354e707363f540358670b71e7178fcba2371c669617b3ae623172b4
+size 588172960
diff --git a/geo_LHC055_AoA_22/boundary_dual_area_geo_LHC055_AoA_22.npy b/geo_LHC055_AoA_22/boundary_dual_area_geo_LHC055_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e866ee4a3b85716ce31318a79c2d4cc87ffccf3c
--- /dev/null
+++ b/geo_LHC055_AoA_22/boundary_dual_area_geo_LHC055_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:20d55044a4770617e588dadc7872bb09c1e2bf60126f55c32f8476d9142f9a20
+size 588189460
diff --git a/geo_LHC055_AoA_4/boundary_dual_area_geo_LHC055_AoA_4.npy b/geo_LHC055_AoA_4/boundary_dual_area_geo_LHC055_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b19d67c0db9ea8b38ace937db23a9b181948d98f
--- /dev/null
+++ b/geo_LHC055_AoA_4/boundary_dual_area_geo_LHC055_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:215cb7cd264de14d24068f386fa311224e941158132581f73f9665a48d28e0a3
+size 539702912
diff --git a/geo_LHC055_AoA_6/boundary_dual_area_geo_LHC055_AoA_6.npy b/geo_LHC055_AoA_6/boundary_dual_area_geo_LHC055_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a83e5daf18028391b299c368ba1b730233e34d6b
--- /dev/null
+++ b/geo_LHC055_AoA_6/boundary_dual_area_geo_LHC055_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:47900c625b78a1c0c758e019aa2c57719ea9c5db6a73e7a059d6a5a394cd165a
+size 534917984
diff --git a/geo_LHC055_AoA_8/boundary_dual_area_geo_LHC055_AoA_8.npy b/geo_LHC055_AoA_8/boundary_dual_area_geo_LHC055_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..38c2ffc14b80524f60191ecdeebd3c04557058c7
--- /dev/null
+++ b/geo_LHC055_AoA_8/boundary_dual_area_geo_LHC055_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:070629acda22747ba91c1036d7ab95d8f7823c718fe7c6076da655449a47d3e9
+size 534290984
diff --git a/geo_LHC057_AoA_10/boundary_dual_area_geo_LHC057_AoA_10.npy b/geo_LHC057_AoA_10/boundary_dual_area_geo_LHC057_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4e1fdf378449a150f4c8064f53a355e272342057
--- /dev/null
+++ b/geo_LHC057_AoA_10/boundary_dual_area_geo_LHC057_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5302f2b1273551bbe436f8b40e95bb2f23ce837736fc807142a4f1dc54f487bc
+size 589769124
diff --git a/geo_LHC059_AoA_12/boundary_dual_area_geo_LHC059_AoA_12.npy b/geo_LHC059_AoA_12/boundary_dual_area_geo_LHC059_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6325f0f501ff211487a3886dd71f35d25938718f
--- /dev/null
+++ b/geo_LHC059_AoA_12/boundary_dual_area_geo_LHC059_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2b5a29c66f1d9a92a804abcb20462893f6e8d84ac6a02ceee021c20c43cea5f1
+size 555309488
diff --git a/geo_LHC060_AoA_12/boundary_dual_area_geo_LHC060_AoA_12.npy b/geo_LHC060_AoA_12/boundary_dual_area_geo_LHC060_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a219b53655f11667fa9e729ed69f8e7e459f7f4c
--- /dev/null
+++ b/geo_LHC060_AoA_12/boundary_dual_area_geo_LHC060_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c657719280c78b5bafc346a9bafb0e16e25b5f1121ae4fd88de32c9335c0c0db
+size 559413620
diff --git a/geo_LHC060_AoA_8/boundary_dual_area_geo_LHC060_AoA_8.npy b/geo_LHC060_AoA_8/boundary_dual_area_geo_LHC060_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c6bb225195bf60991c144b063e5a5e4c7c96e823
--- /dev/null
+++ b/geo_LHC060_AoA_8/boundary_dual_area_geo_LHC060_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:689977cc9ac1165cd86e3f08a310fb77e8a03ce01a4dcd6a1dae528b2ca45ec3
+size 555035368
diff --git a/geo_LHC061_AoA_4/boundary_dual_area_geo_LHC061_AoA_4.npy b/geo_LHC061_AoA_4/boundary_dual_area_geo_LHC061_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d9cf4c141028abb880d9c676139862ec5621e773
--- /dev/null
+++ b/geo_LHC061_AoA_4/boundary_dual_area_geo_LHC061_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4203ca39dca78620383e76d3f4fb309640eb53bc7d4bd767df7338093e2ebcf8
+size 544206088
diff --git a/geo_LHC063_AoA_14/boundary_dual_area_geo_LHC063_AoA_14.npy b/geo_LHC063_AoA_14/boundary_dual_area_geo_LHC063_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fee30a5133bd07e79028796ff6944dd454530d66
--- /dev/null
+++ b/geo_LHC063_AoA_14/boundary_dual_area_geo_LHC063_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eaa09d93fb2083ab55ebb54511dd31b74bd683b153066cfc81b1b35df4f42831
+size 590126472
diff --git a/geo_LHC065_AoA_10/boundary_dual_area_geo_LHC065_AoA_10.npy b/geo_LHC065_AoA_10/boundary_dual_area_geo_LHC065_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..39189afc0160aca7deaefb712d7cc68b515255e1
--- /dev/null
+++ b/geo_LHC065_AoA_10/boundary_dual_area_geo_LHC065_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aaaf5dcb5f00e8577d57cdc47d0a41365fd1c71dfcf4967d84bf9aa8cdeb9bfe
+size 578921912
diff --git a/geo_LHC065_AoA_6/boundary_dual_area_geo_LHC065_AoA_6.npy b/geo_LHC065_AoA_6/boundary_dual_area_geo_LHC065_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..04c5fe49207bcca68d527534290fe45ce24f0f4f
--- /dev/null
+++ b/geo_LHC065_AoA_6/boundary_dual_area_geo_LHC065_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dbab6faf9662addca45065f253886cbc3e3b4d2896fbae44fb9c9f91dc234ea8
+size 545024900
diff --git a/geo_LHC067_AoA_4/boundary_dual_area_geo_LHC067_AoA_4.npy b/geo_LHC067_AoA_4/boundary_dual_area_geo_LHC067_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..be4a441df6747afce1b57cbdf9a5c84cebb9ef87
--- /dev/null
+++ b/geo_LHC067_AoA_4/boundary_dual_area_geo_LHC067_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:041b91c8bea7637ade4dd03d60fab17e01267384fd85abc6a78de0e9e7f6fcb5
+size 523345228
diff --git a/geo_LHC068_AoA_18/boundary_dual_area_geo_LHC068_AoA_18.npy b/geo_LHC068_AoA_18/boundary_dual_area_geo_LHC068_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f43e698d16ecb8d1955c62c3fba46bbb01bae39a
--- /dev/null
+++ b/geo_LHC068_AoA_18/boundary_dual_area_geo_LHC068_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d36f6296e2ca4ca3d58b436d43e5d28523cb27d67e8eb61b57c05d0dc4f6fce
+size 582220796
diff --git a/geo_LHC068_AoA_22/boundary_dual_area_geo_LHC068_AoA_22.npy b/geo_LHC068_AoA_22/boundary_dual_area_geo_LHC068_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2ae1e343f87eecedd7379371b32e132d8e322951
--- /dev/null
+++ b/geo_LHC068_AoA_22/boundary_dual_area_geo_LHC068_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7a0aab59e0297063db427473c1e9d9130272c4251de6a588bc7924c5cb56737b
+size 587694984
diff --git a/geo_LHC068_AoA_4/boundary_dual_area_geo_LHC068_AoA_4.npy b/geo_LHC068_AoA_4/boundary_dual_area_geo_LHC068_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5fb941a7581c1f82f5f0d5c815142c78c17c0f37
--- /dev/null
+++ b/geo_LHC068_AoA_4/boundary_dual_area_geo_LHC068_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:76698f223ff97d388f80bdd411c27db8486aaf0d14f70529cc6b2df48f81ae07
+size 551101004
diff --git a/geo_LHC069_AoA_12/boundary_dual_area_geo_LHC069_AoA_12.npy b/geo_LHC069_AoA_12/boundary_dual_area_geo_LHC069_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..70203d13fb5be4f52900402ce5d7aa104b86b31e
--- /dev/null
+++ b/geo_LHC069_AoA_12/boundary_dual_area_geo_LHC069_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:680586096777560c6a7d06f0a7fcaec2415a97b2f01cfb5ed7a30472d9087a48
+size 561454416
diff --git a/geo_LHC069_AoA_18/boundary_dual_area_geo_LHC069_AoA_18.npy b/geo_LHC069_AoA_18/boundary_dual_area_geo_LHC069_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6e115e20d3b064e5907afe7e3ad887caec096592
--- /dev/null
+++ b/geo_LHC069_AoA_18/boundary_dual_area_geo_LHC069_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f4dae656a441f4207a30fb6b00a2353ff3b0f93b71ba11d3a56144fa33297a74
+size 565802920
diff --git a/geo_LHC069_AoA_20/boundary_dual_area_geo_LHC069_AoA_20.npy b/geo_LHC069_AoA_20/boundary_dual_area_geo_LHC069_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2b471a0835464f13c6fca634b2fb52896146e2d7
--- /dev/null
+++ b/geo_LHC069_AoA_20/boundary_dual_area_geo_LHC069_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4ca307c5bf6536189c38521f9f9f6357bd27863d6cfb3a0be472785fde3017a0
+size 563614364
diff --git a/geo_LHC069_AoA_6/boundary_dual_area_geo_LHC069_AoA_6.npy b/geo_LHC069_AoA_6/boundary_dual_area_geo_LHC069_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..96c8f2eef2609179c16262ea91e45ec4c289fd92
--- /dev/null
+++ b/geo_LHC069_AoA_6/boundary_dual_area_geo_LHC069_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:31ceb44b11a07bb7470572b6a747989dba9c68f9f869b6d899a0c6e0f585f19c
+size 546100528
diff --git a/geo_LHC070_AoA_18/boundary_dual_area_geo_LHC070_AoA_18.npy b/geo_LHC070_AoA_18/boundary_dual_area_geo_LHC070_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a5bbaf82f431b92f16492b02f07b235fa60ab53e
--- /dev/null
+++ b/geo_LHC070_AoA_18/boundary_dual_area_geo_LHC070_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fdc5ee437cd41f60ccb34e506b5db48909eb0d54a3f31b3c9c55448c983933bc
+size 564476140
diff --git a/geo_LHC071_AoA_16/boundary_dual_area_geo_LHC071_AoA_16.npy b/geo_LHC071_AoA_16/boundary_dual_area_geo_LHC071_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7c376888352bfb1af6e613edadb6dd956f23453e
--- /dev/null
+++ b/geo_LHC071_AoA_16/boundary_dual_area_geo_LHC071_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bc13636e8efddd6c1c6df00eb27f15ff3a36558078570e3697b102abd6460afc
+size 585517880
diff --git a/geo_LHC071_AoA_8/boundary_dual_area_geo_LHC071_AoA_8.npy b/geo_LHC071_AoA_8/boundary_dual_area_geo_LHC071_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9da4183e83617e64a44c901ee5538df7c941d33c
--- /dev/null
+++ b/geo_LHC071_AoA_8/boundary_dual_area_geo_LHC071_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:adefe1ad278657f6970b86c5bd4e82ed4fd1969e318151112126dbc8c27ddf46
+size 540276964
diff --git a/geo_LHC072_AoA_6/boundary_dual_area_geo_LHC072_AoA_6.npy b/geo_LHC072_AoA_6/boundary_dual_area_geo_LHC072_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0cf16b494f9819635d58432c89ae1ef10d176b42
--- /dev/null
+++ b/geo_LHC072_AoA_6/boundary_dual_area_geo_LHC072_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0e734957ac5c83e1d97ac185c010d0a02fa35019af828d708e9340cde331cce1
+size 555696672
diff --git a/geo_LHC073_AoA_12/boundary_dual_area_geo_LHC073_AoA_12.npy b/geo_LHC073_AoA_12/boundary_dual_area_geo_LHC073_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a06aec8119caf428d61d108d7a993ebe310b58a1
--- /dev/null
+++ b/geo_LHC073_AoA_12/boundary_dual_area_geo_LHC073_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c90cc519bf5a2e37addfd2e94199c44040ee01ab31e836a5b5cc660ec98f9848
+size 592743028
diff --git a/geo_LHC074_AoA_12/boundary_dual_area_geo_LHC074_AoA_12.npy b/geo_LHC074_AoA_12/boundary_dual_area_geo_LHC074_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..86ef4df1b436750b3bd76744a057a33e3149250b
--- /dev/null
+++ b/geo_LHC074_AoA_12/boundary_dual_area_geo_LHC074_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:64223ded5290a25167f5bc0a5df5c15728f08277f969afd8cbf94e3ac94f9123
+size 564630208
diff --git a/geo_LHC075_AoA_18/boundary_dual_area_geo_LHC075_AoA_18.npy b/geo_LHC075_AoA_18/boundary_dual_area_geo_LHC075_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..929c9ab98cb2bfb4bb273ea8ccdf187c05727941
--- /dev/null
+++ b/geo_LHC075_AoA_18/boundary_dual_area_geo_LHC075_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a769e1c01ac9961fbcb02003aa8751f1fc3d480518000143e958e65eb84fa980
+size 564275268
diff --git a/geo_LHC076_AoA_10/boundary_dual_area_geo_LHC076_AoA_10.npy b/geo_LHC076_AoA_10/boundary_dual_area_geo_LHC076_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cecf9f34bc10cb033495aaa02d999554637df3a4
--- /dev/null
+++ b/geo_LHC076_AoA_10/boundary_dual_area_geo_LHC076_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2dfacf4c8c47c867892756164c35308be02a21141bb78d934819fe3bdbf2b3b9
+size 571639572
diff --git a/geo_LHC076_AoA_12/boundary_dual_area_geo_LHC076_AoA_12.npy b/geo_LHC076_AoA_12/boundary_dual_area_geo_LHC076_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..62a854af7c25ab5c10556619de7ed68b3eb9ef20
--- /dev/null
+++ b/geo_LHC076_AoA_12/boundary_dual_area_geo_LHC076_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d9e69d26b13e1494f410504d6eb0af724f56713c544118e72a1928a262888e5e
+size 580224376
diff --git a/geo_LHC076_AoA_14/boundary_dual_area_geo_LHC076_AoA_14.npy b/geo_LHC076_AoA_14/boundary_dual_area_geo_LHC076_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d8dfcfec5e242dc788ed0ca69f36b9ec37733967
--- /dev/null
+++ b/geo_LHC076_AoA_14/boundary_dual_area_geo_LHC076_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7fa9e9a9e1abc2955d6f999c3a74705149b504604a5fabf89346389659f71e6b
+size 589008976
diff --git a/geo_LHC076_AoA_22/boundary_dual_area_geo_LHC076_AoA_22.npy b/geo_LHC076_AoA_22/boundary_dual_area_geo_LHC076_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..bbb1e5aa377e2a5c95b8b2041d4be963cb3bc3da
--- /dev/null
+++ b/geo_LHC076_AoA_22/boundary_dual_area_geo_LHC076_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9c3e3bd15de85d9b87c0d7e8bbf7f3e113f91107a5495ab69235a4e90addae8a
+size 594693560
diff --git a/geo_LHC077_AoA_14/boundary_dual_area_geo_LHC077_AoA_14.npy b/geo_LHC077_AoA_14/boundary_dual_area_geo_LHC077_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6f02d733f947457b0da0ac78b16023cf03fde4d3
--- /dev/null
+++ b/geo_LHC077_AoA_14/boundary_dual_area_geo_LHC077_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a4139507b4af7e311f1f09a9606388e4bd6207bfd74ea5b05af1c0c61e78decd
+size 586536300
diff --git a/geo_LHC077_AoA_16/boundary_dual_area_geo_LHC077_AoA_16.npy b/geo_LHC077_AoA_16/boundary_dual_area_geo_LHC077_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9e75002ffc4e8467507a62b05b6b275bc26b5097
--- /dev/null
+++ b/geo_LHC077_AoA_16/boundary_dual_area_geo_LHC077_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a83a8d8d4cfc93d5b1fe1d088ded55a07489b24cd0f291dc2a248d570a3b5680
+size 592143712
diff --git a/geo_LHC077_AoA_18/boundary_dual_area_geo_LHC077_AoA_18.npy b/geo_LHC077_AoA_18/boundary_dual_area_geo_LHC077_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..696c6b2fa3335999251b7431f4b2d1838d86af0c
--- /dev/null
+++ b/geo_LHC077_AoA_18/boundary_dual_area_geo_LHC077_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f91f485dd477a367d250dfdbe5847a34402efa84a2dcdaf11f0ffe3132224cb2
+size 588105864
diff --git a/geo_LHC077_AoA_8/boundary_dual_area_geo_LHC077_AoA_8.npy b/geo_LHC077_AoA_8/boundary_dual_area_geo_LHC077_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..54ba1d839e5b77587d5901308e52289ffa5ef729
--- /dev/null
+++ b/geo_LHC077_AoA_8/boundary_dual_area_geo_LHC077_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eccc4f2b1dcb8271654720a9ae7e4ae13488aa287a34f890475aea2d8d9f56c8
+size 561190660
diff --git a/geo_LHC078_AoA_20/boundary_dual_area_geo_LHC078_AoA_20.npy b/geo_LHC078_AoA_20/boundary_dual_area_geo_LHC078_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2e125e1654bec1abb42a6182f045dab31fcfed8b
--- /dev/null
+++ b/geo_LHC078_AoA_20/boundary_dual_area_geo_LHC078_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3dca99b7ab84a0fd5a98744087b6d231d31b2ad7523eba14f556f64a95e39182
+size 594725708
diff --git a/geo_LHC079_AoA_8/boundary_dual_area_geo_LHC079_AoA_8.npy b/geo_LHC079_AoA_8/boundary_dual_area_geo_LHC079_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..909a34a2106a11fc42b99f8de890d5942c5233f7
--- /dev/null
+++ b/geo_LHC079_AoA_8/boundary_dual_area_geo_LHC079_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2fcc40685c16c6efb5739f70e2011bafd03c70bb86db497d7e0d33a9f7be6117
+size 537729988
diff --git a/geo_LHC080_AoA_10/boundary_dual_area_geo_LHC080_AoA_10.npy b/geo_LHC080_AoA_10/boundary_dual_area_geo_LHC080_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..61e411cb1ecdeb45f9571815cf1f49403bf771ed
--- /dev/null
+++ b/geo_LHC080_AoA_10/boundary_dual_area_geo_LHC080_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02b88a87d662ff7d90959bc1b167e7a15db7b4fdd1e288cb4379aaf7a2b1fbb2
+size 578817892
diff --git a/geo_LHC080_AoA_12/boundary_dual_area_geo_LHC080_AoA_12.npy b/geo_LHC080_AoA_12/boundary_dual_area_geo_LHC080_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c1b78ff9d3f7c78b7dd62e6481b548635d43c5ad
--- /dev/null
+++ b/geo_LHC080_AoA_12/boundary_dual_area_geo_LHC080_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bd9dcf708647199aaa3bdb1ba764ba1cd15178e0fe2ab4206dad13e1d04a9c68
+size 588632320
diff --git a/geo_LHC081_AoA_6/boundary_dual_area_geo_LHC081_AoA_6.npy b/geo_LHC081_AoA_6/boundary_dual_area_geo_LHC081_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..15bfa5e5b811ebdcb6e94fb089a03ffcb6ca6055
--- /dev/null
+++ b/geo_LHC081_AoA_6/boundary_dual_area_geo_LHC081_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ebca67eec9dc94a4211e9311f85bc5e78f53f865afbf28da8f76685446ab4853
+size 564217856
diff --git a/geo_LHC083_AoA_4/boundary_dual_area_geo_LHC083_AoA_4.npy b/geo_LHC083_AoA_4/boundary_dual_area_geo_LHC083_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..373d72265094280a3731e0df8f9856da4308fd6c
--- /dev/null
+++ b/geo_LHC083_AoA_4/boundary_dual_area_geo_LHC083_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4f39c9d6d529fc61583058f3a39d59266bd8e9b6cd628d5d1d9cd5c5c0105537
+size 562712436
diff --git a/geo_LHC084_AoA_20/boundary_dual_area_geo_LHC084_AoA_20.npy b/geo_LHC084_AoA_20/boundary_dual_area_geo_LHC084_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f918ee007387ac398d44742514e8a966e467b9b5
--- /dev/null
+++ b/geo_LHC084_AoA_20/boundary_dual_area_geo_LHC084_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ece75300220ef06015d3254f526de8c48a6f6fe46d342bcfa3a4ffb304301b54
+size 551928932
diff --git a/geo_LHC084_AoA_22/boundary_dual_area_geo_LHC084_AoA_22.npy b/geo_LHC084_AoA_22/boundary_dual_area_geo_LHC084_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a79ab3f5cd37427de19e6f493c7a1030363c8df9
--- /dev/null
+++ b/geo_LHC084_AoA_22/boundary_dual_area_geo_LHC084_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6f11effec5bf5e6b2c2791ec4e654d0a8fd81e8e7e6c90cec0c905b3a497f28d
+size 550579272
diff --git a/geo_LHC084_AoA_4/boundary_dual_area_geo_LHC084_AoA_4.npy b/geo_LHC084_AoA_4/boundary_dual_area_geo_LHC084_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ed98696dce5966696b1a9470da89d9d76ad3147b
--- /dev/null
+++ b/geo_LHC084_AoA_4/boundary_dual_area_geo_LHC084_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dfc77a9d25f10a021cd76b5675ca1dfb24c068d77f582fb321d820823494beb6
+size 521377000
diff --git a/geo_LHC084_AoA_6/boundary_dual_area_geo_LHC084_AoA_6.npy b/geo_LHC084_AoA_6/boundary_dual_area_geo_LHC084_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7d42f8b35f115aadb06e258b3a1683abd741e6da
--- /dev/null
+++ b/geo_LHC084_AoA_6/boundary_dual_area_geo_LHC084_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6194ff779eb436ad6bd71515a081c8ee9fc183017416f43a681c09c3271853a8
+size 542238404
diff --git a/geo_LHC084_AoA_8/boundary_dual_area_geo_LHC084_AoA_8.npy b/geo_LHC084_AoA_8/boundary_dual_area_geo_LHC084_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d0a339348e463796e5ca8d7c8153c91ccf04b58f
--- /dev/null
+++ b/geo_LHC084_AoA_8/boundary_dual_area_geo_LHC084_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:78d5c4e2c5189574777b57fd36a0faba0b8aca8e364f192967d4248b4c5dce57
+size 550422804
diff --git a/geo_LHC085_AoA_14/boundary_dual_area_geo_LHC085_AoA_14.npy b/geo_LHC085_AoA_14/boundary_dual_area_geo_LHC085_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..68720ece65d53dee98e4dcc9b40773ce000fae91
--- /dev/null
+++ b/geo_LHC085_AoA_14/boundary_dual_area_geo_LHC085_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:154a2dca687c5801bdbe6a6cb22e99061a5f75a88fc27f644fdf9b6add4eda56
+size 589436848
diff --git a/geo_LHC085_AoA_18/boundary_dual_area_geo_LHC085_AoA_18.npy b/geo_LHC085_AoA_18/boundary_dual_area_geo_LHC085_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..952ddce62c5435446520ae162356236bdecee3c8
--- /dev/null
+++ b/geo_LHC085_AoA_18/boundary_dual_area_geo_LHC085_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:76a7ab06c920b2301bd5e021d1d29ea9aee9e70bf57e2b00c65af3facbf79e10
+size 592668696
diff --git a/geo_LHC085_AoA_22/boundary_dual_area_geo_LHC085_AoA_22.npy b/geo_LHC085_AoA_22/boundary_dual_area_geo_LHC085_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2ef5b4d9d4642e1389198bb08f9408e9804ad4af
--- /dev/null
+++ b/geo_LHC085_AoA_22/boundary_dual_area_geo_LHC085_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3fdf3ee0542c840adfd0c5eda66cd7ab1070121e9e88c798e121611a652a874a
+size 593744884
diff --git a/geo_LHC085_AoA_4/boundary_dual_area_geo_LHC085_AoA_4.npy b/geo_LHC085_AoA_4/boundary_dual_area_geo_LHC085_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..bbd5846a3c1bdc326af0911709328dd664010cc3
--- /dev/null
+++ b/geo_LHC085_AoA_4/boundary_dual_area_geo_LHC085_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7b82ab71236bba30c483d13697444b9a68973fc81ac1e844770f054ff20b2f98
+size 548962504
diff --git a/geo_LHC085_AoA_8/boundary_dual_area_geo_LHC085_AoA_8.npy b/geo_LHC085_AoA_8/boundary_dual_area_geo_LHC085_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0a99b556ee66ab0930f103dd6f5c0dbf82aab65b
--- /dev/null
+++ b/geo_LHC085_AoA_8/boundary_dual_area_geo_LHC085_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3f1732ccde6a2de52836a1797372808c564556496947659823bc64b3be092765
+size 555581456
diff --git a/geo_LHC086_AoA_20/boundary_dual_area_geo_LHC086_AoA_20.npy b/geo_LHC086_AoA_20/boundary_dual_area_geo_LHC086_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fb56c96f361a50669199c618df56110345369c31
--- /dev/null
+++ b/geo_LHC086_AoA_20/boundary_dual_area_geo_LHC086_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4bc4e7ca219c6961d2bc97c4b2b801d89b8f273edb9c1f2232b260f076c8f713
+size 593339420
diff --git a/geo_LHC087_AoA_12/boundary_dual_area_geo_LHC087_AoA_12.npy b/geo_LHC087_AoA_12/boundary_dual_area_geo_LHC087_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..53f4336ddd36f052ddfe93049f8a83edac7fc011
--- /dev/null
+++ b/geo_LHC087_AoA_12/boundary_dual_area_geo_LHC087_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d20ea3f573933b8fcb3518238a39e3d7ac8089db32f61a393bff5af9efd24a4
+size 562655232
diff --git a/geo_LHC087_AoA_18/boundary_dual_area_geo_LHC087_AoA_18.npy b/geo_LHC087_AoA_18/boundary_dual_area_geo_LHC087_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9930f5c2c192d46cddf38cc994211a472799a2b5
--- /dev/null
+++ b/geo_LHC087_AoA_18/boundary_dual_area_geo_LHC087_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f0c5619a62b727690a02eb67ee635f6c06e355b5f4b680fc2fba596565a7db1d
+size 564554900
diff --git a/geo_LHC088_AoA_4/boundary_dual_area_geo_LHC088_AoA_4.npy b/geo_LHC088_AoA_4/boundary_dual_area_geo_LHC088_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..31d39bc24b3eab32f25f6fe20893c5aab7161e31
--- /dev/null
+++ b/geo_LHC088_AoA_4/boundary_dual_area_geo_LHC088_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cdc4d55fadc5da89efe31b5d2408a17524e9cec15e73465be19a4deedf88ec6a
+size 520733020
diff --git a/geo_LHC089_AoA_16/boundary_dual_area_geo_LHC089_AoA_16.npy b/geo_LHC089_AoA_16/boundary_dual_area_geo_LHC089_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2527e4e963d2d60182357b8f3d53b4734b72a981
--- /dev/null
+++ b/geo_LHC089_AoA_16/boundary_dual_area_geo_LHC089_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57b424d2d67628e61f89cb551deb5a072b74c6f55360b3dd2ab618aa1102c7e8
+size 591406252
diff --git a/geo_LHC089_AoA_4/boundary_dual_area_geo_LHC089_AoA_4.npy b/geo_LHC089_AoA_4/boundary_dual_area_geo_LHC089_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..08ac83258ae73fe85f21e41ca6bdfa41e0e2caeb
--- /dev/null
+++ b/geo_LHC089_AoA_4/boundary_dual_area_geo_LHC089_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f28cc4160a24d24ede88a0d999149242856a9038b30a8e817db6f16928194118
+size 546212428
diff --git a/geo_LHC090_AoA_14/boundary_dual_area_geo_LHC090_AoA_14.npy b/geo_LHC090_AoA_14/boundary_dual_area_geo_LHC090_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..08da3909c42feb23581753971b4d806fbcf11934
--- /dev/null
+++ b/geo_LHC090_AoA_14/boundary_dual_area_geo_LHC090_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbe42a35157337882ef409ea2094f54ea46a51bf3896a3d96ec037bfde230428
+size 576606132
diff --git a/geo_LHC090_AoA_16/boundary_dual_area_geo_LHC090_AoA_16.npy b/geo_LHC090_AoA_16/boundary_dual_area_geo_LHC090_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..172d7aaab1a8cb4665f0cc1cbd43b00664f9d933
--- /dev/null
+++ b/geo_LHC090_AoA_16/boundary_dual_area_geo_LHC090_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:11690bb64b60a4141ce6e7ea09b1565eac601d12d331cf53ec1e8348a8dcb8de
+size 584403096
diff --git a/geo_LHC090_AoA_18/boundary_dual_area_geo_LHC090_AoA_18.npy b/geo_LHC090_AoA_18/boundary_dual_area_geo_LHC090_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0c5e8eb0f7d9c2f6784ecd9bc3b476abf6f8defd
--- /dev/null
+++ b/geo_LHC090_AoA_18/boundary_dual_area_geo_LHC090_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8ca991cd03751cf98d2cb0fcab545a9b665e51859d9976e48cfe3c5d4fb655b1
+size 588158380
diff --git a/geo_LHC091_AoA_6/boundary_dual_area_geo_LHC091_AoA_6.npy b/geo_LHC091_AoA_6/boundary_dual_area_geo_LHC091_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..46badae91d85deacae110058f99554b14ead17fe
--- /dev/null
+++ b/geo_LHC091_AoA_6/boundary_dual_area_geo_LHC091_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f067f830dffbee998eab880561d261517907a88937f677672605c1625fe42fab
+size 509173436
diff --git a/geo_LHC092_AoA_10/boundary_dual_area_geo_LHC092_AoA_10.npy b/geo_LHC092_AoA_10/boundary_dual_area_geo_LHC092_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..16bd24501c1ae62893efd346dd5318e648fbcec9
--- /dev/null
+++ b/geo_LHC092_AoA_10/boundary_dual_area_geo_LHC092_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cb163f65a9a87cc8b01be9706df86fd8c5f9d3fc16fc5c9fc07e953bd9ee5045
+size 551563448
diff --git a/geo_LHC092_AoA_12/boundary_dual_area_geo_LHC092_AoA_12.npy b/geo_LHC092_AoA_12/boundary_dual_area_geo_LHC092_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d57d41bbe14c0dd1ad0abbc0b6dc4ab9516a121f
--- /dev/null
+++ b/geo_LHC092_AoA_12/boundary_dual_area_geo_LHC092_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:46db60a211721b69fbad9f7384eea5fc4885cce5a8981df73b2daa94d1198501
+size 555302788
diff --git a/geo_LHC092_AoA_14/boundary_dual_area_geo_LHC092_AoA_14.npy b/geo_LHC092_AoA_14/boundary_dual_area_geo_LHC092_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..28060f503df634e691ecfaaeae41b6b7e7e21a9f
--- /dev/null
+++ b/geo_LHC092_AoA_14/boundary_dual_area_geo_LHC092_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57044ba3b05242c2621aa4f520bcbb47e98d7704e183ac7cfc75395a2afc969d
+size 555841128
diff --git a/geo_LHC092_AoA_16/boundary_dual_area_geo_LHC092_AoA_16.npy b/geo_LHC092_AoA_16/boundary_dual_area_geo_LHC092_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a0f4de0eba7fc3b7deaa977e362b4b4acae5a7a4
--- /dev/null
+++ b/geo_LHC092_AoA_16/boundary_dual_area_geo_LHC092_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d48cfb471a5072863ce6fa40874019950bba67322debc8d39845e1f4db9b15cc
+size 554395680
diff --git a/geo_LHC092_AoA_18/boundary_dual_area_geo_LHC092_AoA_18.npy b/geo_LHC092_AoA_18/boundary_dual_area_geo_LHC092_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a378853b0dcc9f7623ba21830568c3f493101822
--- /dev/null
+++ b/geo_LHC092_AoA_18/boundary_dual_area_geo_LHC092_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:219731e6c1ac2353c0fb450c2340304af52fd6dfb9fcb7c5dd9107ae61312963
+size 552524576
diff --git a/geo_LHC092_AoA_22/boundary_dual_area_geo_LHC092_AoA_22.npy b/geo_LHC092_AoA_22/boundary_dual_area_geo_LHC092_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..327101816415d68563a843994b5f7019009558cd
--- /dev/null
+++ b/geo_LHC092_AoA_22/boundary_dual_area_geo_LHC092_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:03503e70597da20f70c2d89c567d1439b6930f3a3acfb4cce9b8744aa421b937
+size 549392756
diff --git a/geo_LHC092_AoA_8/boundary_dual_area_geo_LHC092_AoA_8.npy b/geo_LHC092_AoA_8/boundary_dual_area_geo_LHC092_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..daa7193288abf7e50b9fc9924e798ec5df255027
--- /dev/null
+++ b/geo_LHC092_AoA_8/boundary_dual_area_geo_LHC092_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a7fd155a719cbe8f70bcd3ffa53654ed6ab99ea55ce62552ccc64dce3291c4e4
+size 544597076
diff --git a/geo_LHC093_AoA_16/boundary_dual_area_geo_LHC093_AoA_16.npy b/geo_LHC093_AoA_16/boundary_dual_area_geo_LHC093_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d80f0eef0636e20a5009a3986b22d758071b3587
--- /dev/null
+++ b/geo_LHC093_AoA_16/boundary_dual_area_geo_LHC093_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ced347ccc5d53e3475b64265f6cb2c2098cfb9631df613025961b21c9edad83a
+size 563165096
diff --git a/geo_LHC093_AoA_22/boundary_dual_area_geo_LHC093_AoA_22.npy b/geo_LHC093_AoA_22/boundary_dual_area_geo_LHC093_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d3c799e671d9fc49aaced7d0e388f0d0131a6596
--- /dev/null
+++ b/geo_LHC093_AoA_22/boundary_dual_area_geo_LHC093_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:287fc00c7c9b469c67b009d4999ae5ae2b07d3c458f8394140b1a0c5a853da4f
+size 559247700
diff --git a/geo_LHC095_AoA_6/boundary_dual_area_geo_LHC095_AoA_6.npy b/geo_LHC095_AoA_6/boundary_dual_area_geo_LHC095_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..40743e4420de224e061bcad4a9b30dd35a856715
--- /dev/null
+++ b/geo_LHC095_AoA_6/boundary_dual_area_geo_LHC095_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dfd144e292518f7d83ceebd258f0d7adf3f30f26a20d4c1266222293ce1e0c07
+size 560816572
diff --git a/geo_LHC096_AoA_10/boundary_dual_area_geo_LHC096_AoA_10.npy b/geo_LHC096_AoA_10/boundary_dual_area_geo_LHC096_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1e296d24d4280ed04c839960705c59d67754ea52
--- /dev/null
+++ b/geo_LHC096_AoA_10/boundary_dual_area_geo_LHC096_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:26c9453629659326265c322bcf13d7a1e071aa547f00425b652013f763ac1108
+size 554195952
diff --git a/geo_LHC096_AoA_20/boundary_dual_area_geo_LHC096_AoA_20.npy b/geo_LHC096_AoA_20/boundary_dual_area_geo_LHC096_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..006ab54739a1de1e4dde968fb153aec98a8ac904
--- /dev/null
+++ b/geo_LHC096_AoA_20/boundary_dual_area_geo_LHC096_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4a020f25cd38be14fb2ca1bbd305fcada91cd551b4eb9623d4e62bee190cb7c9
+size 558063772
diff --git a/geo_LHC096_AoA_22/boundary_dual_area_geo_LHC096_AoA_22.npy b/geo_LHC096_AoA_22/boundary_dual_area_geo_LHC096_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..28c1da6c052ac6044365268c55505a3ecc80649c
--- /dev/null
+++ b/geo_LHC096_AoA_22/boundary_dual_area_geo_LHC096_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8312576df579d20e3c64b2ffceb4c8d1fdd00dc49efc7becba2b8a781940dad1
+size 547538360
diff --git a/geo_LHC097_AoA_22/boundary_dual_area_geo_LHC097_AoA_22.npy b/geo_LHC097_AoA_22/boundary_dual_area_geo_LHC097_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..39b0fbf017ae6dee601a4f5d0682e3eebfeb9a86
--- /dev/null
+++ b/geo_LHC097_AoA_22/boundary_dual_area_geo_LHC097_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a18c0b89a079552fa1f6f302777721ac02be78b701db6560a3ee31d50738db1e
+size 562523684
diff --git a/geo_LHC098_AoA_16/boundary_dual_area_geo_LHC098_AoA_16.npy b/geo_LHC098_AoA_16/boundary_dual_area_geo_LHC098_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..de15b21b9fe7dcdffce9344ae3e8e4378a22ddc8
--- /dev/null
+++ b/geo_LHC098_AoA_16/boundary_dual_area_geo_LHC098_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ffa0e750697aefc30b59b8af7fc16783d2b1f53d1162060e1c56e4b655d89c85
+size 556850772
diff --git a/geo_LHC098_AoA_8/boundary_dual_area_geo_LHC098_AoA_8.npy b/geo_LHC098_AoA_8/boundary_dual_area_geo_LHC098_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f8ff28789507ee38829a70494b1ea1f362770151
--- /dev/null
+++ b/geo_LHC098_AoA_8/boundary_dual_area_geo_LHC098_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:61a4baea04fb8dd0c3183177c5d4f357e5d4ba482cea2900fadfa1e10b1b457c
+size 550060084
diff --git a/geo_LHC099_AoA_14/boundary_dual_area_geo_LHC099_AoA_14.npy b/geo_LHC099_AoA_14/boundary_dual_area_geo_LHC099_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..49c6d81d30f12a69feb0ca3482cb751711af3f70
--- /dev/null
+++ b/geo_LHC099_AoA_14/boundary_dual_area_geo_LHC099_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2e4c775c60d4b151c7f93595c08e14fcd4d89c13ef228ffd3da28d1861ab7e81
+size 579073796
diff --git a/geo_LHC101_AoA_12/boundary_dual_area_geo_LHC101_AoA_12.npy b/geo_LHC101_AoA_12/boundary_dual_area_geo_LHC101_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..54243515b37ad77878ab6da8a61414606389969c
--- /dev/null
+++ b/geo_LHC101_AoA_12/boundary_dual_area_geo_LHC101_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eb1592564b29c27e573624e000e5592dc0d8b389f52ba31af865fbf43dbefc76
+size 587909712
diff --git a/geo_LHC101_AoA_16/boundary_dual_area_geo_LHC101_AoA_16.npy b/geo_LHC101_AoA_16/boundary_dual_area_geo_LHC101_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8c3f7a937d6069f2c553cd9a263642536dcde7c8
--- /dev/null
+++ b/geo_LHC101_AoA_16/boundary_dual_area_geo_LHC101_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02182c259132b322fae8587683c150002a0e13edb425647c71dadbca067d2166
+size 597168016
diff --git a/geo_LHC102_AoA_10/boundary_dual_area_geo_LHC102_AoA_10.npy b/geo_LHC102_AoA_10/boundary_dual_area_geo_LHC102_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..10bcb5e9fd116d1c9c326f25a0a93f52a20c8a28
--- /dev/null
+++ b/geo_LHC102_AoA_10/boundary_dual_area_geo_LHC102_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf7d60d67b701cc4ed352b767043ac2e80c3de7a23358656f0317866da8bfd81
+size 585865536
diff --git a/geo_LHC102_AoA_16/boundary_dual_area_geo_LHC102_AoA_16.npy b/geo_LHC102_AoA_16/boundary_dual_area_geo_LHC102_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e8b691da58e6efd77defcf3fc07dba10f79074cd
--- /dev/null
+++ b/geo_LHC102_AoA_16/boundary_dual_area_geo_LHC102_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5fb0d8ecef5cd383498046ef63b0366b060f28b13bbb43328debb3faabe497d3
+size 570468428
diff --git a/geo_LHC103_AoA_12/boundary_dual_area_geo_LHC103_AoA_12.npy b/geo_LHC103_AoA_12/boundary_dual_area_geo_LHC103_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ed2f6f4c49f199a3dd24a0fbb9c1e7ae42536ac7
--- /dev/null
+++ b/geo_LHC103_AoA_12/boundary_dual_area_geo_LHC103_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8eaf94287b485600f3c7320ded93a470db5e156ba20ca6f47b433be93fc79ae0
+size 557493524
diff --git a/geo_LHC103_AoA_14/boundary_dual_area_geo_LHC103_AoA_14.npy b/geo_LHC103_AoA_14/boundary_dual_area_geo_LHC103_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..478b8b3c44d574247280b68d0f3193d08b48e810
--- /dev/null
+++ b/geo_LHC103_AoA_14/boundary_dual_area_geo_LHC103_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:62df70f0ff1784d0b7c577c942fc207e74a2185f186fff316467e02e2710a262
+size 567681460
diff --git a/geo_LHC103_AoA_4/boundary_dual_area_geo_LHC103_AoA_4.npy b/geo_LHC103_AoA_4/boundary_dual_area_geo_LHC103_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..390388ac25b3fc95bba10f313ec9bf9c2dd429e7
--- /dev/null
+++ b/geo_LHC103_AoA_4/boundary_dual_area_geo_LHC103_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bdb479514789dde07f9b052f225c0801821371810eee17137cb23ca17feeea46
+size 535558908
diff --git a/geo_LHC103_AoA_6/boundary_dual_area_geo_LHC103_AoA_6.npy b/geo_LHC103_AoA_6/boundary_dual_area_geo_LHC103_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..649732f57ceafbcfad79e60e4f43a0284393d358
--- /dev/null
+++ b/geo_LHC103_AoA_6/boundary_dual_area_geo_LHC103_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:967aa019b46442476596a1792044c4b2adffcfb3246f122b3364db1bae56b0d2
+size 529814940
diff --git a/geo_LHC106_AoA_20/boundary_dual_area_geo_LHC106_AoA_20.npy b/geo_LHC106_AoA_20/boundary_dual_area_geo_LHC106_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b5221e0d95887fcf635b39621a778a6514052cab
--- /dev/null
+++ b/geo_LHC106_AoA_20/boundary_dual_area_geo_LHC106_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3c4663b5cd8e4aa0c2f069c27fc5671e3761d0cc5b29093548128f5659af170d
+size 582432324
diff --git a/geo_LHC106_AoA_8/boundary_dual_area_geo_LHC106_AoA_8.npy b/geo_LHC106_AoA_8/boundary_dual_area_geo_LHC106_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7f1ee8ed9b956f352276a5096d15ed9d16e154f7
--- /dev/null
+++ b/geo_LHC106_AoA_8/boundary_dual_area_geo_LHC106_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e8646a9105effdb0a9aca950152180653638ca5b2461669cfaa6eeaf9e1b5f1d
+size 538655520
diff --git a/geo_LHC108_AoA_18/boundary_dual_area_geo_LHC108_AoA_18.npy b/geo_LHC108_AoA_18/boundary_dual_area_geo_LHC108_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..71efbd4b5f012450aa5afd10df08549a94d94343
--- /dev/null
+++ b/geo_LHC108_AoA_18/boundary_dual_area_geo_LHC108_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:247fe6d269e4ff8d070636c83f26c439401c0dd63c31119d2081177a912fdda9
+size 565046704
diff --git a/geo_LHC108_AoA_4/boundary_dual_area_geo_LHC108_AoA_4.npy b/geo_LHC108_AoA_4/boundary_dual_area_geo_LHC108_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4607de61ee1fc80af557d6ba067e9a79bf61ad28
--- /dev/null
+++ b/geo_LHC108_AoA_4/boundary_dual_area_geo_LHC108_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:61c64a840b73032681c9b4283efec4956adaf99a1a6270a069f5968d52b14eda
+size 515296680
diff --git a/geo_LHC109_AoA_14/boundary_dual_area_geo_LHC109_AoA_14.npy b/geo_LHC109_AoA_14/boundary_dual_area_geo_LHC109_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6f8e6007e9df6d75ee85a608424840ae1dc2202a
--- /dev/null
+++ b/geo_LHC109_AoA_14/boundary_dual_area_geo_LHC109_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:92cb797a24c630b5b1fb476169bedceee500ec545c2629fd9216fdf0b559e181
+size 565913728
diff --git a/geo_LHC109_AoA_18/boundary_dual_area_geo_LHC109_AoA_18.npy b/geo_LHC109_AoA_18/boundary_dual_area_geo_LHC109_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..221385088995a94bd5528731d9b20eaaa7d0e5d2
--- /dev/null
+++ b/geo_LHC109_AoA_18/boundary_dual_area_geo_LHC109_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b2ef2a83a3f1f91d0e1672bcc9fafb8fe676feccc9fdc238a9ddad6e840003d4
+size 568427160
diff --git a/geo_LHC110_AoA_14/boundary_dual_area_geo_LHC110_AoA_14.npy b/geo_LHC110_AoA_14/boundary_dual_area_geo_LHC110_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..716fa43dcca49773afb50446ead9f6d23876b9da
--- /dev/null
+++ b/geo_LHC110_AoA_14/boundary_dual_area_geo_LHC110_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:67f71342ca188af93a9098996d36ee5f8d8495127225439f8e61347311c95191
+size 557953476
diff --git a/geo_LHC110_AoA_18/boundary_dual_area_geo_LHC110_AoA_18.npy b/geo_LHC110_AoA_18/boundary_dual_area_geo_LHC110_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..caa773969f6a4c05a483a573dbb3aedf463d86cd
--- /dev/null
+++ b/geo_LHC110_AoA_18/boundary_dual_area_geo_LHC110_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bcb9d6e36091fb2b51cf34ff0cd8158547394f8dd039da82e5bde357e56bfed1
+size 562358052
diff --git a/geo_LHC110_AoA_4/boundary_dual_area_geo_LHC110_AoA_4.npy b/geo_LHC110_AoA_4/boundary_dual_area_geo_LHC110_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c9dccc29f58dd63b413fb572dc109ccbb1860e1f
--- /dev/null
+++ b/geo_LHC110_AoA_4/boundary_dual_area_geo_LHC110_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f5890e84c5118fb683d60f11b4f91bb47fdd2ee15c3d76d71c7dcc2b92a1cf4a
+size 520456276
diff --git a/geo_LHC111_AoA_22/boundary_dual_area_geo_LHC111_AoA_22.npy b/geo_LHC111_AoA_22/boundary_dual_area_geo_LHC111_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..24b040013e8a9c00acf505ec40d2beb5c879c685
--- /dev/null
+++ b/geo_LHC111_AoA_22/boundary_dual_area_geo_LHC111_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:75ef42987c96d8fb03300eb43a8c85de8353ab7de2147233554b89f0ef0e1dd6
+size 590628604
diff --git a/geo_LHC112_AoA_20/boundary_dual_area_geo_LHC112_AoA_20.npy b/geo_LHC112_AoA_20/boundary_dual_area_geo_LHC112_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7ca4bdb17944b25cbab492ce32dbc1c5a0cb3c58
--- /dev/null
+++ b/geo_LHC112_AoA_20/boundary_dual_area_geo_LHC112_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b24d424f7660dd4c745d5edc8fde772553040f7fd1af7ce7a55411c62f2c131e
+size 572051168
diff --git a/geo_LHC112_AoA_6/boundary_dual_area_geo_LHC112_AoA_6.npy b/geo_LHC112_AoA_6/boundary_dual_area_geo_LHC112_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..91d731ca4202503b411fbd1d0cb23cda88ae5fd0
--- /dev/null
+++ b/geo_LHC112_AoA_6/boundary_dual_area_geo_LHC112_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b91fe9d5884cdff37c03b00d894c35b0b6a85e06480cda45f78b46f77b64998c
+size 543596508
diff --git a/geo_LHC113_AoA_16/boundary_dual_area_geo_LHC113_AoA_16.npy b/geo_LHC113_AoA_16/boundary_dual_area_geo_LHC113_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9cd087c5941cad04fec019cb437f5ecd321b94e4
--- /dev/null
+++ b/geo_LHC113_AoA_16/boundary_dual_area_geo_LHC113_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7338930f322ffa93da9577ff3446f5274ca8165525111f1d942b822a4f7cb176
+size 554060676
diff --git a/geo_LHC113_AoA_8/boundary_dual_area_geo_LHC113_AoA_8.npy b/geo_LHC113_AoA_8/boundary_dual_area_geo_LHC113_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..60f34a5a412d7921a95fe169acdf5bc03aad2f5d
--- /dev/null
+++ b/geo_LHC113_AoA_8/boundary_dual_area_geo_LHC113_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0525e1b0b5e858732c9ba8bbcecbc21bb6c5a293af69c25ea69b3cf8d13c0265
+size 551921656
diff --git a/geo_LHC114_AoA_14/boundary_dual_area_geo_LHC114_AoA_14.npy b/geo_LHC114_AoA_14/boundary_dual_area_geo_LHC114_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..64b84d611e6ace441076534417deba11973eb60e
--- /dev/null
+++ b/geo_LHC114_AoA_14/boundary_dual_area_geo_LHC114_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4d6d0205a0eb70e0635d4e485551c9412935ba5d443d20c278e47b3f0d1935bb
+size 605563092
diff --git a/geo_LHC114_AoA_16/boundary_dual_area_geo_LHC114_AoA_16.npy b/geo_LHC114_AoA_16/boundary_dual_area_geo_LHC114_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..912925236427463d14d5983938ca4d392bbbc87a
--- /dev/null
+++ b/geo_LHC114_AoA_16/boundary_dual_area_geo_LHC114_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8f919e55b8c7ae985601ae1771a6155c43e390a53e2006866018e31c9468bf37
+size 600492704
diff --git a/geo_LHC115_AoA_16/boundary_dual_area_geo_LHC115_AoA_16.npy b/geo_LHC115_AoA_16/boundary_dual_area_geo_LHC115_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..06e213703829fbfe191f9cbbe092d5c8e8de4823
--- /dev/null
+++ b/geo_LHC115_AoA_16/boundary_dual_area_geo_LHC115_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:84c0895cce41897ad08f26bb3bc13121febb03c0123e9d911c5d667ce5f13367
+size 560441420
diff --git a/geo_LHC115_AoA_18/boundary_dual_area_geo_LHC115_AoA_18.npy b/geo_LHC115_AoA_18/boundary_dual_area_geo_LHC115_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..626f9fbec9f1e87c5fb048a56ea5f0db68680f9c
--- /dev/null
+++ b/geo_LHC115_AoA_18/boundary_dual_area_geo_LHC115_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:38b8d147d78dc8bd29cdef3bba22bd09bb60ff18d1b402fb639012a2a1eaa9b8
+size 558175636
diff --git a/geo_LHC116_AoA_18/boundary_dual_area_geo_LHC116_AoA_18.npy b/geo_LHC116_AoA_18/boundary_dual_area_geo_LHC116_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c339bd49a6ee5ad7625cc82321fa9411dbc279a8
--- /dev/null
+++ b/geo_LHC116_AoA_18/boundary_dual_area_geo_LHC116_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ca6888ac814272aa2e1a797b1c9f0e57c9384e702461dd8053ac2e477eccc74f
+size 588495944
diff --git a/geo_LHC118_AoA_12/boundary_dual_area_geo_LHC118_AoA_12.npy b/geo_LHC118_AoA_12/boundary_dual_area_geo_LHC118_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1cbdff870faa0fd6bbe9b0eab7810ebb443cc280
--- /dev/null
+++ b/geo_LHC118_AoA_12/boundary_dual_area_geo_LHC118_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2d59e0fa30370af61db9c908258885df1725a500fb640552d3586699b2fa475a
+size 572951088
diff --git a/geo_LHC119_AoA_14/boundary_dual_area_geo_LHC119_AoA_14.npy b/geo_LHC119_AoA_14/boundary_dual_area_geo_LHC119_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a36adb0d1209b626a44b50d3f151583ed9808c25
--- /dev/null
+++ b/geo_LHC119_AoA_14/boundary_dual_area_geo_LHC119_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8e43f2f53e1d373007d8eab42d48824b693660816dbd41b6622a2d9d64391c6f
+size 560024556
diff --git a/geo_LHC120_AoA_22/boundary_dual_area_geo_LHC120_AoA_22.npy b/geo_LHC120_AoA_22/boundary_dual_area_geo_LHC120_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..56d5ad9552720a11c853d433390afbbc9b1b5900
--- /dev/null
+++ b/geo_LHC120_AoA_22/boundary_dual_area_geo_LHC120_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e8f5127985e0e795b54e4e38df4f07b95d3b14cb922e0cd9ac4bf05895503106
+size 601580320
diff --git a/geo_LHC121_AoA_10/boundary_dual_area_geo_LHC121_AoA_10.npy b/geo_LHC121_AoA_10/boundary_dual_area_geo_LHC121_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2b3a2955f2ba8cc1ebaa3e4c8d21c6f475f9067f
--- /dev/null
+++ b/geo_LHC121_AoA_10/boundary_dual_area_geo_LHC121_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:781bdd07311b904231b6fba5dcbba6b8889f8395b89a69477a29e8bb469c38af
+size 569513560
diff --git a/geo_LHC121_AoA_16/boundary_dual_area_geo_LHC121_AoA_16.npy b/geo_LHC121_AoA_16/boundary_dual_area_geo_LHC121_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e2e2d4d4432d1f526b29895e963755d40f7dacea
--- /dev/null
+++ b/geo_LHC121_AoA_16/boundary_dual_area_geo_LHC121_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:54d486ad4a18485d65ff0eee532c52391ef82ebc772afc0f3817878d8643d740
+size 583284084
diff --git a/geo_LHC121_AoA_4/boundary_dual_area_geo_LHC121_AoA_4.npy b/geo_LHC121_AoA_4/boundary_dual_area_geo_LHC121_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7bc2d846bbcda1f4cbedf3081ff5521c49a8ee4d
--- /dev/null
+++ b/geo_LHC121_AoA_4/boundary_dual_area_geo_LHC121_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a96157c95e9c1de9d883d39a6e183a3c7ae35553371cf0286768695606b2fc91
+size 544548852
diff --git a/geo_LHC121_AoA_8/boundary_dual_area_geo_LHC121_AoA_8.npy b/geo_LHC121_AoA_8/boundary_dual_area_geo_LHC121_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..94761952bbe27dcb523be066ff828ecaf228e6df
--- /dev/null
+++ b/geo_LHC121_AoA_8/boundary_dual_area_geo_LHC121_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2ebf2fd10b025ca9ab5f1ac6e7e56d4c00240302a9bf44f0b28cff7e09ab0535
+size 552760904
diff --git a/geo_LHC122_AoA_10/boundary_dual_area_geo_LHC122_AoA_10.npy b/geo_LHC122_AoA_10/boundary_dual_area_geo_LHC122_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..10fefc9ad903aea41695fa675b36d0632ad6f728
--- /dev/null
+++ b/geo_LHC122_AoA_10/boundary_dual_area_geo_LHC122_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f43d399d13921263812880fe546a8f210046f29937561c1984ed22f7c17b0db9
+size 552944904
diff --git a/geo_LHC122_AoA_14/boundary_dual_area_geo_LHC122_AoA_14.npy b/geo_LHC122_AoA_14/boundary_dual_area_geo_LHC122_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8a9ccc62217a74ab403ca20d7c23d20c14b5d47b
--- /dev/null
+++ b/geo_LHC122_AoA_14/boundary_dual_area_geo_LHC122_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8c2e175cf67ecb71ad00771037145762698b9a07378ae012629ad54b990784c4
+size 556028868
diff --git a/geo_LHC122_AoA_22/boundary_dual_area_geo_LHC122_AoA_22.npy b/geo_LHC122_AoA_22/boundary_dual_area_geo_LHC122_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d56ce8d9584b0989177f4dbbcb39df590d562fad
--- /dev/null
+++ b/geo_LHC122_AoA_22/boundary_dual_area_geo_LHC122_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6ddd5133683ef0514a65bf99f7e8b34f09002087c460936ad46b4e16a9a667e5
+size 552110836
diff --git a/geo_LHC123_AoA_22/boundary_dual_area_geo_LHC123_AoA_22.npy b/geo_LHC123_AoA_22/boundary_dual_area_geo_LHC123_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8d38f4b0e08150737b0b1214e9fd961cc7f27cb2
--- /dev/null
+++ b/geo_LHC123_AoA_22/boundary_dual_area_geo_LHC123_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5caddb0f51b416c9ecbca6bf2764433db63cbbc73e3667c08607973c49ae73e3
+size 583865264
diff --git a/geo_LHC125_AoA_18/boundary_dual_area_geo_LHC125_AoA_18.npy b/geo_LHC125_AoA_18/boundary_dual_area_geo_LHC125_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0b4bc505d042350a9b626f8a5725624f00015d63
--- /dev/null
+++ b/geo_LHC125_AoA_18/boundary_dual_area_geo_LHC125_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:99b7b26964bf721371a46d7afcae243a37793f49b37ac90b1716e34a09bda86f
+size 549127608
diff --git a/geo_LHC125_AoA_6/boundary_dual_area_geo_LHC125_AoA_6.npy b/geo_LHC125_AoA_6/boundary_dual_area_geo_LHC125_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..27e2a7ab2b99622a720816ebf5c567a8018e6453
--- /dev/null
+++ b/geo_LHC125_AoA_6/boundary_dual_area_geo_LHC125_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1f5dfc2cd6ac97572e466cb95b0aa003e9f64b7d7e372eb688d14d8658b8b3c1
+size 540564676
diff --git a/geo_LHC126_AoA_14/boundary_dual_area_geo_LHC126_AoA_14.npy b/geo_LHC126_AoA_14/boundary_dual_area_geo_LHC126_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cfbfd4d6aec3baa3f6ab3c34e85078adea36090c
--- /dev/null
+++ b/geo_LHC126_AoA_14/boundary_dual_area_geo_LHC126_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:73560b41cbcab5f8370856b09e85581a32e3b049608eb070b34319950ffb5296
+size 555878324
diff --git a/geo_LHC127_AoA_12/boundary_dual_area_geo_LHC127_AoA_12.npy b/geo_LHC127_AoA_12/boundary_dual_area_geo_LHC127_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..43806e6258eea35dcd8c75776f184310d7486819
--- /dev/null
+++ b/geo_LHC127_AoA_12/boundary_dual_area_geo_LHC127_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:29de7160bdc1eae3d2cd6f90fcf8c3e9960f7127bc9d5f036962e0d29848aaae
+size 585405016
diff --git a/geo_LHC128_AoA_22/boundary_dual_area_geo_LHC128_AoA_22.npy b/geo_LHC128_AoA_22/boundary_dual_area_geo_LHC128_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..23b5fe21aca0c47c546adbe4803e9bd1ac3e9364
--- /dev/null
+++ b/geo_LHC128_AoA_22/boundary_dual_area_geo_LHC128_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9ced1f59065d39c512a7ba67fe59477758f42ba2ae7844396f1052378adbdfdd
+size 563111252
diff --git a/geo_LHC128_AoA_6/boundary_dual_area_geo_LHC128_AoA_6.npy b/geo_LHC128_AoA_6/boundary_dual_area_geo_LHC128_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6d768bc45b2b3025caaee9448740c20b8cf0459f
--- /dev/null
+++ b/geo_LHC128_AoA_6/boundary_dual_area_geo_LHC128_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:31bb4133362bbca4ce78d6f2770b2afb479aa367e03cb1dfbb8da3e86cdc7ac3
+size 528506000
diff --git a/geo_LHC129_AoA_8/boundary_dual_area_geo_LHC129_AoA_8.npy b/geo_LHC129_AoA_8/boundary_dual_area_geo_LHC129_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..98ff7ae1027ba3054a401766011d3675907bfa4c
--- /dev/null
+++ b/geo_LHC129_AoA_8/boundary_dual_area_geo_LHC129_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9846cdb98a360fc370c68baa6eef09aec9d922b9d02652db5147a372a9b2f538
+size 559885516
diff --git a/geo_LHC130_AoA_14/boundary_dual_area_geo_LHC130_AoA_14.npy b/geo_LHC130_AoA_14/boundary_dual_area_geo_LHC130_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a3756c332aa58a62f61b40a8599d862048dccc30
--- /dev/null
+++ b/geo_LHC130_AoA_14/boundary_dual_area_geo_LHC130_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2ae5b97d712d69b1322e1fc23c48ed8237bd8b81a950cc8b41d7a5881a9a17b5
+size 567742304
diff --git a/geo_LHC130_AoA_22/boundary_dual_area_geo_LHC130_AoA_22.npy b/geo_LHC130_AoA_22/boundary_dual_area_geo_LHC130_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..40cf5735bef527a8bb48c01ec94bd5e66b8536d0
--- /dev/null
+++ b/geo_LHC130_AoA_22/boundary_dual_area_geo_LHC130_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d2fd2ddbd35f24cec98617c1872978ce1d67443b29a88c51ba9367c8daba63f0
+size 554837736
diff --git a/geo_LHC130_AoA_8/boundary_dual_area_geo_LHC130_AoA_8.npy b/geo_LHC130_AoA_8/boundary_dual_area_geo_LHC130_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3b4cdd88d91a3986e098bd0e25c192abccd98d5e
--- /dev/null
+++ b/geo_LHC130_AoA_8/boundary_dual_area_geo_LHC130_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:db57af42de97ea26a7c8f88be10ebc9c79d303add73bd2c3340525bc9caaa6bc
+size 553427808
diff --git a/geo_LHC132_AoA_16/boundary_dual_area_geo_LHC132_AoA_16.npy b/geo_LHC132_AoA_16/boundary_dual_area_geo_LHC132_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..143da30b08adcce86c62dcfb8e81f1e66b7fc1f4
--- /dev/null
+++ b/geo_LHC132_AoA_16/boundary_dual_area_geo_LHC132_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6bd33e8484fb23b729a426e5154739a3541b6cb1d4841dd85330c9009c88ac5a
+size 605590548
diff --git a/geo_LHC133_AoA_18/boundary_dual_area_geo_LHC133_AoA_18.npy b/geo_LHC133_AoA_18/boundary_dual_area_geo_LHC133_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..36c3e4555b28e13c48cfad8aded2353e12e4f5ca
--- /dev/null
+++ b/geo_LHC133_AoA_18/boundary_dual_area_geo_LHC133_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3b1cab58c38fc403b66037458c60e5ba6a41229d3f5f1454a4b2f77bf2bb8d38
+size 590177832
diff --git a/geo_LHC135_AoA_20/boundary_dual_area_geo_LHC135_AoA_20.npy b/geo_LHC135_AoA_20/boundary_dual_area_geo_LHC135_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..77fbe1bc5d4047129d6d0ff7b4d52c61e2803c05
--- /dev/null
+++ b/geo_LHC135_AoA_20/boundary_dual_area_geo_LHC135_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fadba8e6baefaeee5f0de60357194e1ae93b7d8f8d72e908f28e88e3b7fc377d
+size 562510852
diff --git a/geo_LHC136_AoA_10/boundary_dual_area_geo_LHC136_AoA_10.npy b/geo_LHC136_AoA_10/boundary_dual_area_geo_LHC136_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f8da3e3b82d9b3ed0904024e11106370d01d73e4
--- /dev/null
+++ b/geo_LHC136_AoA_10/boundary_dual_area_geo_LHC136_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:056ecb59b9a248760b31fbb83635cefce00a0d5841f0ad7b7ca73cb55bc70f96
+size 564728300
diff --git a/geo_LHC137_AoA_10/boundary_dual_area_geo_LHC137_AoA_10.npy b/geo_LHC137_AoA_10/boundary_dual_area_geo_LHC137_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..bf87e9ca10a1c983edf21f1f9927712e3f2c6dea
--- /dev/null
+++ b/geo_LHC137_AoA_10/boundary_dual_area_geo_LHC137_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4ccab1aa570458c654838f940c9873806783cfe2f24ce2b0efd97559b64e2a6b
+size 552660088
diff --git a/geo_LHC137_AoA_4/boundary_dual_area_geo_LHC137_AoA_4.npy b/geo_LHC137_AoA_4/boundary_dual_area_geo_LHC137_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4b51eda4e0029a0000972267dca1f079ae422656
--- /dev/null
+++ b/geo_LHC137_AoA_4/boundary_dual_area_geo_LHC137_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c7a9c39dd0086c9dd4bd96b0b88e33ddd2ced4d11af6f06f3a72d83f39f5a178
+size 534122952
diff --git a/geo_LHC138_AoA_20/boundary_dual_area_geo_LHC138_AoA_20.npy b/geo_LHC138_AoA_20/boundary_dual_area_geo_LHC138_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0e25138a11affb6c5b78d01624c7fb1ee1991a2e
--- /dev/null
+++ b/geo_LHC138_AoA_20/boundary_dual_area_geo_LHC138_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:51b43d36a9c34034a534ffb201306f4674d2e4a08386858e3e271937aaad6c1a
+size 599278852
diff --git a/geo_LHC140_AoA_16/boundary_dual_area_geo_LHC140_AoA_16.npy b/geo_LHC140_AoA_16/boundary_dual_area_geo_LHC140_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..72374ceaec5131db207e67da586c526260af2694
--- /dev/null
+++ b/geo_LHC140_AoA_16/boundary_dual_area_geo_LHC140_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d002821d71c7917bc1f346d0766d8d187da334055d401525e1ad513e9979b34f
+size 569022968
diff --git a/geo_LHC140_AoA_22/boundary_dual_area_geo_LHC140_AoA_22.npy b/geo_LHC140_AoA_22/boundary_dual_area_geo_LHC140_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f70e5a7f2210cbb222a8e7f5c3c5cc03d3850c3d
--- /dev/null
+++ b/geo_LHC140_AoA_22/boundary_dual_area_geo_LHC140_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:37fdcfcfda0ee9d7bd3c7766ec2ec397d22c0c2bfe3f0928d9db9fbeb79302a9
+size 566993856
diff --git a/geo_LHC140_AoA_6/boundary_dual_area_geo_LHC140_AoA_6.npy b/geo_LHC140_AoA_6/boundary_dual_area_geo_LHC140_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7ef28d8932e639d6485ff62363b7386bab8ed6cc
--- /dev/null
+++ b/geo_LHC140_AoA_6/boundary_dual_area_geo_LHC140_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:087a9a160902edf5de57765462b94b9d91247b4331b69ca645b283aa8999b343
+size 561021824
diff --git a/geo_LHC141_AoA_10/boundary_dual_area_geo_LHC141_AoA_10.npy b/geo_LHC141_AoA_10/boundary_dual_area_geo_LHC141_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..297f7d19dcfdd5af43d6008357d30ad1ee246f8c
--- /dev/null
+++ b/geo_LHC141_AoA_10/boundary_dual_area_geo_LHC141_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e91770e8868f7bc8847fe89a3540f1d868fb18be5f29de601f0a2bdb8be1ecc8
+size 584868160
diff --git a/geo_LHC142_AoA_18/boundary_dual_area_geo_LHC142_AoA_18.npy b/geo_LHC142_AoA_18/boundary_dual_area_geo_LHC142_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..11d741e73b3621aa29a954101b22ef0cc4be8b63
--- /dev/null
+++ b/geo_LHC142_AoA_18/boundary_dual_area_geo_LHC142_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bd6eb4592ff11b597a8fc1f9dc8cdf62a4afc71b2db91ce72a48e35ef06d8303
+size 570751036
diff --git a/geo_LHC145_AoA_16/boundary_dual_area_geo_LHC145_AoA_16.npy b/geo_LHC145_AoA_16/boundary_dual_area_geo_LHC145_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b3dfc779c8f1b4d5b099cfedc15aa6fa92582511
--- /dev/null
+++ b/geo_LHC145_AoA_16/boundary_dual_area_geo_LHC145_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eee5d126b763189de9cba40e342db8f871f98f517ecdf18ca6325f5d99e6a34c
+size 557569548
diff --git a/geo_LHC146_AoA_16/boundary_dual_area_geo_LHC146_AoA_16.npy b/geo_LHC146_AoA_16/boundary_dual_area_geo_LHC146_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..864fbbb545ced8f7303795f93f5f048ebc56eca3
--- /dev/null
+++ b/geo_LHC146_AoA_16/boundary_dual_area_geo_LHC146_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c989df9c332ac660875674a82b9e50a93804abe0d626421461e20c9244f6b317
+size 602720376
diff --git a/geo_LHC148_AoA_8/boundary_dual_area_geo_LHC148_AoA_8.npy b/geo_LHC148_AoA_8/boundary_dual_area_geo_LHC148_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..dc3cf2fc98cc79196fd511ec5a69df2bb401b019
--- /dev/null
+++ b/geo_LHC148_AoA_8/boundary_dual_area_geo_LHC148_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:60870479d19329e2cbb9fa512d031aa3a0e4451e80d980cad6d9c9502298067b
+size 576836748
diff --git a/geo_LHC149_AoA_4/boundary_dual_area_geo_LHC149_AoA_4.npy b/geo_LHC149_AoA_4/boundary_dual_area_geo_LHC149_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e42fd39c5d2dea67572a97f7f026400fa28bb137
--- /dev/null
+++ b/geo_LHC149_AoA_4/boundary_dual_area_geo_LHC149_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c44f40275f7213f264e7e38dfcd3723e7c6b388333276b2cca41ac4dc1cff346
+size 554174104
diff --git a/geo_LHC150_AoA_22/boundary_dual_area_geo_LHC150_AoA_22.npy b/geo_LHC150_AoA_22/boundary_dual_area_geo_LHC150_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7f0c4bd939166af50e6e0c5646b397377e09e7c3
--- /dev/null
+++ b/geo_LHC150_AoA_22/boundary_dual_area_geo_LHC150_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e4ee4d387ea9cfcd7f47b21144cacb3849ad9963b396d66ea7a8589759ed5dcf
+size 586962084
diff --git a/geo_LHC151_AoA_4/boundary_dual_area_geo_LHC151_AoA_4.npy b/geo_LHC151_AoA_4/boundary_dual_area_geo_LHC151_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f4c83a99582b2dcd1704a653d29b5211a65032bf
--- /dev/null
+++ b/geo_LHC151_AoA_4/boundary_dual_area_geo_LHC151_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5f7c2e03023583bcabb544a736595da2f4fb433dcf8278af7d1a9a366aea4c34
+size 539489476
diff --git a/geo_LHC152_AoA_12/boundary_dual_area_geo_LHC152_AoA_12.npy b/geo_LHC152_AoA_12/boundary_dual_area_geo_LHC152_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..04cbc4d8c9502abc53eade9d77729c0e1426fcd3
--- /dev/null
+++ b/geo_LHC152_AoA_12/boundary_dual_area_geo_LHC152_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cfe54aa3ce94aedf0f9ad65722ae7f68094bd035a06c4b14bd626ef5e2a23b8e
+size 567231636
diff --git a/geo_LHC153_AoA_22/boundary_dual_area_geo_LHC153_AoA_22.npy b/geo_LHC153_AoA_22/boundary_dual_area_geo_LHC153_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ce5f1fd18b5bfff8cd9dc464601f1b30774f3cfb
--- /dev/null
+++ b/geo_LHC153_AoA_22/boundary_dual_area_geo_LHC153_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c920227a6a75393cc98bf51d11b1ddc7f5f3385ceee907df87891cadaafaa31a
+size 558997268
diff --git a/geo_LHC154_AoA_10/boundary_dual_area_geo_LHC154_AoA_10.npy b/geo_LHC154_AoA_10/boundary_dual_area_geo_LHC154_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..809df7c08cd9d4081865121267bf834d3f6b3c66
--- /dev/null
+++ b/geo_LHC154_AoA_10/boundary_dual_area_geo_LHC154_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9b993e5f0ef39f2a23e7ddba2c5127bf26a6ef5742c8e62f85cd1c92e783b73d
+size 553555364
diff --git a/geo_LHC154_AoA_18/boundary_dual_area_geo_LHC154_AoA_18.npy b/geo_LHC154_AoA_18/boundary_dual_area_geo_LHC154_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a7bbf6ac6974fc0b7a19773fff256ed1ed3b3759
--- /dev/null
+++ b/geo_LHC154_AoA_18/boundary_dual_area_geo_LHC154_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3da66fcc7cfbcc1c0a14539e16670286e6d484c6196376062dcfd3bdb4240801
+size 581009272
diff --git a/geo_LHC156_AoA_20/boundary_dual_area_geo_LHC156_AoA_20.npy b/geo_LHC156_AoA_20/boundary_dual_area_geo_LHC156_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0f1ae3b110cc51558cd0a0253d56a107ac9f7261
--- /dev/null
+++ b/geo_LHC156_AoA_20/boundary_dual_area_geo_LHC156_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ac594cc64f82176cc9320687c1d797ce49125bfc812c5196caf4fd761e962109
+size 544487896
diff --git a/geo_LHC157_AoA_10/boundary_dual_area_geo_LHC157_AoA_10.npy b/geo_LHC157_AoA_10/boundary_dual_area_geo_LHC157_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d43c2f2053f9ac1a1fc3edee25ce55721a00389b
--- /dev/null
+++ b/geo_LHC157_AoA_10/boundary_dual_area_geo_LHC157_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:852fa0fa572d4f6c15aa7fd540928da1fb6194682d9dec7a71a59e94c2152e9e
+size 568214268
diff --git a/geo_LHC157_AoA_4/boundary_dual_area_geo_LHC157_AoA_4.npy b/geo_LHC157_AoA_4/boundary_dual_area_geo_LHC157_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3cd9ff7fc38c991e01bf14794bdf964abf71de56
--- /dev/null
+++ b/geo_LHC157_AoA_4/boundary_dual_area_geo_LHC157_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:87b6e6d4a99af4f962e5454fb7d802efe0cf22a091cd67dbd155d6e02448b572
+size 545164872
diff --git a/geo_LHC158_AoA_10/boundary_dual_area_geo_LHC158_AoA_10.npy b/geo_LHC158_AoA_10/boundary_dual_area_geo_LHC158_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..adebb5672b295da16e47d84d7a745ef0fc315691
--- /dev/null
+++ b/geo_LHC158_AoA_10/boundary_dual_area_geo_LHC158_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1061129972d0d47627ba63ec3f17389dfdc7b5e44512d82152e4723359b38957
+size 572069608
diff --git a/geo_LHC158_AoA_20/boundary_dual_area_geo_LHC158_AoA_20.npy b/geo_LHC158_AoA_20/boundary_dual_area_geo_LHC158_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..68aa046b312f1431769d330426df5a1d80939b57
--- /dev/null
+++ b/geo_LHC158_AoA_20/boundary_dual_area_geo_LHC158_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ab29b1ae2b5b99f3e78712907bb6c5c0c410f8dc9db19ebe80f716a3a25c7a1c
+size 564472568
diff --git a/geo_LHC158_AoA_6/boundary_dual_area_geo_LHC158_AoA_6.npy b/geo_LHC158_AoA_6/boundary_dual_area_geo_LHC158_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9beca0a06554997ea8fb12a1bb9652910cbde91e
--- /dev/null
+++ b/geo_LHC158_AoA_6/boundary_dual_area_geo_LHC158_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:711dfe1b4c4be770d117d39acef2175a89dfdf22929f7f36f086105df12fc4b2
+size 558062072
diff --git a/geo_LHC159_AoA_10/boundary_dual_area_geo_LHC159_AoA_10.npy b/geo_LHC159_AoA_10/boundary_dual_area_geo_LHC159_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1738e019c459cf0fa316891c5600b106cb184a31
--- /dev/null
+++ b/geo_LHC159_AoA_10/boundary_dual_area_geo_LHC159_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0180467ba636ba737e5b46c3b3bf066ccc38e90f406c1c08dd3e978c793f1e13
+size 581544408
diff --git a/geo_LHC159_AoA_16/boundary_dual_area_geo_LHC159_AoA_16.npy b/geo_LHC159_AoA_16/boundary_dual_area_geo_LHC159_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1231f53f8c6b9c0f32e7463b9b04c305283cd80b
--- /dev/null
+++ b/geo_LHC159_AoA_16/boundary_dual_area_geo_LHC159_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:46c76aca3a8ad4c1c57ae699ba0b386bbe1f70f065c02153c6bdedd6013258d0
+size 597418848
diff --git a/geo_LHC159_AoA_22/boundary_dual_area_geo_LHC159_AoA_22.npy b/geo_LHC159_AoA_22/boundary_dual_area_geo_LHC159_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cc59f8df5fa5795492de536336c3e21bccb230bd
--- /dev/null
+++ b/geo_LHC159_AoA_22/boundary_dual_area_geo_LHC159_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d6b3a86c58938832836a792acba946fe0efeaab35ba4e83527f5858dc7bcac9
+size 592474808
diff --git a/geo_LHC160_AoA_16/boundary_dual_area_geo_LHC160_AoA_16.npy b/geo_LHC160_AoA_16/boundary_dual_area_geo_LHC160_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..31ede256c03f940b7984578d26ca109d79a32ab5
--- /dev/null
+++ b/geo_LHC160_AoA_16/boundary_dual_area_geo_LHC160_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:99e328275ac30bf5593cff638a64546efa3285d8af75d853e0fa142b63535053
+size 586884764
diff --git a/geo_LHC160_AoA_6/boundary_dual_area_geo_LHC160_AoA_6.npy b/geo_LHC160_AoA_6/boundary_dual_area_geo_LHC160_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..43bd92cf105c732d550a8318fa75f0e9522449cc
--- /dev/null
+++ b/geo_LHC160_AoA_6/boundary_dual_area_geo_LHC160_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b017b79e1921a0ca0fdb495ce0a221f747e36807a1ea65704aace69259df68da
+size 543651276
diff --git a/geo_LHC161_AoA_10/boundary_dual_area_geo_LHC161_AoA_10.npy b/geo_LHC161_AoA_10/boundary_dual_area_geo_LHC161_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a3402cd347c7e0574d63b258afca9d47c30c9589
--- /dev/null
+++ b/geo_LHC161_AoA_10/boundary_dual_area_geo_LHC161_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fa6d599e9476d0ef07248a6c5f883db39a24a1d82a8fe011cceaf327b8699323
+size 546672620
diff --git a/geo_LHC161_AoA_8/boundary_dual_area_geo_LHC161_AoA_8.npy b/geo_LHC161_AoA_8/boundary_dual_area_geo_LHC161_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ae17c5e8d03b24b432873f7e57b107be973ee128
--- /dev/null
+++ b/geo_LHC161_AoA_8/boundary_dual_area_geo_LHC161_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7980fbe210d3182707e1620c2a7e5d00f83db72fd4b4faca6688b305f9f2398e
+size 542070376
diff --git a/geo_LHC162_AoA_18/boundary_dual_area_geo_LHC162_AoA_18.npy b/geo_LHC162_AoA_18/boundary_dual_area_geo_LHC162_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9f45f1fcc8cf18bb6b470673b432408851a49fe0
--- /dev/null
+++ b/geo_LHC162_AoA_18/boundary_dual_area_geo_LHC162_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:67378174744751bf9712f58c9d41b6362b53e1111d08b6274c556a13a654e6b4
+size 551876668
diff --git a/geo_LHC162_AoA_20/boundary_dual_area_geo_LHC162_AoA_20.npy b/geo_LHC162_AoA_20/boundary_dual_area_geo_LHC162_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..446a3603664b0285221d62d802b607c96427607b
--- /dev/null
+++ b/geo_LHC162_AoA_20/boundary_dual_area_geo_LHC162_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0a3a2c106797044e1781199cf149d59042d6897dc45f2d560c2e1056e0a892ae
+size 547626100
diff --git a/geo_LHC163_AoA_16/boundary_dual_area_geo_LHC163_AoA_16.npy b/geo_LHC163_AoA_16/boundary_dual_area_geo_LHC163_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..47964e56419951569f31e77893fce819af3db71b
--- /dev/null
+++ b/geo_LHC163_AoA_16/boundary_dual_area_geo_LHC163_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:59fc015f4dfb762464bf3123f657012342e7079a9f271a5faa8998f384f678be
+size 568585456
diff --git a/geo_LHC164_AoA_20/boundary_dual_area_geo_LHC164_AoA_20.npy b/geo_LHC164_AoA_20/boundary_dual_area_geo_LHC164_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..448e11b6508aee21305375d539f5cf2f14522b4d
--- /dev/null
+++ b/geo_LHC164_AoA_20/boundary_dual_area_geo_LHC164_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e4bad6b06871688ff2c8c3e5464a14a4fd73479850927517c6f532f97d4ab493
+size 600525404
diff --git a/geo_LHC164_AoA_22/boundary_dual_area_geo_LHC164_AoA_22.npy b/geo_LHC164_AoA_22/boundary_dual_area_geo_LHC164_AoA_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e0a2721bb440f6e3007f631157f56e226304b5ef
--- /dev/null
+++ b/geo_LHC164_AoA_22/boundary_dual_area_geo_LHC164_AoA_22.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dd2c605d35171ac8c6af1dc95d3ad505087c81022c3faf3dd6df10397e8fafdf
+size 600454320
diff --git a/geo_LHC165_AoA_12/boundary_dual_area_geo_LHC165_AoA_12.npy b/geo_LHC165_AoA_12/boundary_dual_area_geo_LHC165_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a049afccb0b6f9be59f7b5998be45a875c16ea10
--- /dev/null
+++ b/geo_LHC165_AoA_12/boundary_dual_area_geo_LHC165_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:20a44e309ad780004efc8b7e5ab0744c8da9b61e76a84f2c681b38e4d45fef0f
+size 562450880
diff --git a/geo_LHC165_AoA_6/boundary_dual_area_geo_LHC165_AoA_6.npy b/geo_LHC165_AoA_6/boundary_dual_area_geo_LHC165_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..922158456ca80b22b9754a68f24fda3265fee494
--- /dev/null
+++ b/geo_LHC165_AoA_6/boundary_dual_area_geo_LHC165_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0e54d59a02f6d9d6dd9ae739fcf7eda6efad05994fb757aee8813090c0ee01a1
+size 537322024
diff --git a/geo_LHC169_AoA_8/boundary_dual_area_geo_LHC169_AoA_8.npy b/geo_LHC169_AoA_8/boundary_dual_area_geo_LHC169_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..00881c6fcc37ac062553b370f4b639b9863950dd
--- /dev/null
+++ b/geo_LHC169_AoA_8/boundary_dual_area_geo_LHC169_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c9a09b2618605c99db95f2192f543e29be391f9b8311eebcb455a399544bdb8f
+size 550516236
diff --git a/geo_LHC170_AoA_20/boundary_dual_area_geo_LHC170_AoA_20.npy b/geo_LHC170_AoA_20/boundary_dual_area_geo_LHC170_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0e46f4798008f9d814f2642b60fdc1ea32eeb67b
--- /dev/null
+++ b/geo_LHC170_AoA_20/boundary_dual_area_geo_LHC170_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:104ca5748093bedc5579f4e07b9c2416892381547b493e12f922f2673615058b
+size 559195456
diff --git a/geo_LHC171_AoA_10/boundary_dual_area_geo_LHC171_AoA_10.npy b/geo_LHC171_AoA_10/boundary_dual_area_geo_LHC171_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f2427c361f7e576f926195dbde1ec3d8321ca280
--- /dev/null
+++ b/geo_LHC171_AoA_10/boundary_dual_area_geo_LHC171_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ea6697e45d2f004a04f572a36bd3e538fbcc486b2b33f60c9a687de3d47705fb
+size 564495624
diff --git a/geo_LHC171_AoA_16/boundary_dual_area_geo_LHC171_AoA_16.npy b/geo_LHC171_AoA_16/boundary_dual_area_geo_LHC171_AoA_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..dd5bf294b230cbd8105a187246f256e1e80a35ed
--- /dev/null
+++ b/geo_LHC171_AoA_16/boundary_dual_area_geo_LHC171_AoA_16.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:676054a8e3b1de83bbd2f1644202fa966a598c93ef88e6e5494b828dd17a3f88
+size 563933112
diff --git a/geo_LHC173_AoA_12/boundary_dual_area_geo_LHC173_AoA_12.npy b/geo_LHC173_AoA_12/boundary_dual_area_geo_LHC173_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7df19c6cb52e2de0e17d12360b43e8ac6d759c8b
--- /dev/null
+++ b/geo_LHC173_AoA_12/boundary_dual_area_geo_LHC173_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2eaeb4fc2d4a3997e563aceb947922c05d946c4d25c340483dfb9902315fa7a2
+size 548499796
diff --git a/geo_LHC173_AoA_8/boundary_dual_area_geo_LHC173_AoA_8.npy b/geo_LHC173_AoA_8/boundary_dual_area_geo_LHC173_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1fe21ab1c2cb88d6a7cc51b003608abcec804a5e
--- /dev/null
+++ b/geo_LHC173_AoA_8/boundary_dual_area_geo_LHC173_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7f7bef245903a01fa01aaebc8eaaad475edc445abeca82e4d944c48a7fdd571d
+size 537722844
diff --git a/geo_LHC175_AoA_14/boundary_dual_area_geo_LHC175_AoA_14.npy b/geo_LHC175_AoA_14/boundary_dual_area_geo_LHC175_AoA_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2bc8ab3573112ce58d5695d925be897220440f01
--- /dev/null
+++ b/geo_LHC175_AoA_14/boundary_dual_area_geo_LHC175_AoA_14.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a3b72f93508f9e23edfb0941fb98b6220022c7d8b8b3dc477c1afd36fcf903c0
+size 601325236
diff --git a/geo_LHC176_AoA_10/boundary_dual_area_geo_LHC176_AoA_10.npy b/geo_LHC176_AoA_10/boundary_dual_area_geo_LHC176_AoA_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fd120dc9c267f9abd12af4deb5ecd4b0ac47cc65
--- /dev/null
+++ b/geo_LHC176_AoA_10/boundary_dual_area_geo_LHC176_AoA_10.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9f353280b7d2e6e86c60d07907beaf11e6fcffee46077b19b2024886534dc10b
+size 547836448
diff --git a/geo_LHC176_AoA_12/boundary_dual_area_geo_LHC176_AoA_12.npy b/geo_LHC176_AoA_12/boundary_dual_area_geo_LHC176_AoA_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..113f81a4a057931814f2c4554da62bbb00370734
--- /dev/null
+++ b/geo_LHC176_AoA_12/boundary_dual_area_geo_LHC176_AoA_12.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ad0a026565a598a1557565013ed0eb11f05d6c9c221e502f53ef51db809a45c3
+size 553357716
diff --git a/geo_LHC176_AoA_8/boundary_dual_area_geo_LHC176_AoA_8.npy b/geo_LHC176_AoA_8/boundary_dual_area_geo_LHC176_AoA_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5d665cbbda817fba79e7f68dcf1a8fb3c761524c
--- /dev/null
+++ b/geo_LHC176_AoA_8/boundary_dual_area_geo_LHC176_AoA_8.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:19d97e8a35c22003d6f1fd0991800f434484823a23e44720822f6596e6c3b16c
+size 540214780
diff --git a/geo_LHC178_AoA_4/boundary_dual_area_geo_LHC178_AoA_4.npy b/geo_LHC178_AoA_4/boundary_dual_area_geo_LHC178_AoA_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cfb57ac6ff49c15f29d85c5c458c64e8fc1398f7
--- /dev/null
+++ b/geo_LHC178_AoA_4/boundary_dual_area_geo_LHC178_AoA_4.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fe145c740d860bed23b1aef739acbecd36a31af0593527906497734b27c2fdef
+size 527154500
diff --git a/geo_LHC179_AoA_18/boundary_dual_area_geo_LHC179_AoA_18.npy b/geo_LHC179_AoA_18/boundary_dual_area_geo_LHC179_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c96c06b841c39061b47f083b936bbb1ea617da0b
--- /dev/null
+++ b/geo_LHC179_AoA_18/boundary_dual_area_geo_LHC179_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:15871602f21d6eae4db85f35d940230a89ed63c7296f4eb7285f676b7b79c936
+size 584906268
diff --git a/geo_LHC180_AoA_18/boundary_dual_area_geo_LHC180_AoA_18.npy b/geo_LHC180_AoA_18/boundary_dual_area_geo_LHC180_AoA_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..383cf1cc9b9243f5645c9c73831ddcdeb442dfc3
--- /dev/null
+++ b/geo_LHC180_AoA_18/boundary_dual_area_geo_LHC180_AoA_18.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:827070a4d1b4e0c563b522f839766ff99ca38d1f24105ca45744983db5a6d019
+size 594057912
diff --git a/geo_LHC180_AoA_20/boundary_dual_area_geo_LHC180_AoA_20.npy b/geo_LHC180_AoA_20/boundary_dual_area_geo_LHC180_AoA_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..51453074c94c7cd2e41672e8824823e33a535f6a
--- /dev/null
+++ b/geo_LHC180_AoA_20/boundary_dual_area_geo_LHC180_AoA_20.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3b12a7dfeb5ee0cafbad7d0952a90d8195e840b866e8da51f915bd387f698b9b
+size 593104288
diff --git a/geo_LHC180_AoA_6/boundary_dual_area_geo_LHC180_AoA_6.npy b/geo_LHC180_AoA_6/boundary_dual_area_geo_LHC180_AoA_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d9ff90533276181d65f5161c41118731f73eb9ab
--- /dev/null
+++ b/geo_LHC180_AoA_6/boundary_dual_area_geo_LHC180_AoA_6.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:30bf00f963b93dafd5c8e655f9def3c254143efe0829abbbe8d89a095b19d436
+size 562629028
diff --git a/surface_dual_areas/cases/geo_LHC001_AoA_22.json b/surface_dual_areas/cases/geo_LHC001_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..61045b67912584d47a354ff9be7ff6c4e41478f0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC001_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC001_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC001_AoA_22/boundary_dual_area_geo_LHC001_AoA_22.npy",
+    "sha256": "efecd99dfbb7017ea087cce5d4888c40550c803aaa306e77d8e78bf3c1234b08",
+    "shape": [
+      147498393
+    ],
+    "size_bytes": 589993700
+  },
+  "runtime": {
+    "accumulation_seconds": 11.365781838074327,
+    "completed_at_utc": "2026-08-07T07:18:05.497298Z",
+    "elapsed_seconds": 36.08971566497348,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.50444105011411,
+    "geometry_read_seconds": 16.23990809894167,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:17:29.407491Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC001_AoA_22/boundary_geo_LHC001_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC001_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624623000000000,
+    "extracted_vtu_size_bytes": 22665808335,
+    "geometry_sha256": "33041d566d38c53505a83b0b5876a5671cef9f8dabda5460c412b050b8526b22",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4325403,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1446545,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2833866,
+      "13": 881684,
+      "14": 1341039,
+      "15": 466889,
+      "16": 888625,
+      "17": 346777,
+      "18": 728491,
+      "19": 292963,
+      "20": 657441,
+      "21": 218562,
+      "22": 365484,
+      "23": 122183,
+      "24": 219683,
+      "25": 72678,
+      "26": 95563,
+      "27": 52980,
+      "28": 124264,
+      "29": 53085,
+      "3": 58988,
+      "30": 115110,
+      "31": 49469,
+      "32": 109087,
+      "33": 38697,
+      "34": 65812,
+      "35": 27572,
+      "36": 62662,
+      "37": 22961,
+      "38": 39330,
+      "39": 16463,
+      "4": 132652,
+      "40": 29859,
+      "41": 10903,
+      "42": 14307,
+      "43": 5865,
+      "44": 7665,
+      "45": 3691,
+      "46": 4267,
+      "47": 2499,
+      "48": 3543,
+      "49": 2121,
+      "5": 948158,
+      "50": 2988,
+      "51": 1851,
+      "52": 2793,
+      "53": 1783,
+      "54": 2461,
+      "55": 1743,
+      "56": 2519,
+      "57": 1750,
+      "58": 2292,
+      "59": 1722,
+      "6": 5302690,
+      "60": 2503,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 2151108,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 440,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6567665,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2072922,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58988,
+      "7": 33253638,
+      "9": 132652
+    },
+    "connectivity_max": 147498392,
+    "connectivity_min": 0,
+    "n_cells": 33445278,
+    "n_connectivity_values": 361876219,
+    "n_fan_triangles": 294985663,
+    "n_points": 147498393
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.27323298468399e-11,
+    "float64_area_closure_relative": 1.8051048099727316e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294985663,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947666.8056057673,
+    "surface_area_float64_in2": 1947666.8056889956,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947666.8056889605,
+    "zero_area_triangles": 236238,
+    "zero_weight_points": 5771
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC001_AoA_4.json b/surface_dual_areas/cases/geo_LHC001_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..3db2dfac77a5aa0d2d9d40c4cd63df30af573703
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC001_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC001_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC001_AoA_4/boundary_dual_area_geo_LHC001_AoA_4.npy",
+    "sha256": "54542164a2615f8f99c8e6d0bb5aa5baff36d24b4291a61ebe158528dcdd9c6e",
+    "shape": [
+      136566001
+    ],
+    "size_bytes": 546264132
+  },
+  "runtime": {
+    "accumulation_seconds": 10.773389539215714,
+    "completed_at_utc": "2026-08-07T07:16:16.736699Z",
+    "elapsed_seconds": 22.124931565020233,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.056171285919845,
+    "geometry_read_seconds": 3.7783622960560024,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:15:54.611677Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC001_AoA_4/boundary_geo_LHC001_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC001_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624478000000000,
+    "extracted_vtu_size_bytes": 20965007469,
+    "geometry_sha256": "6ec36080772f71f6d25fc10bdf26fd14e0ab5fdfeca6bae7ec1779d1069f5c7d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2935401,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1004965,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2179744,
+      "13": 818947,
+      "14": 1792863,
+      "15": 586399,
+      "16": 1042041,
+      "17": 385552,
+      "18": 740851,
+      "19": 297025,
+      "20": 659566,
+      "21": 220524,
+      "22": 361152,
+      "23": 122653,
+      "24": 213765,
+      "25": 72474,
+      "26": 94317,
+      "27": 52915,
+      "28": 124298,
+      "29": 53101,
+      "3": 53641,
+      "30": 115106,
+      "31": 49465,
+      "32": 109090,
+      "33": 38703,
+      "34": 65807,
+      "35": 27571,
+      "36": 62661,
+      "37": 22959,
+      "38": 39333,
+      "39": 16462,
+      "4": 122026,
+      "40": 29860,
+      "41": 10905,
+      "42": 14305,
+      "43": 5865,
+      "44": 7667,
+      "45": 3690,
+      "46": 4266,
+      "47": 2499,
+      "48": 3543,
+      "49": 2121,
+      "5": 937256,
+      "50": 2988,
+      "51": 1851,
+      "52": 2793,
+      "53": 1783,
+      "54": 2461,
+      "55": 1743,
+      "56": 2519,
+      "57": 1750,
+      "58": 2292,
+      "59": 1722,
+      "6": 5275712,
+      "60": 2503,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1976905,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5714024,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1618002,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53641,
+      "7": 29957337,
+      "9": 122026
+    },
+    "connectivity_max": 136566000,
+    "connectivity_min": 0,
+    "n_cells": 30133004,
+    "n_connectivity_values": 333386887,
+    "n_fan_triangles": 273120879,
+    "n_points": 136566001
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.256863739652439e-11,
+    "float64_area_closure_relative": 4.781730374173605e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273120879,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947668.5251974035,
+    "surface_area_float64_in2": 1947668.525280313,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947668.525280314,
+    "zero_area_triangles": 221980,
+    "zero_weight_points": 4758
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC002_AoA_20.json b/surface_dual_areas/cases/geo_LHC002_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..e09fcbf74ac6d4eace18acde59dcfad2a3506372
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC002_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC002_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC002_AoA_20/boundary_dual_area_geo_LHC002_AoA_20.npy",
+    "sha256": "e32954641c1b71fe705218dd149e3d03a754ccf3456d030e5420989a622296ad",
+    "shape": [
+      140489414
+    ],
+    "size_bytes": 561957784
+  },
+  "runtime": {
+    "accumulation_seconds": 10.82094221492298,
+    "completed_at_utc": "2026-08-07T07:18:45.201804Z",
+    "elapsed_seconds": 20.517629760084674,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.180706229992211,
+    "geometry_read_seconds": 1.8126034999731928,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:18:24.684088Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC002_AoA_20/boundary_geo_LHC002_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC002_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624407000000000,
+    "extracted_vtu_size_bytes": 21579358634,
+    "geometry_sha256": "d15b66e3159facd6742472c7daeca7e9208f40c5dea9d8ba687fd49bfa123cca",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3907149,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1184837,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2649278,
+      "13": 765340,
+      "14": 1334267,
+      "15": 460080,
+      "16": 918079,
+      "17": 358320,
+      "18": 757390,
+      "19": 306342,
+      "20": 673950,
+      "21": 227062,
+      "22": 358592,
+      "23": 122988,
+      "24": 204411,
+      "25": 69447,
+      "26": 93387,
+      "27": 51793,
+      "28": 124336,
+      "29": 53078,
+      "3": 51519,
+      "30": 115902,
+      "31": 49827,
+      "32": 109633,
+      "33": 39207,
+      "34": 66976,
+      "35": 28207,
+      "36": 62571,
+      "37": 22874,
+      "38": 38262,
+      "39": 16170,
+      "4": 116387,
+      "40": 28934,
+      "41": 10587,
+      "42": 14186,
+      "43": 5744,
+      "44": 7700,
+      "45": 3595,
+      "46": 4140,
+      "47": 2475,
+      "48": 3441,
+      "49": 2075,
+      "5": 937795,
+      "50": 2795,
+      "51": 1715,
+      "52": 2507,
+      "53": 1641,
+      "54": 2275,
+      "55": 1617,
+      "56": 2421,
+      "57": 1704,
+      "58": 2263,
+      "59": 1737,
+      "6": 5180810,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2032449,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6059839,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1805282,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51519,
+      "7": 31312539,
+      "9": 116387
+    },
+    "connectivity_max": 140489413,
+    "connectivity_min": 0,
+    "n_cells": 31480445,
+    "n_connectivity_values": 343928597,
+    "n_fan_triangles": 280967707,
+    "n_points": 140489414
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.176736663700867e-11,
+    "float64_area_closure_relative": 2.907537168655816e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280967707,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937894.943179536,
+    "surface_area_float64_in2": 1937894.9432410977,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937894.943241154,
+    "zero_area_triangles": 238876,
+    "zero_weight_points": 5497
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC002_AoA_4.json b/surface_dual_areas/cases/geo_LHC002_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..f0ec54932c9297da58d6cc2f9284662f8206db50
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC002_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC002_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC002_AoA_4/boundary_dual_area_geo_LHC002_AoA_4.npy",
+    "sha256": "ff5323b978c1d551ea496c10620dbc2c650a60ee017b0eda0398580fd4c1dc6c",
+    "shape": [
+      129920263
+    ],
+    "size_bytes": 519681180
+  },
+  "runtime": {
+    "accumulation_seconds": 11.554951037978753,
+    "completed_at_utc": "2026-08-07T07:18:14.237917Z",
+    "elapsed_seconds": 43.87440935592167,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.933179567102343,
+    "geometry_read_seconds": 25.082473610993475,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:17:30.363388Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC002_AoA_4/boundary_geo_LHC002_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC002_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624395000000000,
+    "extracted_vtu_size_bytes": 19937149310,
+    "geometry_sha256": "bbcd02819adbebed661ee296aa106cc0d6a1a72df0a94ba452f6effaffca3525",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2388100,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 833588,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1877028,
+      "13": 726096,
+      "14": 1753388,
+      "15": 557307,
+      "16": 1080417,
+      "17": 389795,
+      "18": 771633,
+      "19": 309945,
+      "20": 680889,
+      "21": 228866,
+      "22": 363252,
+      "23": 123725,
+      "24": 205681,
+      "25": 69131,
+      "26": 93830,
+      "27": 51719,
+      "28": 124514,
+      "29": 53089,
+      "3": 48072,
+      "30": 115933,
+      "31": 49791,
+      "32": 109657,
+      "33": 39209,
+      "34": 66975,
+      "35": 28213,
+      "36": 62591,
+      "37": 22876,
+      "38": 38275,
+      "39": 16179,
+      "4": 111157,
+      "40": 28941,
+      "41": 10588,
+      "42": 14200,
+      "43": 5748,
+      "44": 7719,
+      "45": 3595,
+      "46": 4136,
+      "47": 2476,
+      "48": 3448,
+      "49": 2074,
+      "5": 930987,
+      "50": 2798,
+      "51": 1716,
+      "52": 2508,
+      "53": 1642,
+      "54": 2275,
+      "55": 1617,
+      "56": 2421,
+      "57": 1705,
+      "58": 2263,
+      "59": 1736,
+      "6": 5198896,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1907087,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5368143,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1438749,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 48072,
+      "7": 28202217,
+      "9": 111157
+    },
+    "connectivity_max": 129920262,
+    "connectivity_min": 0,
+    "n_cells": 28361446,
+    "n_connectivity_values": 316552297,
+    "n_fan_triangles": 259829405,
+    "n_points": 129920263
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.32216998951074e-11,
+    "float64_area_closure_relative": 6.115433109934022e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 259829405,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937897.046463829,
+    "surface_area_float64_in2": 1937897.0465282092,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937897.0465283277,
+    "zero_area_triangles": 218580,
+    "zero_weight_points": 4334
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC003_AoA_10.json b/surface_dual_areas/cases/geo_LHC003_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..d87f40fc842d945aba2922ba8dc22168e4c1de4b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC003_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC003_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC003_AoA_10/boundary_dual_area_geo_LHC003_AoA_10.npy",
+    "sha256": "ce6dc4f13b815fc5f3b36824ec8239b6e59e99faf5b90c046604858bb05982df",
+    "shape": [
+      145190253
+    ],
+    "size_bytes": 580761140
+  },
+  "runtime": {
+    "accumulation_seconds": 11.190588128054515,
+    "completed_at_utc": "2026-08-07T07:18:43.707429Z",
+    "elapsed_seconds": 22.571794396964833,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.446542487014085,
+    "geometry_read_seconds": 2.071315029868856,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:18:21.135548Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC003_AoA_10/boundary_geo_LHC003_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC003_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624397000000000,
+    "extracted_vtu_size_bytes": 22307984005,
+    "geometry_sha256": "04803d7c8f4f0ce6108dfd3c42e34bc205e73a0827206a20d528e42fb9e7dff6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3966166,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1279952,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2809633,
+      "13": 825733,
+      "14": 1405547,
+      "15": 472472,
+      "16": 949647,
+      "17": 367738,
+      "18": 758215,
+      "19": 309610,
+      "20": 673322,
+      "21": 224715,
+      "22": 349757,
+      "23": 119866,
+      "24": 200187,
+      "25": 69722,
+      "26": 92657,
+      "27": 51857,
+      "28": 123710,
+      "29": 53024,
+      "3": 57665,
+      "30": 115288,
+      "31": 49546,
+      "32": 108934,
+      "33": 38854,
+      "34": 66328,
+      "35": 27692,
+      "36": 61787,
+      "37": 22850,
+      "38": 38599,
+      "39": 16385,
+      "4": 131163,
+      "40": 30077,
+      "41": 11042,
+      "42": 14789,
+      "43": 6021,
+      "44": 7770,
+      "45": 3658,
+      "46": 4133,
+      "47": 2500,
+      "48": 3535,
+      "49": 2109,
+      "5": 945940,
+      "50": 2916,
+      "51": 1834,
+      "52": 2762,
+      "53": 1770,
+      "54": 2487,
+      "55": 1724,
+      "56": 2538,
+      "57": 1758,
+      "58": 2293,
+      "59": 1755,
+      "6": 5396887,
+      "60": 2509,
+      "61": 1628,
+      "62": 2260,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2075855,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6517192,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1891461,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 57665,
+      "7": 32607664,
+      "9": 131163
+    },
+    "connectivity_max": 145190252,
+    "connectivity_min": 0,
+    "n_cells": 32796492,
+    "n_connectivity_values": 355962372,
+    "n_fan_triangles": 290369388,
+    "n_points": 145190253
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.533908169938168e-11,
+    "float64_area_closure_relative": 4.176277013359861e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290369388,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945701.7427815702,
+    "surface_area_float64_in2": 1945701.7428503295,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945701.7428504108,
+    "zero_area_triangles": 239053,
+    "zero_weight_points": 5894
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC003_AoA_18.json b/surface_dual_areas/cases/geo_LHC003_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..71d19a8a6cacd58679bcf9959203e91f546dd875
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC003_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC003_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC003_AoA_18/boundary_dual_area_geo_LHC003_AoA_18.npy",
+    "sha256": "13296288c3cc71afa530e2df818e7b8e8e7685c369434074a179d9efbf65676f",
+    "shape": [
+      149402499
+    ],
+    "size_bytes": 597610124
+  },
+  "runtime": {
+    "accumulation_seconds": 11.301937883952633,
+    "completed_at_utc": "2026-08-07T07:17:03.065128Z",
+    "elapsed_seconds": 22.781769267981872,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.221249674912542,
+    "geometry_read_seconds": 2.9685034819412977,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:16:40.283270Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC003_AoA_18/boundary_geo_LHC003_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC003_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624538000000000,
+    "extracted_vtu_size_bytes": 22962705538,
+    "geometry_sha256": "fbe8accb7746c401dfb31d1f92dbdb8eafe250fa4446c951ead3e35c73a8a9db",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4628330,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1443877,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3044667,
+      "13": 838066,
+      "14": 1219998,
+      "15": 427418,
+      "16": 874497,
+      "17": 353803,
+      "18": 754938,
+      "19": 309609,
+      "20": 676163,
+      "21": 225658,
+      "22": 351171,
+      "23": 120046,
+      "24": 201222,
+      "25": 69835,
+      "26": 92864,
+      "27": 51956,
+      "28": 123713,
+      "29": 53045,
+      "3": 59729,
+      "30": 115292,
+      "31": 49556,
+      "32": 108963,
+      "33": 38842,
+      "34": 66336,
+      "35": 27701,
+      "36": 61794,
+      "37": 22849,
+      "38": 38596,
+      "39": 16388,
+      "4": 135609,
+      "40": 30077,
+      "41": 11045,
+      "42": 14789,
+      "43": 6022,
+      "44": 7770,
+      "45": 3659,
+      "46": 4133,
+      "47": 2500,
+      "48": 3535,
+      "49": 2108,
+      "5": 946808,
+      "50": 2917,
+      "51": 1834,
+      "52": 2762,
+      "53": 1770,
+      "54": 2487,
+      "55": 1724,
+      "56": 2538,
+      "57": 1758,
+      "58": 2293,
+      "59": 1755,
+      "6": 5349722,
+      "60": 2509,
+      "61": 1628,
+      "62": 2260,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2138033,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6805682,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2075540,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59729,
+      "7": 33853519,
+      "9": 135609
+    },
+    "connectivity_max": 149402498,
+    "connectivity_min": 0,
+    "n_cells": 34048857,
+    "n_connectivity_values": 366891594,
+    "n_fan_triangles": 298793880,
+    "n_points": 149402499
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.535835806958126e-11,
+    "float64_area_closure_relative": 2.094122330505185e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 298793880,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945701.167713402,
+    "surface_area_float64_in2": 1945701.1677821989,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945701.1677822396,
+    "zero_area_triangles": 244837,
+    "zero_weight_points": 6248
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC004_AoA_22.json b/surface_dual_areas/cases/geo_LHC004_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..3d05578735c0ac6b0937f1c02b7c1a5442f149ef
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC004_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC004_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC004_AoA_22/boundary_dual_area_geo_LHC004_AoA_22.npy",
+    "sha256": "ef9c62f8ff2b8d001b34cf92dd3f37e5e2cde40e6d00e312fca71828add49b9b",
+    "shape": [
+      136881847
+    ],
+    "size_bytes": 547527516
+  },
+  "runtime": {
+    "accumulation_seconds": 10.304970412980765,
+    "completed_at_utc": "2026-08-07T07:17:24.650647Z",
+    "elapsed_seconds": 20.239859384018928,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0651083819102496,
+    "geometry_read_seconds": 2.303996368078515,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:17:04.410702Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC004_AoA_22/boundary_geo_LHC004_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC004_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624524000000000,
+    "extracted_vtu_size_bytes": 21021593553,
+    "geometry_sha256": "def7aca2a0da0c2b62e429cd4a64fee96ab2ea4799f7b3d5f88a717c590b971c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3624981,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1116907,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2398360,
+      "13": 735207,
+      "14": 1320262,
+      "15": 456086,
+      "16": 940596,
+      "17": 356434,
+      "18": 757675,
+      "19": 304821,
+      "20": 676812,
+      "21": 228815,
+      "22": 371734,
+      "23": 127799,
+      "24": 205654,
+      "25": 70245,
+      "26": 93658,
+      "27": 51886,
+      "28": 124516,
+      "29": 53135,
+      "3": 47950,
+      "30": 114828,
+      "31": 49602,
+      "32": 110149,
+      "33": 39130,
+      "34": 67656,
+      "35": 28161,
+      "36": 62747,
+      "37": 22847,
+      "38": 38297,
+      "39": 15784,
+      "4": 112255,
+      "40": 28734,
+      "41": 10501,
+      "42": 13926,
+      "43": 5747,
+      "44": 7711,
+      "45": 3678,
+      "46": 4181,
+      "47": 2496,
+      "48": 3582,
+      "49": 2144,
+      "5": 945974,
+      "50": 2845,
+      "51": 1778,
+      "52": 2582,
+      "53": 1650,
+      "54": 2256,
+      "55": 1632,
+      "56": 2456,
+      "57": 1718,
+      "58": 2245,
+      "59": 1678,
+      "6": 5142295,
+      "60": 2466,
+      "61": 1650,
+      "62": 2224,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2023943,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5818889,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1743838,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 47950,
+      "7": 30366419,
+      "9": 112255
+    },
+    "connectivity_max": 136881846,
+    "connectivity_min": 0,
+    "n_cells": 30526624,
+    "n_connectivity_values": 334805866,
+    "n_fan_triangles": 273752618,
+    "n_points": 136881847
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.734964144482731e-11,
+    "float64_area_closure_relative": 3.539645540394887e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273752618,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1933871.86514852,
+    "surface_area_float64_in2": 1933871.8652207495,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1933871.865220818,
+    "zero_area_triangles": 235174,
+    "zero_weight_points": 5392
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC005_AoA_16.json b/surface_dual_areas/cases/geo_LHC005_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..c1577a122bd1fa11b521ba04d91a17a39877943c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC005_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC005_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC005_AoA_16/boundary_dual_area_geo_LHC005_AoA_16.npy",
+    "sha256": "ebfbfac4fdd87fc678315a3702c3b9ef2d234c5d069689d4d6599bc5c020b3d6",
+    "shape": [
+      140340563
+    ],
+    "size_bytes": 561362380
+  },
+  "runtime": {
+    "accumulation_seconds": 11.773751658853143,
+    "completed_at_utc": "2026-08-07T07:19:22.530739Z",
+    "elapsed_seconds": 24.571321554947644,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2855348279699683,
+    "geometry_read_seconds": 2.500588068040088,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:18:57.959327Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC005_AoA_16/boundary_geo_LHC005_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC005_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624395000000000,
+    "extracted_vtu_size_bytes": 21557832766,
+    "geometry_sha256": "366a72d9643ad0b7a4f8a1f01c296cb477b556f166357fcce6b3669075a074ca",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3936753,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1230290,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2644159,
+      "13": 778690,
+      "14": 1333539,
+      "15": 452113,
+      "16": 897747,
+      "17": 352027,
+      "18": 745381,
+      "19": 301710,
+      "20": 662539,
+      "21": 223282,
+      "22": 350081,
+      "23": 121411,
+      "24": 206224,
+      "25": 68860,
+      "26": 95505,
+      "27": 52069,
+      "28": 124641,
+      "29": 53118,
+      "3": 50995,
+      "30": 114125,
+      "31": 48980,
+      "32": 107208,
+      "33": 38325,
+      "34": 65949,
+      "35": 27563,
+      "36": 62635,
+      "37": 22855,
+      "38": 39911,
+      "39": 16453,
+      "4": 114804,
+      "40": 30078,
+      "41": 11030,
+      "42": 14496,
+      "43": 5888,
+      "44": 7685,
+      "45": 3672,
+      "46": 4256,
+      "47": 2479,
+      "48": 3519,
+      "49": 2126,
+      "5": 921977,
+      "50": 2975,
+      "51": 1827,
+      "52": 2821,
+      "53": 1768,
+      "54": 2464,
+      "55": 1735,
+      "56": 2555,
+      "57": 1768,
+      "58": 2292,
+      "59": 1733,
+      "6": 5212691,
+      "60": 2502,
+      "61": 1657,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2004696,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6071856,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1819178,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50995,
+      "7": 31334814,
+      "9": 114804
+    },
+    "connectivity_max": 140340562,
+    "connectivity_min": 0,
+    "n_cells": 31500613,
+    "n_connectivity_values": 343671216,
+    "n_fan_triangles": 280669990,
+    "n_points": 140340563
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.509014149102277e-11,
+    "float64_area_closure_relative": 3.1594449868500025e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280669990,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938139.7534593677,
+    "surface_area_float64_in2": 1938139.7535273773,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938139.753527316,
+    "zero_area_triangles": 236917,
+    "zero_weight_points": 5440
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC006_AoA_12.json b/surface_dual_areas/cases/geo_LHC006_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..dbd408cb89d4cfe235debef2362c12182922695a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC006_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC006_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC006_AoA_12/boundary_dual_area_geo_LHC006_AoA_12.npy",
+    "sha256": "dd1f25980e470a47242a4ae871afe4e06c296e35a647b9fea5fb50a3298a805e",
+    "shape": [
+      146607595
+    ],
+    "size_bytes": 586430508
+  },
+  "runtime": {
+    "accumulation_seconds": 11.51776338997297,
+    "completed_at_utc": "2026-08-07T07:20:50.958149Z",
+    "elapsed_seconds": 53.62606412312016,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5057084900327027,
+    "geometry_read_seconds": 33.256261432077736,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:19:57.332003Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC006_AoA_12/boundary_geo_LHC006_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC006_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624504000000000,
+    "extracted_vtu_size_bytes": 22525991238,
+    "geometry_sha256": "ef3aace53bf43e9b5737a3ccd43df219f761b758bb6521e003eddeeac51dd619",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4237283,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1357368,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2883456,
+      "13": 853784,
+      "14": 1375066,
+      "15": 471420,
+      "16": 923244,
+      "17": 359741,
+      "18": 740479,
+      "19": 302422,
+      "20": 665792,
+      "21": 222325,
+      "22": 353118,
+      "23": 121520,
+      "24": 204284,
+      "25": 70239,
+      "26": 92698,
+      "27": 51722,
+      "28": 123941,
+      "29": 52655,
+      "3": 58548,
+      "30": 115238,
+      "31": 49157,
+      "32": 108157,
+      "33": 38461,
+      "34": 65975,
+      "35": 27744,
+      "36": 63112,
+      "37": 22894,
+      "38": 39305,
+      "39": 16420,
+      "4": 131886,
+      "40": 30389,
+      "41": 10981,
+      "42": 14661,
+      "43": 5985,
+      "44": 7674,
+      "45": 3722,
+      "46": 4286,
+      "47": 2498,
+      "48": 3552,
+      "49": 2142,
+      "5": 940302,
+      "50": 2947,
+      "51": 1819,
+      "52": 2754,
+      "53": 1821,
+      "54": 2441,
+      "55": 1750,
+      "56": 2550,
+      "57": 1754,
+      "58": 2284,
+      "59": 1729,
+      "6": 5264517,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2085327,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6548135,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1957537,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58548,
+      "7": 32935683,
+      "9": 131886
+    },
+    "connectivity_max": 146607594,
+    "connectivity_min": 0,
+    "n_cells": 33126117,
+    "n_connectivity_values": 359456305,
+    "n_fan_triangles": 293204071,
+    "n_points": 146607595
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.733910114618659e-11,
+    "float64_area_closure_relative": 4.055074399427602e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293204071,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946439.9520476377,
+    "surface_area_float64_in2": 1946439.952120316,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946439.952120395,
+    "zero_area_triangles": 238782,
+    "zero_weight_points": 5870
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC006_AoA_14.json b/surface_dual_areas/cases/geo_LHC006_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..56c1310aaaed59136cc86149696d7988566fa73f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC006_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC006_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC006_AoA_14/boundary_dual_area_geo_LHC006_AoA_14.npy",
+    "sha256": "a8607b85b011f72ecb22d847eaf05481ac48a3b578d2ad37b4b686809bb721e3",
+    "shape": [
+      147336340
+    ],
+    "size_bytes": 589345488
+  },
+  "runtime": {
+    "accumulation_seconds": 11.287185659864917,
+    "completed_at_utc": "2026-08-07T07:20:27.886759Z",
+    "elapsed_seconds": 53.68154618400149,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3502999350894243,
+    "geometry_read_seconds": 34.056852924171835,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:19:34.205131Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC006_AoA_14/boundary_geo_LHC006_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC006_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624424000000000,
+    "extracted_vtu_size_bytes": 22638900448,
+    "geometry_sha256": "204af8fe004a08c19e18cdba8f94dc14e544e90e73f36d3c04093b00a25b3bcf",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4345214,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1400743,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2922728,
+      "13": 860615,
+      "14": 1352961,
+      "15": 460335,
+      "16": 906554,
+      "17": 354843,
+      "18": 740477,
+      "19": 302577,
+      "20": 666499,
+      "21": 222406,
+      "22": 353076,
+      "23": 121505,
+      "24": 203924,
+      "25": 70260,
+      "26": 92653,
+      "27": 51723,
+      "28": 123939,
+      "29": 52653,
+      "3": 58334,
+      "30": 115225,
+      "31": 49158,
+      "32": 108156,
+      "33": 38461,
+      "34": 65972,
+      "35": 27748,
+      "36": 63110,
+      "37": 22893,
+      "38": 39306,
+      "39": 16418,
+      "4": 132361,
+      "40": 30389,
+      "41": 10982,
+      "42": 14663,
+      "43": 5983,
+      "44": 7674,
+      "45": 3724,
+      "46": 4286,
+      "47": 2499,
+      "48": 3552,
+      "49": 2140,
+      "5": 935788,
+      "50": 2948,
+      "51": 1819,
+      "52": 2755,
+      "53": 1821,
+      "54": 2439,
+      "55": 1750,
+      "56": 2550,
+      "57": 1754,
+      "58": 2284,
+      "59": 1729,
+      "6": 5242020,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2095060,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6581125,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2000648,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58334,
+      "7": 33137620,
+      "9": 132361
+    },
+    "connectivity_max": 147336339,
+    "connectivity_min": 0,
+    "n_cells": 33328315,
+    "n_connectivity_values": 361318191,
+    "n_fan_triangles": 294661561,
+    "n_points": 147336340
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.7774630458280005e-11,
+    "float64_area_closure_relative": 1.6985856275889704e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294661561,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946440.077002761,
+    "surface_area_float64_in2": 1946440.077076287,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946440.07707632,
+    "zero_area_triangles": 239481,
+    "zero_weight_points": 5924
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC006_AoA_18.json b/surface_dual_areas/cases/geo_LHC006_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..56138d8c6953b1965926e71ea39ffe2640f7320d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC006_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC006_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC006_AoA_18/boundary_dual_area_geo_LHC006_AoA_18.npy",
+    "sha256": "77c0fad006253d8686a023993d256e3745cf7d92c7d0ce8d48ab8bf82bd3fb1b",
+    "shape": [
+      146867833
+    ],
+    "size_bytes": 587471460
+  },
+  "runtime": {
+    "accumulation_seconds": 11.424585201079026,
+    "completed_at_utc": "2026-08-07T07:20:50.159124Z",
+    "elapsed_seconds": 70.86707888101228,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.283044846029952,
+    "geometry_read_seconds": 2.9807179421186447,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:19:39.291956Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC006_AoA_18/boundary_geo_LHC006_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC006_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624380000000000,
+    "extracted_vtu_size_bytes": 22566920012,
+    "geometry_sha256": "499af81bdb8b2e1b0cf026a4762fdb70f6fda199e1d49785a885542a7dd75dd8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4411307,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1404732,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2873953,
+      "13": 845816,
+      "14": 1276824,
+      "15": 446470,
+      "16": 872545,
+      "17": 350410,
+      "18": 743845,
+      "19": 305579,
+      "20": 674389,
+      "21": 226662,
+      "22": 362909,
+      "23": 124702,
+      "24": 211926,
+      "25": 71909,
+      "26": 94171,
+      "27": 52055,
+      "28": 124035,
+      "29": 52681,
+      "3": 58551,
+      "30": 115232,
+      "31": 49155,
+      "32": 108157,
+      "33": 38464,
+      "34": 65976,
+      "35": 27748,
+      "36": 63110,
+      "37": 22892,
+      "38": 39306,
+      "39": 16419,
+      "4": 133226,
+      "40": 30389,
+      "41": 10982,
+      "42": 14663,
+      "43": 5983,
+      "44": 7674,
+      "45": 3723,
+      "46": 4285,
+      "47": 2498,
+      "48": 3552,
+      "49": 2141,
+      "5": 932463,
+      "50": 2948,
+      "51": 1819,
+      "52": 2754,
+      "53": 1821,
+      "54": 2441,
+      "55": 1750,
+      "56": 2550,
+      "57": 1754,
+      "58": 2284,
+      "59": 1728,
+      "6": 5206378,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1376,
+      "66": 1817,
+      "67": 1100,
+      "68": 1464,
+      "69": 904,
+      "7": 2093209,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6579613,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 2014994,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58551,
+      "7": 33030882,
+      "9": 133226
+    },
+    "connectivity_max": 146867832,
+    "connectivity_min": 0,
+    "n_cells": 33222659,
+    "n_connectivity_values": 360169865,
+    "n_fan_triangles": 293724547,
+    "n_points": 146867833
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.822797203507414e-11,
+    "float64_area_closure_relative": 3.181856475436576e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293724547,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946440.7551903813,
+    "surface_area_float64_in2": 1946440.7552647898,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946440.7552648517,
+    "zero_area_triangles": 238151,
+    "zero_weight_points": 5909
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC006_AoA_22.json b/surface_dual_areas/cases/geo_LHC006_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..0f9668c359665e1d7909a7e644f889de3bbfcb7f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC006_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC006_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC006_AoA_22/boundary_dual_area_geo_LHC006_AoA_22.npy",
+    "sha256": "9b08573aac57cdfe00547967e76c8f6de979faa4a22da436c7d25f31fd7e5363",
+    "shape": [
+      145339619
+    ],
+    "size_bytes": 581358604
+  },
+  "runtime": {
+    "accumulation_seconds": 11.693195418920368,
+    "completed_at_utc": "2026-08-07T07:19:54.307957Z",
+    "elapsed_seconds": 22.64822591491975,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2367187119089067,
+    "geometry_read_seconds": 2.3554505608044565,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:19:31.659591Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC006_AoA_22/boundary_geo_LHC006_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC006_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624533000000000,
+    "extracted_vtu_size_bytes": 22331072590,
+    "geometry_sha256": "dd66be82b943eb977729baa63456aaa2411b3ef0d6779eac0bdc3432cae1140c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4193208,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1367402,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2792252,
+      "13": 836149,
+      "14": 1254299,
+      "15": 448071,
+      "16": 876380,
+      "17": 350902,
+      "18": 742105,
+      "19": 304938,
+      "20": 678494,
+      "21": 228259,
+      "22": 374814,
+      "23": 127257,
+      "24": 220319,
+      "25": 73294,
+      "26": 95680,
+      "27": 52332,
+      "28": 124182,
+      "29": 52694,
+      "3": 58880,
+      "30": 115242,
+      "31": 49157,
+      "32": 108155,
+      "33": 38463,
+      "34": 65974,
+      "35": 27740,
+      "36": 63113,
+      "37": 22897,
+      "38": 39304,
+      "39": 16418,
+      "4": 133875,
+      "40": 30389,
+      "41": 10982,
+      "42": 14661,
+      "43": 5983,
+      "44": 7675,
+      "45": 3725,
+      "46": 4285,
+      "47": 2498,
+      "48": 3552,
+      "49": 2142,
+      "5": 943451,
+      "50": 2947,
+      "51": 1819,
+      "52": 2754,
+      "53": 1821,
+      "54": 2441,
+      "55": 1750,
+      "56": 2550,
+      "57": 1754,
+      "58": 2284,
+      "59": 1729,
+      "6": 5252024,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2094841,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6504438,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1977939,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58880,
+      "7": 32643034,
+      "9": 133875
+    },
+    "connectivity_max": 145339618,
+    "connectivity_min": 0,
+    "n_cells": 32835789,
+    "n_connectivity_values": 356339697,
+    "n_fan_triangles": 290668119,
+    "n_points": 145339619
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.686323295436159e-11,
+    "float64_area_closure_relative": 8.253685669578288e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290668119,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946441.2693518074,
+    "surface_area_float64_in2": 1946441.2694235595,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946441.2694235756,
+    "zero_area_triangles": 236811,
+    "zero_weight_points": 5726
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC006_AoA_4.json b/surface_dual_areas/cases/geo_LHC006_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..a414169fd6fb22ea9ba3a3f0edddb85e3efc995a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC006_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC006_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC006_AoA_4/boundary_dual_area_geo_LHC006_AoA_4.npy",
+    "sha256": "03313e54a325b1be2b8418b8ea2302eee3e4ac19bb679c38ac3fc346ad5317bd",
+    "shape": [
+      137239418
+    ],
+    "size_bytes": 548957800
+  },
+  "runtime": {
+    "accumulation_seconds": 11.980947891948745,
+    "completed_at_utc": "2026-08-07T07:15:27.310577Z",
+    "elapsed_seconds": 21.19099088991061,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0511142001487315,
+    "geometry_read_seconds": 1.7228949109558016,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": null,
+    "slurm_array_task_id": null,
+    "slurm_job_id": "5945277",
+    "started_at_utc": "2026-08-07T07:15:06.119505Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC006_AoA_4/boundary_geo_LHC006_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC006_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624622000000000,
+    "extracted_vtu_size_bytes": 21069669867,
+    "geometry_sha256": "733bd99fe5dd865b7ab0e664169d9d5af8189d151ad958d0f6903e8cf518037b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3036640,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1002300,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2278808,
+      "13": 806481,
+      "14": 1725342,
+      "15": 568990,
+      "16": 1032568,
+      "17": 389653,
+      "18": 751579,
+      "19": 306394,
+      "20": 670420,
+      "21": 224138,
+      "22": 356905,
+      "23": 122796,
+      "24": 206267,
+      "25": 70764,
+      "26": 93036,
+      "27": 51816,
+      "28": 124055,
+      "29": 52669,
+      "3": 57142,
+      "30": 115247,
+      "31": 49153,
+      "32": 108168,
+      "33": 38461,
+      "34": 65972,
+      "35": 27747,
+      "36": 63113,
+      "37": 22893,
+      "38": 39305,
+      "39": 16418,
+      "4": 129742,
+      "40": 30389,
+      "41": 10981,
+      "42": 14661,
+      "43": 5985,
+      "44": 7674,
+      "45": 3723,
+      "46": 4287,
+      "47": 2499,
+      "48": 3552,
+      "49": 2141,
+      "5": 934537,
+      "50": 2947,
+      "51": 1819,
+      "52": 2755,
+      "53": 1821,
+      "54": 2439,
+      "55": 1750,
+      "56": 2550,
+      "57": 1754,
+      "58": 2284,
+      "59": 1729,
+      "6": 5237742,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1944520,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5891072,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1589171,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57142,
+      "7": 30145986,
+      "9": 129742
+    },
+    "connectivity_max": 137239417,
+    "connectivity_min": 0,
+    "n_cells": 30332870,
+    "n_connectivity_values": 335133457,
+    "n_fan_triangles": 274467717,
+    "n_points": 137239418
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.767218957511089e-11,
+    "float64_area_closure_relative": 2.4641422550844754e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": -4.7264620661735535e-08,
+    "n_fan_triangles": 274467717,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946442.519376626,
+    "surface_area_float64_in2": 1946442.5194499528,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946442.5194500007,
+    "zero_area_triangles": 225107,
+    "zero_weight_points": 4947
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC007_AoA_18.json b/surface_dual_areas/cases/geo_LHC007_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..54c0b2e591046f7ad3184d7bd0340add3669af27
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC007_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC007_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC007_AoA_18/boundary_dual_area_geo_LHC007_AoA_18.npy",
+    "sha256": "24c5506c950a82013ba2ad106bf671d6e2eeda6e655d64bf2aeef3ac6f72844f",
+    "shape": [
+      141687516
+    ],
+    "size_bytes": 566750192
+  },
+  "runtime": {
+    "accumulation_seconds": 11.068065998144448,
+    "completed_at_utc": "2026-08-07T07:20:51.210096Z",
+    "elapsed_seconds": 22.415692942216992,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4073331579566,
+    "geometry_read_seconds": 2.421561449067667,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:20:28.794321Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC007_AoA_18/boundary_geo_LHC007_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC007_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624464000000000,
+    "extracted_vtu_size_bytes": 21771054406,
+    "geometry_sha256": "566374e7b440de089a159c8839299d7a3415d3a84e2bfd5c87b3f2b88d04a859",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4209243,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1243385,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2641472,
+      "13": 750490,
+      "14": 1162010,
+      "15": 423519,
+      "16": 891814,
+      "17": 351629,
+      "18": 754841,
+      "19": 305935,
+      "20": 667462,
+      "21": 228642,
+      "22": 361967,
+      "23": 125857,
+      "24": 204191,
+      "25": 71005,
+      "26": 95316,
+      "27": 52596,
+      "28": 124560,
+      "29": 53382,
+      "3": 51552,
+      "30": 114892,
+      "31": 49378,
+      "32": 108059,
+      "33": 38447,
+      "34": 65609,
+      "35": 27588,
+      "36": 62250,
+      "37": 22790,
+      "38": 38983,
+      "39": 16330,
+      "4": 120460,
+      "40": 30209,
+      "41": 11027,
+      "42": 14534,
+      "43": 5997,
+      "44": 7893,
+      "45": 3744,
+      "46": 4246,
+      "47": 2524,
+      "48": 3613,
+      "49": 2206,
+      "5": 948583,
+      "50": 2947,
+      "51": 1837,
+      "52": 2729,
+      "53": 1788,
+      "54": 2438,
+      "55": 1742,
+      "56": 2526,
+      "57": 1787,
+      "58": 2272,
+      "59": 1693,
+      "6": 5319570,
+      "60": 2472,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2055322,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6302185,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1863286,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51552,
+      "7": 31883501,
+      "9": 120460
+    },
+    "connectivity_max": 141687515,
+    "connectivity_min": 0,
+    "n_cells": 32055513,
+    "n_connectivity_values": 347474934,
+    "n_fan_triangles": 283363908,
+    "n_points": 141687516
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3441643552463276e-11,
+    "float64_area_closure_relative": 5.997778831841445e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283363908,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937091.9541513862,
+    "surface_area_float64_in2": 1937091.9542161657,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937091.9542162819,
+    "zero_area_triangles": 237530,
+    "zero_weight_points": 5570
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC007_AoA_20.json b/surface_dual_areas/cases/geo_LHC007_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..ac85ac741109b946d41d3e71102fc25c9540f4b9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC007_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC007_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC007_AoA_20/boundary_dual_area_geo_LHC007_AoA_20.npy",
+    "sha256": "db23339394190704fd7ca676e2e1b704fb08a06588db2a9ee38ac58454fccf4f",
+    "shape": [
+      139219738
+    ],
+    "size_bytes": 556879080
+  },
+  "runtime": {
+    "accumulation_seconds": 10.984577076043934,
+    "completed_at_utc": "2026-08-07T07:20:45.422927Z",
+    "elapsed_seconds": 20.498357206117362,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1056715750601143,
+    "geometry_read_seconds": 1.77630569296889,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:20:24.924493Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC007_AoA_20/boundary_geo_LHC007_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC007_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624661000000000,
+    "extracted_vtu_size_bytes": 21387594387,
+    "geometry_sha256": "d494d7d9362f42c3882e5089fa57f12ecbf7a3bb17fd76b19060dd51cbd886e4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3933990,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1176270,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2525591,
+      "13": 729656,
+      "14": 1185680,
+      "15": 426539,
+      "16": 899598,
+      "17": 352607,
+      "18": 759191,
+      "19": 308063,
+      "20": 673613,
+      "21": 231711,
+      "22": 369476,
+      "23": 128385,
+      "24": 209043,
+      "25": 72376,
+      "26": 96335,
+      "27": 52940,
+      "28": 124636,
+      "29": 53409,
+      "3": 50191,
+      "30": 114912,
+      "31": 49374,
+      "32": 108091,
+      "33": 38451,
+      "34": 65623,
+      "35": 27590,
+      "36": 62253,
+      "37": 22796,
+      "38": 38987,
+      "39": 16329,
+      "4": 117572,
+      "40": 30207,
+      "41": 11029,
+      "42": 14531,
+      "43": 5997,
+      "44": 7894,
+      "45": 3743,
+      "46": 4246,
+      "47": 2522,
+      "48": 3613,
+      "49": 2207,
+      "5": 942783,
+      "50": 2947,
+      "51": 1837,
+      "52": 2729,
+      "53": 1788,
+      "54": 2439,
+      "55": 1742,
+      "56": 2526,
+      "57": 1787,
+      "58": 2272,
+      "59": 1693,
+      "6": 5281030,
+      "60": 2472,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2022616,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6138769,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1788972,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50191,
+      "7": 31158595,
+      "9": 117572
+    },
+    "connectivity_max": 139219737,
+    "connectivity_min": 0,
+    "n_cells": 31326358,
+    "n_connectivity_values": 341081068,
+    "n_fan_triangles": 278428352,
+    "n_points": 139219738
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3339339252894366e-11,
+    "float64_area_closure_relative": 3.245289445076694e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278428352,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937092.9727028806,
+    "surface_area_float64_in2": 1937092.972767462,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937092.9727673992,
+    "zero_area_triangles": 234668,
+    "zero_weight_points": 5415
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC007_AoA_22.json b/surface_dual_areas/cases/geo_LHC007_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..6e717c74886faa6aa9d22a096520f18d0d845744
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC007_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC007_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC007_AoA_22/boundary_dual_area_geo_LHC007_AoA_22.npy",
+    "sha256": "db7bdb0b111a05dc951d0f7101a6c0d99d629e8eec3987aa64f5583c4f3a99f1",
+    "shape": [
+      137989469
+    ],
+    "size_bytes": 551958004
+  },
+  "runtime": {
+    "accumulation_seconds": 10.822886376874521,
+    "completed_at_utc": "2026-08-07T07:21:13.166085Z",
+    "elapsed_seconds": 22.01532210712321,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2622227899264544,
+    "geometry_read_seconds": 2.191730519058183,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:20:51.150673Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC007_AoA_22/boundary_geo_LHC007_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC007_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624677000000000,
+    "extracted_vtu_size_bytes": 21196534050,
+    "geometry_sha256": "590f29ea0921be447ecc8ab97113b80b4ffb5eeacf7c2205431924c37fb7c4ae",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3799791,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1143688,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2453691,
+      "13": 716179,
+      "14": 1200267,
+      "15": 426135,
+      "16": 905386,
+      "17": 353471,
+      "18": 761287,
+      "19": 309244,
+      "20": 677710,
+      "21": 233539,
+      "22": 373762,
+      "23": 129901,
+      "24": 211046,
+      "25": 72758,
+      "26": 96873,
+      "27": 53078,
+      "28": 124686,
+      "29": 53419,
+      "3": 49053,
+      "30": 114917,
+      "31": 49376,
+      "32": 108097,
+      "33": 38446,
+      "34": 65616,
+      "35": 27587,
+      "36": 62257,
+      "37": 22800,
+      "38": 38986,
+      "39": 16328,
+      "4": 115574,
+      "40": 30206,
+      "41": 11032,
+      "42": 14531,
+      "43": 5996,
+      "44": 7896,
+      "45": 3742,
+      "46": 4245,
+      "47": 2523,
+      "48": 3614,
+      "49": 2206,
+      "5": 939899,
+      "50": 2947,
+      "51": 1837,
+      "52": 2729,
+      "53": 1788,
+      "54": 2439,
+      "55": 1742,
+      "56": 2526,
+      "57": 1787,
+      "58": 2272,
+      "59": 1693,
+      "6": 5265309,
+      "60": 2472,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2010777,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6056619,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1758673,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49053,
+      "7": 30802510,
+      "9": 115574
+    },
+    "connectivity_max": 137989468,
+    "connectivity_min": 0,
+    "n_cells": 30967137,
+    "n_connectivity_values": 337902088,
+    "n_fan_triangles": 275967814,
+    "n_points": 137989469
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.266359735518937e-11,
+    "float64_area_closure_relative": 3.4856812005773315e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275967814,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937093.0034058555,
+    "surface_area_float64_in2": 1937093.003469128,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937093.0034690604,
+    "zero_area_triangles": 233337,
+    "zero_weight_points": 5339
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC008_AoA_10.json b/surface_dual_areas/cases/geo_LHC008_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..c011d5d11ffd614714748a7ad5470e19e06ef8b8
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC008_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC008_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC008_AoA_10/boundary_dual_area_geo_LHC008_AoA_10.npy",
+    "sha256": "79b2e61fdc17d8fb210e954c6f64711bf6c20c2faa548bd0e4dd69aeb214f71d",
+    "shape": [
+      144783110
+    ],
+    "size_bytes": 579132568
+  },
+  "runtime": {
+    "accumulation_seconds": 11.02541656116955,
+    "completed_at_utc": "2026-08-07T07:18:34.889799Z",
+    "elapsed_seconds": 22.16691143391654,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1003210889175534,
+    "geometry_read_seconds": 3.003435968887061,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:18:12.722768Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC008_AoA_10/boundary_geo_LHC008_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC008_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624605000000000,
+    "extracted_vtu_size_bytes": 22242861609,
+    "geometry_sha256": "02beab585052ee8e888f5b8c48b23dda54007d7b5ccffd5e3b9ec289e747cabb",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3929651,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1230703,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2721930,
+      "13": 838243,
+      "14": 1547350,
+      "15": 512857,
+      "16": 964988,
+      "17": 363790,
+      "18": 728434,
+      "19": 293777,
+      "20": 654455,
+      "21": 219872,
+      "22": 359325,
+      "23": 121317,
+      "24": 206905,
+      "25": 71412,
+      "26": 94619,
+      "27": 52389,
+      "28": 123495,
+      "29": 52959,
+      "3": 55599,
+      "30": 115221,
+      "31": 49467,
+      "32": 109065,
+      "33": 38884,
+      "34": 66896,
+      "35": 28040,
+      "36": 62673,
+      "37": 23088,
+      "38": 38671,
+      "39": 16348,
+      "4": 128786,
+      "40": 29347,
+      "41": 10730,
+      "42": 14332,
+      "43": 5798,
+      "44": 7620,
+      "45": 3588,
+      "46": 4094,
+      "47": 2470,
+      "48": 3463,
+      "49": 2143,
+      "5": 939864,
+      "50": 2937,
+      "51": 1852,
+      "52": 2791,
+      "53": 1762,
+      "54": 2488,
+      "55": 1700,
+      "56": 2524,
+      "57": 1743,
+      "58": 2285,
+      "59": 1751,
+      "6": 5365813,
+      "60": 2510,
+      "61": 1626,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2042755,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6461907,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1841857,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 55599,
+      "7": 32417499,
+      "9": 128786
+    },
+    "connectivity_max": 144783109,
+    "connectivity_min": 0,
+    "n_cells": 32601884,
+    "n_connectivity_values": 354758866,
+    "n_fan_triangles": 289555098,
+    "n_points": 144783110
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.657161025706636e-11,
+    "float64_area_closure_relative": 9.174300921396532e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 289555098,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946536.3650705605,
+    "surface_area_float64_in2": 1946536.3651417485,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946536.365141927,
+    "zero_area_triangles": 233871,
+    "zero_weight_points": 5609
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC009_AoA_12.json b/surface_dual_areas/cases/geo_LHC009_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9f143f543e826ea06d30b1babe083a575eead76
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC009_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC009_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC009_AoA_12/boundary_dual_area_geo_LHC009_AoA_12.npy",
+    "sha256": "1fea9d3f5fa9bcda6195402c10600786ab7c46258efefe06a1e302e61ab12d0d",
+    "shape": [
+      137040521
+    ],
+    "size_bytes": 548162212
+  },
+  "runtime": {
+    "accumulation_seconds": 10.416755243903026,
+    "completed_at_utc": "2026-08-07T07:18:54.065824Z",
+    "elapsed_seconds": 21.259742075111717,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0876542599871755,
+    "geometry_read_seconds": 2.827692304039374,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:18:32.805992Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC009_AoA_12/boundary_geo_LHC009_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC009_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624494000000000,
+    "extracted_vtu_size_bytes": 21043912444,
+    "geometry_sha256": "7573d1f598f8dca1fee9ddef7b3a45c7b299826339085c34d2d82355fa503842",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3590355,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1103149,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2485158,
+      "13": 740658,
+      "14": 1349588,
+      "15": 457930,
+      "16": 926652,
+      "17": 356142,
+      "18": 764090,
+      "19": 308818,
+      "20": 680819,
+      "21": 233028,
+      "22": 369512,
+      "23": 127924,
+      "24": 204675,
+      "25": 70323,
+      "26": 94652,
+      "27": 52258,
+      "28": 124942,
+      "29": 53290,
+      "3": 50111,
+      "30": 114727,
+      "31": 49335,
+      "32": 108164,
+      "33": 38771,
+      "34": 66533,
+      "35": 28188,
+      "36": 63044,
+      "37": 22949,
+      "38": 38495,
+      "39": 16029,
+      "4": 111837,
+      "40": 29004,
+      "41": 10583,
+      "42": 13938,
+      "43": 5812,
+      "44": 7863,
+      "45": 3686,
+      "46": 4256,
+      "47": 2560,
+      "48": 3632,
+      "49": 2191,
+      "5": 923561,
+      "50": 2878,
+      "51": 1755,
+      "52": 2562,
+      "53": 1638,
+      "54": 2220,
+      "55": 1627,
+      "56": 2437,
+      "57": 1733,
+      "58": 2250,
+      "59": 1681,
+      "6": 5127478,
+      "60": 2464,
+      "61": 1650,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1981256,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5808265,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1709878,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50111,
+      "7": 30318095,
+      "9": 111837
+    },
+    "connectivity_max": 137040520,
+    "connectivity_min": 0,
+    "n_cells": 30480043,
+    "n_connectivity_values": 335030010,
+    "n_fan_triangles": 274069924,
+    "n_points": 137040521
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.392172712043943e-11,
+    "float64_area_closure_relative": 1.6712224139213287e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274069924,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936514.2064396422,
+    "surface_area_float64_in2": 1936514.2065053321,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936514.2065053645,
+    "zero_area_triangles": 236072,
+    "zero_weight_points": 5487
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC009_AoA_20.json b/surface_dual_areas/cases/geo_LHC009_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..35f69db29f5548ce3ca4c61effe7b361f20face6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC009_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC009_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC009_AoA_20/boundary_dual_area_geo_LHC009_AoA_20.npy",
+    "sha256": "01c18767b107858b6a4223d5f215493e206a51c9dc9979506c78f9cd1b3ff613",
+    "shape": [
+      136344800
+    ],
+    "size_bytes": 545379328
+  },
+  "runtime": {
+    "accumulation_seconds": 10.55872357194312,
+    "completed_at_utc": "2026-08-07T07:19:02.904436Z",
+    "elapsed_seconds": 20.3834217810072,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.961266151862219,
+    "geometry_read_seconds": 2.1351557970046997,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:18:42.520931Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC009_AoA_20/boundary_geo_LHC009_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC009_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624447000000000,
+    "extracted_vtu_size_bytes": 20936823094,
+    "geometry_sha256": "6893eaeff543657cf9e878fe37108baff8eb43c2492ccf520c2594777be6c8bb",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3491556,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1080482,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2416551,
+      "13": 728028,
+      "14": 1349908,
+      "15": 457203,
+      "16": 935826,
+      "17": 356868,
+      "18": 762249,
+      "19": 308422,
+      "20": 680289,
+      "21": 233606,
+      "22": 373215,
+      "23": 129722,
+      "24": 209525,
+      "25": 72012,
+      "26": 95832,
+      "27": 52758,
+      "28": 125037,
+      "29": 53339,
+      "3": 49549,
+      "30": 114735,
+      "31": 49315,
+      "32": 108146,
+      "33": 38767,
+      "34": 66538,
+      "35": 28181,
+      "36": 63049,
+      "37": 22943,
+      "38": 38500,
+      "39": 16036,
+      "4": 112233,
+      "40": 28999,
+      "41": 10575,
+      "42": 13937,
+      "43": 5806,
+      "44": 7863,
+      "45": 3696,
+      "46": 4250,
+      "47": 2558,
+      "48": 3630,
+      "49": 2192,
+      "5": 927288,
+      "50": 2877,
+      "51": 1754,
+      "52": 2562,
+      "53": 1639,
+      "54": 2220,
+      "55": 1627,
+      "56": 2437,
+      "57": 1733,
+      "58": 2250,
+      "59": 1681,
+      "6": 5150912,
+      "60": 2464,
+      "61": 1650,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1982610,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5809955,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1696513,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49549,
+      "7": 30153355,
+      "9": 112233
+    },
+    "connectivity_max": 136344799,
+    "connectivity_min": 0,
+    "n_cells": 30315137,
+    "n_connectivity_values": 333308757,
+    "n_fan_triangles": 272678483,
+    "n_points": 136344800
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.535127921393941e-11,
+    "float64_area_closure_relative": 9.378081457718957e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272678483,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936514.4444775486,
+    "surface_area_float64_in2": 1936514.4445460069,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936514.444546025,
+    "zero_area_triangles": 235625,
+    "zero_weight_points": 5439
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC010_AoA_14.json b/surface_dual_areas/cases/geo_LHC010_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..e319dcd30377f54797f677cc72284f0125344e66
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC010_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC010_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC010_AoA_14/boundary_dual_area_geo_LHC010_AoA_14.npy",
+    "sha256": "726f242168aaf0ec3984331744010cd387e1509b26719e9ac93834fbeccafa2a",
+    "shape": [
+      139530172
+    ],
+    "size_bytes": 558120816
+  },
+  "runtime": {
+    "accumulation_seconds": 10.69078163895756,
+    "completed_at_utc": "2026-08-07T07:21:13.178589Z",
+    "elapsed_seconds": 21.630844583036378,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.261166450101882,
+    "geometry_read_seconds": 2.193019481142983,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:20:51.547651Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC010_AoA_14/boundary_geo_LHC010_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC010_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624634000000000,
+    "extracted_vtu_size_bytes": 21428876660,
+    "geometry_sha256": "87c2f96783d2a42e6758aee49aed57f2c9b04a35d6812ab616912b59beebf06f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3803309,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1157097,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2666793,
+      "13": 777293,
+      "14": 1369449,
+      "15": 464750,
+      "16": 921986,
+      "17": 354008,
+      "18": 752179,
+      "19": 303896,
+      "20": 680111,
+      "21": 227832,
+      "22": 359670,
+      "23": 124047,
+      "24": 201981,
+      "25": 69962,
+      "26": 92361,
+      "27": 52288,
+      "28": 124624,
+      "29": 53423,
+      "3": 52493,
+      "30": 114750,
+      "31": 49541,
+      "32": 108935,
+      "33": 39002,
+      "34": 67124,
+      "35": 28266,
+      "36": 61805,
+      "37": 22786,
+      "38": 37650,
+      "39": 15946,
+      "4": 118007,
+      "40": 28793,
+      "41": 10537,
+      "42": 14143,
+      "43": 5826,
+      "44": 7728,
+      "45": 3616,
+      "46": 4185,
+      "47": 2552,
+      "48": 3568,
+      "49": 2106,
+      "5": 918995,
+      "50": 2828,
+      "51": 1760,
+      "52": 2559,
+      "53": 1671,
+      "54": 2279,
+      "55": 1634,
+      "56": 2443,
+      "57": 1711,
+      "58": 2268,
+      "59": 1734,
+      "6": 5134804,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1973575,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5982725,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1729416,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52493,
+      "7": 30969379,
+      "9": 118007
+    },
+    "connectivity_max": 139530171,
+    "connectivity_min": 0,
+    "n_cells": 31139879,
+    "n_connectivity_values": 341328980,
+    "n_fan_triangles": 279049222,
+    "n_points": 139530172
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.358203634042159e-11,
+    "float64_area_closure_relative": 6.448707835909111e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279049222,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938838.8933005992,
+    "surface_area_float64_in2": 1938838.8933657093,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938838.8933658344,
+    "zero_area_triangles": 239452,
+    "zero_weight_points": 5729
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC010_AoA_20.json b/surface_dual_areas/cases/geo_LHC010_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..bd888af3bfd7161fb186b7b2a8dfaeb7fdfcea04
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC010_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC010_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC010_AoA_20/boundary_dual_area_geo_LHC010_AoA_20.npy",
+    "sha256": "14ee7966466d175ab9d015b1aedaaced662b96b85af186772caa717d00cd3761",
+    "shape": [
+      140800409
+    ],
+    "size_bytes": 563201764
+  },
+  "runtime": {
+    "accumulation_seconds": 10.684194222092628,
+    "completed_at_utc": "2026-08-07T07:18:55.477290Z",
+    "elapsed_seconds": 21.218849535100162,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0197522670496255,
+    "geometry_read_seconds": 2.6793443700298667,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:18:34.258345Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC010_AoA_20/boundary_geo_LHC010_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC010_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624611000000000,
+    "extracted_vtu_size_bytes": 21626902236,
+    "geometry_sha256": "4aa8e3761bd8c5af3d598f9fb6c9532f41938921b2c874d93db111f93c99b5e9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4020866,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1204436,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2688394,
+      "13": 771195,
+      "14": 1324526,
+      "15": 451689,
+      "16": 909951,
+      "17": 350083,
+      "18": 753887,
+      "19": 303657,
+      "20": 677425,
+      "21": 227529,
+      "22": 357461,
+      "23": 123856,
+      "24": 203302,
+      "25": 70602,
+      "26": 93091,
+      "27": 52535,
+      "28": 124649,
+      "29": 53405,
+      "3": 52688,
+      "30": 114710,
+      "31": 49535,
+      "32": 108916,
+      "33": 39010,
+      "34": 67148,
+      "35": 28271,
+      "36": 61812,
+      "37": 22809,
+      "38": 37660,
+      "39": 15946,
+      "4": 120101,
+      "40": 28801,
+      "41": 10542,
+      "42": 14143,
+      "43": 5829,
+      "44": 7728,
+      "45": 3609,
+      "46": 4187,
+      "47": 2555,
+      "48": 3571,
+      "49": 2107,
+      "5": 923728,
+      "50": 2828,
+      "51": 1763,
+      "52": 2558,
+      "53": 1670,
+      "54": 2278,
+      "55": 1634,
+      "56": 2444,
+      "57": 1711,
+      "58": 2268,
+      "59": 1733,
+      "6": 5144484,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1403,
+      "66": 1790,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1997431,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6074204,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1793088,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52688,
+      "7": 31368310,
+      "9": 120101
+    },
+    "connectivity_max": 140800408,
+    "connectivity_min": 0,
+    "n_cells": 31541099,
+    "n_connectivity_values": 344671894,
+    "n_fan_triangles": 281589696,
+    "n_points": 140800409
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3108890298765664e-11,
+    "float64_area_closure_relative": 6.965084681974308e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281589696,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938838.9299022085,
+    "surface_area_float64_in2": 1938838.9299664013,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938838.9299665364,
+    "zero_area_triangles": 240337,
+    "zero_weight_points": 5724
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC010_AoA_6.json b/surface_dual_areas/cases/geo_LHC010_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d8e848c6922c45485cdc0aa398be36bf2f9fcf1
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC010_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC010_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC010_AoA_6/boundary_dual_area_geo_LHC010_AoA_6.npy",
+    "sha256": "dbb8a8f962993a44749ad50c5e901b48f0d7d9ed6cea7e5130e1f93a2076e7bf",
+    "shape": [
+      129621716
+    ],
+    "size_bytes": 518486992
+  },
+  "runtime": {
+    "accumulation_seconds": 9.960383598925546,
+    "completed_at_utc": "2026-08-07T07:22:20.812534Z",
+    "elapsed_seconds": 63.94512910814956,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9897351688705385,
+    "geometry_read_seconds": 2.3360447860322893,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:21:16.867294Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC010_AoA_6/boundary_geo_LHC010_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC010_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624500000000000,
+    "extracted_vtu_size_bytes": 19889034596,
+    "geometry_sha256": "63feb2a5ccfb38049dd2c35ff4614b611b5ba685cb7a453b2685aac8e87ba849",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2435364,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 835099,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1935003,
+      "13": 731835,
+      "14": 1766604,
+      "15": 554006,
+      "16": 1070613,
+      "17": 381891,
+      "18": 765076,
+      "19": 306778,
+      "20": 682774,
+      "21": 229193,
+      "22": 363468,
+      "23": 125253,
+      "24": 204392,
+      "25": 70673,
+      "26": 92867,
+      "27": 52488,
+      "28": 124721,
+      "29": 53478,
+      "3": 47910,
+      "30": 114766,
+      "31": 49536,
+      "32": 108943,
+      "33": 39006,
+      "34": 67123,
+      "35": 28266,
+      "36": 61800,
+      "37": 22790,
+      "38": 37648,
+      "39": 15942,
+      "4": 112692,
+      "40": 28796,
+      "41": 10533,
+      "42": 14142,
+      "43": 5828,
+      "44": 7724,
+      "45": 3617,
+      "46": 4194,
+      "47": 2556,
+      "48": 3570,
+      "49": 2106,
+      "5": 915511,
+      "50": 2827,
+      "51": 1762,
+      "52": 2560,
+      "53": 1671,
+      "54": 2277,
+      "55": 1634,
+      "56": 2443,
+      "57": 1711,
+      "58": 2268,
+      "59": 1734,
+      "6": 5127119,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1857954,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5288400,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1400262,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 47910,
+      "7": 28043654,
+      "9": 112692
+    },
+    "connectivity_max": 129621715,
+    "connectivity_min": 0,
+    "n_cells": 28204256,
+    "n_connectivity_values": 315640822,
+    "n_fan_triangles": 259232310,
+    "n_points": 129621716
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.351354169966029e-11,
+    "float64_area_closure_relative": 5.548042922086835e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 259232310,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938841.4775281223,
+    "surface_area_float64_in2": 1938841.4775930997,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938841.4775932073,
+    "zero_area_triangles": 222336,
+    "zero_weight_points": 4594
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC010_AoA_8.json b/surface_dual_areas/cases/geo_LHC010_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..355ecdacf6f884157c1c54f7b9fc8269f908a868
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC010_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC010_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC010_AoA_8/boundary_dual_area_geo_LHC010_AoA_8.npy",
+    "sha256": "282999b29120f35da343d7bda0d04e64460e95d379ec956ed647326cbe573637",
+    "shape": [
+      136281329
+    ],
+    "size_bytes": 545125444
+  },
+  "runtime": {
+    "accumulation_seconds": 10.786167168989778,
+    "completed_at_utc": "2026-08-07T07:22:22.077583Z",
+    "elapsed_seconds": 49.1580850421451,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.350996895926073,
+    "geometry_read_seconds": 30.477290539070964,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:21:32.919408Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC010_AoA_8/boundary_geo_LHC010_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC010_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624555000000000,
+    "extracted_vtu_size_bytes": 20924119396,
+    "geometry_sha256": "a6f4a8a60ec29358189be3f51ab183c7be0102ab442e538788687ef963a4b0ea",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3300656,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1071133,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2423237,
+      "13": 771374,
+      "14": 1496423,
+      "15": 487187,
+      "16": 982637,
+      "17": 362053,
+      "18": 757470,
+      "19": 304456,
+      "20": 682311,
+      "21": 228364,
+      "22": 360710,
+      "23": 124487,
+      "24": 201892,
+      "25": 70215,
+      "26": 92083,
+      "27": 52361,
+      "28": 124596,
+      "29": 53442,
+      "3": 51980,
+      "30": 114761,
+      "31": 49541,
+      "32": 108934,
+      "33": 39004,
+      "34": 67129,
+      "35": 28265,
+      "36": 61806,
+      "37": 22787,
+      "38": 37649,
+      "39": 15943,
+      "4": 117216,
+      "40": 28794,
+      "41": 10535,
+      "42": 14146,
+      "43": 5828,
+      "44": 7724,
+      "45": 3616,
+      "46": 4191,
+      "47": 2554,
+      "48": 3571,
+      "49": 2107,
+      "5": 920746,
+      "50": 2827,
+      "51": 1762,
+      "52": 2559,
+      "53": 1671,
+      "54": 2279,
+      "55": 1634,
+      "56": 2443,
+      "57": 1711,
+      "58": 2268,
+      "59": 1733,
+      "6": 5141041,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1403,
+      "66": 1790,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1944545,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5752710,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1634582,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51980,
+      "7": 30013543,
+      "9": 117216
+    },
+    "connectivity_max": 136281328,
+    "connectivity_min": 0,
+    "n_cells": 30182739,
+    "n_connectivity_values": 332917014,
+    "n_fan_triangles": 272551536,
+    "n_points": 136281329
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4374128284908104e-11,
+    "float64_area_closure_relative": 8.862468356936502e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272551536,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938839.249859343,
+    "surface_area_float64_in2": 1938839.249925989,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938839.2499261608,
+    "zero_area_triangles": 234943,
+    "zero_weight_points": 5401
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC011_AoA_20.json b/surface_dual_areas/cases/geo_LHC011_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f109dc460d1e1cc9209b2cd99978f8847ed2e16
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC011_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC011_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC011_AoA_20/boundary_dual_area_geo_LHC011_AoA_20.npy",
+    "sha256": "95682a4fed3d76ef7c7a5cc0c16bafe36f940c3796b240a345b1440fb2d59f92",
+    "shape": [
+      150100407
+    ],
+    "size_bytes": 600401756
+  },
+  "runtime": {
+    "accumulation_seconds": 11.564304458908737,
+    "completed_at_utc": "2026-08-07T07:19:40.916129Z",
+    "elapsed_seconds": 23.55946027277969,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.366249068873003,
+    "geometry_read_seconds": 3.3623861388769,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:19:17.356575Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC011_AoA_20/boundary_geo_LHC011_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC011_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624627000000000,
+    "extracted_vtu_size_bytes": 23065393221,
+    "geometry_sha256": "35d56184b569165360afdf743fa0c8de58bc5bcd2d634b507d81cfbe7acb5112",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4628809,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1348354,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3171728,
+      "13": 870347,
+      "14": 1398152,
+      "15": 492736,
+      "16": 924189,
+      "17": 366241,
+      "18": 756151,
+      "19": 306297,
+      "20": 680995,
+      "21": 221957,
+      "22": 343066,
+      "23": 114931,
+      "24": 179397,
+      "25": 64668,
+      "26": 85094,
+      "27": 50386,
+      "28": 122888,
+      "29": 52752,
+      "3": 61817,
+      "30": 114192,
+      "31": 49364,
+      "32": 108920,
+      "33": 39121,
+      "34": 68064,
+      "35": 28235,
+      "36": 62817,
+      "37": 22757,
+      "38": 37941,
+      "39": 15887,
+      "4": 135991,
+      "40": 28946,
+      "41": 10554,
+      "42": 14262,
+      "43": 5815,
+      "44": 7752,
+      "45": 3659,
+      "46": 4294,
+      "47": 2522,
+      "48": 3469,
+      "49": 2062,
+      "5": 960351,
+      "50": 2733,
+      "51": 1713,
+      "52": 2408,
+      "53": 1587,
+      "54": 2152,
+      "55": 1580,
+      "56": 2437,
+      "57": 1672,
+      "58": 2273,
+      "59": 1681,
+      "6": 5236567,
+      "60": 2439,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2115959,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6694338,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1966853,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61817,
+      "7": 33826940,
+      "9": 135991
+    },
+    "connectivity_max": 150100406,
+    "connectivity_min": 0,
+    "n_cells": 34024748,
+    "n_connectivity_values": 368239195,
+    "n_fan_triangles": 300189699,
+    "n_points": 150100407
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.2737601755679344e-11,
+    "float64_area_closure_relative": 6.189673701137129e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 300189699,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944746.1784906667,
+    "surface_area_float64_in2": 1944746.1785737805,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944746.1785739008,
+    "zero_area_triangles": 250540,
+    "zero_weight_points": 6431
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC011_AoA_22.json b/surface_dual_areas/cases/geo_LHC011_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..18ab76623889fb1cd3f7c883fabbd0512338fefc
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC011_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC011_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC011_AoA_22/boundary_dual_area_geo_LHC011_AoA_22.npy",
+    "sha256": "e5fbaecd8ed074c86376dc0b460d28595be91b94a1a1cbe4bc5133b2d0b09f92",
+    "shape": [
+      150559940
+    ],
+    "size_bytes": 602239888
+  },
+  "runtime": {
+    "accumulation_seconds": 11.573497115867212,
+    "completed_at_utc": "2026-08-07T07:19:43.346022Z",
+    "elapsed_seconds": 21.82327390811406,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2739337978418916,
+    "geometry_read_seconds": 2.048002652125433,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:19:21.522665Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC011_AoA_22/boundary_geo_LHC011_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC011_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624668000000000,
+    "extracted_vtu_size_bytes": 23136760805,
+    "geometry_sha256": "41337447938ac837ccf923fc57c02818f1581881bbcfa52333f352415ab18427",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4667114,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1366305,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3191981,
+      "13": 879218,
+      "14": 1409376,
+      "15": 493047,
+      "16": 919855,
+      "17": 364417,
+      "18": 753686,
+      "19": 305443,
+      "20": 677545,
+      "21": 221083,
+      "22": 340858,
+      "23": 114521,
+      "24": 178947,
+      "25": 64568,
+      "26": 85061,
+      "27": 50397,
+      "28": 122915,
+      "29": 52765,
+      "3": 62037,
+      "30": 114199,
+      "31": 49381,
+      "32": 108920,
+      "33": 39137,
+      "34": 68054,
+      "35": 28229,
+      "36": 62816,
+      "37": 22738,
+      "38": 37942,
+      "39": 15877,
+      "4": 136437,
+      "40": 28916,
+      "41": 10540,
+      "42": 14267,
+      "43": 5815,
+      "44": 7747,
+      "45": 3661,
+      "46": 4285,
+      "47": 2522,
+      "48": 3469,
+      "49": 2065,
+      "5": 963671,
+      "50": 2731,
+      "51": 1715,
+      "52": 2406,
+      "53": 1582,
+      "54": 2153,
+      "55": 1581,
+      "56": 2437,
+      "57": 1671,
+      "58": 2273,
+      "59": 1681,
+      "6": 5247163,
+      "60": 2439,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2124435,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6709416,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1983080,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 62037,
+      "7": 33960542,
+      "9": 136437
+    },
+    "connectivity_max": 150559939,
+    "connectivity_min": 0,
+    "n_cells": 34159016,
+    "n_connectivity_values": 369426797,
+    "n_fan_triangles": 301108765,
+    "n_points": 150559940
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.261955802017328e-11,
+    "float64_area_closure_relative": 6.201646432981659e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 301108765,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944746.0397960576,
+    "surface_area_float64_in2": 1944746.0398789418,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944746.0398790624,
+    "zero_area_triangles": 251534,
+    "zero_weight_points": 6474
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC011_AoA_6.json b/surface_dual_areas/cases/geo_LHC011_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..fbccc38841e45e326969382e190e8c6788897781
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC011_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC011_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC011_AoA_6/boundary_dual_area_geo_LHC011_AoA_6.npy",
+    "sha256": "8131f83e86e11933b4d92d2ab5c7b1aafa2683f22b2b79235bb59c06bec864e7",
+    "shape": [
+      136185971
+    ],
+    "size_bytes": 544744012
+  },
+  "runtime": {
+    "accumulation_seconds": 10.583275299984962,
+    "completed_at_utc": "2026-08-07T07:23:03.464691Z",
+    "elapsed_seconds": 20.54571199999191,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2640184711199254,
+    "geometry_read_seconds": 2.1140254219062626,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:22:42.918833Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC011_AoA_6/boundary_geo_LHC011_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC011_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624611000000000,
+    "extracted_vtu_size_bytes": 20902855001,
+    "geometry_sha256": "017847cc5ad4fbff596700359cba89d5bc6b9b7554a9460476369f04bf469208",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2776634,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 863307,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2226081,
+      "13": 802136,
+      "14": 1895182,
+      "15": 617402,
+      "16": 1107637,
+      "17": 405433,
+      "18": 777017,
+      "19": 312107,
+      "20": 690962,
+      "21": 225456,
+      "22": 353920,
+      "23": 117206,
+      "24": 183993,
+      "25": 65429,
+      "26": 85626,
+      "27": 50486,
+      "28": 122986,
+      "29": 52769,
+      "3": 55568,
+      "30": 114174,
+      "31": 49375,
+      "32": 108942,
+      "33": 39111,
+      "34": 68053,
+      "35": 28245,
+      "36": 62829,
+      "37": 22750,
+      "38": 37950,
+      "39": 15885,
+      "4": 126447,
+      "40": 28944,
+      "41": 10550,
+      "42": 14270,
+      "43": 5820,
+      "44": 7752,
+      "45": 3658,
+      "46": 4287,
+      "47": 2527,
+      "48": 3466,
+      "49": 2066,
+      "5": 950734,
+      "50": 2733,
+      "51": 1718,
+      "52": 2409,
+      "53": 1586,
+      "54": 2150,
+      "55": 1582,
+      "56": 2436,
+      "57": 1671,
+      "58": 2273,
+      "59": 1681,
+      "6": 5212477,
+      "60": 2439,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 1933935,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5750872,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1461120,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 55568,
+      "7": 29714665,
+      "9": 126447
+    },
+    "connectivity_max": 136185970,
+    "connectivity_min": 0,
+    "n_cells": 29896680,
+    "n_connectivity_values": 332154188,
+    "n_fan_triangles": 272360828,
+    "n_points": 136185971
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.201966725175251e-11,
+    "float64_area_closure_relative": 2.298675436238046e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272360828,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944749.6969309044,
+    "surface_area_float64_in2": 1944749.6970126221,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944749.6970126668,
+    "zero_area_triangles": 227634,
+    "zero_weight_points": 4948
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC012_AoA_6.json b/surface_dual_areas/cases/geo_LHC012_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe4e7338d45d183f5e43c270f03904f2db2ccb80
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC012_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC012_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC012_AoA_6/boundary_dual_area_geo_LHC012_AoA_6.npy",
+    "sha256": "7a6b6f9b7d8bf5bed29aa2eec5a2a94c3f7777f737500bd4478430591b3cbefb",
+    "shape": [
+      134732986
+    ],
+    "size_bytes": 538932072
+  },
+  "runtime": {
+    "accumulation_seconds": 10.250382191035897,
+    "completed_at_utc": "2026-08-07T07:19:36.509143Z",
+    "elapsed_seconds": 20.273416185984388,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9310883060097694,
+    "geometry_read_seconds": 2.31226097792387,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:19:16.235635Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC012_AoA_6/boundary_geo_LHC012_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC012_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624681000000000,
+    "extracted_vtu_size_bytes": 20684358755,
+    "geometry_sha256": "e57ac68373bb3cd2e65d4fdb639361dfc2fffc1a413fcf73e2cbc5746acd041b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3074711,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 981324,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2293424,
+      "13": 746306,
+      "14": 1607130,
+      "15": 506372,
+      "16": 1028526,
+      "17": 367438,
+      "18": 748352,
+      "19": 298936,
+      "20": 659955,
+      "21": 224247,
+      "22": 355287,
+      "23": 125171,
+      "24": 204782,
+      "25": 72641,
+      "26": 95015,
+      "27": 53016,
+      "28": 123766,
+      "29": 53104,
+      "3": 48121,
+      "30": 114479,
+      "31": 49413,
+      "32": 108798,
+      "33": 38639,
+      "34": 66751,
+      "35": 28192,
+      "36": 62686,
+      "37": 23209,
+      "38": 38870,
+      "39": 16536,
+      "4": 108843,
+      "40": 29501,
+      "41": 10748,
+      "42": 14338,
+      "43": 5853,
+      "44": 7633,
+      "45": 3605,
+      "46": 4123,
+      "47": 2503,
+      "48": 3495,
+      "49": 2108,
+      "5": 922134,
+      "50": 2957,
+      "51": 1886,
+      "52": 2746,
+      "53": 1790,
+      "54": 2454,
+      "55": 1712,
+      "56": 2516,
+      "57": 1752,
+      "58": 2286,
+      "59": 1748,
+      "6": 5198106,
+      "60": 2507,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1937052,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5672465,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1575893,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 48121,
+      "7": 29601539,
+      "9": 108843
+    },
+    "connectivity_max": 134732985,
+    "connectivity_min": 0,
+    "n_cells": 29758503,
+    "n_connectivity_values": 328971859,
+    "n_fan_triangles": 269454853,
+    "n_points": 134732986
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.8352767976618606e-11,
+    "float64_area_closure_relative": 6.763902344317873e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 269454853,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937988.5412186673,
+    "surface_area_float64_in2": 1937988.5412929945,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937988.5412931256,
+    "zero_area_triangles": 225616,
+    "zero_weight_points": 4806
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC013_AoA_18.json b/surface_dual_areas/cases/geo_LHC013_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..d01ae14faddfa4f6ce305d0e22446231e5fcb942
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC013_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC013_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC013_AoA_18/boundary_dual_area_geo_LHC013_AoA_18.npy",
+    "sha256": "daa117dbdd0a4d32b86beff8ce4928676dcc6df9ec7d8426c33ff777f481071a",
+    "shape": [
+      138152386
+    ],
+    "size_bytes": 552609672
+  },
+  "runtime": {
+    "accumulation_seconds": 11.22831481602043,
+    "completed_at_utc": "2026-08-07T07:25:13.502116Z",
+    "elapsed_seconds": 65.66253625694662,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 4.1499756870325655,
+    "geometry_read_seconds": 45.01691972208209,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:24:07.839494Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC013_AoA_18/boundary_geo_LHC013_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC013_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624528000000000,
+    "extracted_vtu_size_bytes": 21218585634,
+    "geometry_sha256": "929a76d2a0bdb1f1efe486ab35251a3ede664aa6abdaed301e0ea0cf6880b924",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3788126,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1152577,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2455047,
+      "13": 739890,
+      "14": 1313409,
+      "15": 449737,
+      "16": 935759,
+      "17": 357582,
+      "18": 763884,
+      "19": 307634,
+      "20": 679567,
+      "21": 229118,
+      "22": 364530,
+      "23": 124764,
+      "24": 198937,
+      "25": 68835,
+      "26": 93070,
+      "27": 51740,
+      "28": 123661,
+      "29": 53226,
+      "3": 47650,
+      "30": 115272,
+      "31": 49650,
+      "32": 109462,
+      "33": 39149,
+      "34": 67442,
+      "35": 28110,
+      "36": 62820,
+      "37": 22766,
+      "38": 38159,
+      "39": 15844,
+      "4": 113209,
+      "40": 28896,
+      "41": 10457,
+      "42": 13924,
+      "43": 5739,
+      "44": 7778,
+      "45": 3699,
+      "46": 4277,
+      "47": 2521,
+      "48": 3601,
+      "49": 2165,
+      "5": 941073,
+      "50": 2839,
+      "51": 1745,
+      "52": 2546,
+      "53": 1632,
+      "54": 2199,
+      "55": 1611,
+      "56": 2423,
+      "57": 1707,
+      "58": 2254,
+      "59": 1681,
+      "6": 5160161,
+      "60": 2463,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2027431,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5887396,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1781183,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 47650,
+      "7": 30723858,
+      "9": 113209
+    },
+    "connectivity_max": 138152385,
+    "connectivity_min": 0,
+    "n_cells": 30884717,
+    "n_connectivity_values": 338063128,
+    "n_fan_triangles": 276293694,
+    "n_points": 138152386
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.8075526362688717e-11,
+    "float64_area_closure_relative": 9.752710956341448e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276293694,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1933747.674862772,
+    "surface_area_float64_in2": 1933747.674917063,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1933747.6749170818,
+    "zero_area_triangles": 234540,
+    "zero_weight_points": 5252
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC013_AoA_22.json b/surface_dual_areas/cases/geo_LHC013_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..b6b3d231844eefe2a234fec846c8621faea8ff74
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC013_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC013_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC013_AoA_22/boundary_dual_area_geo_LHC013_AoA_22.npy",
+    "sha256": "1ecea2f26a28b24cb07ba0ac90b3a3821b0a5a234fa52d2134bce5efd1388183",
+    "shape": [
+      136756295
+    ],
+    "size_bytes": 547025308
+  },
+  "runtime": {
+    "accumulation_seconds": 10.636949058854952,
+    "completed_at_utc": "2026-08-07T07:24:36.514074Z",
+    "elapsed_seconds": 22.304761220002547,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1488808658905327,
+    "geometry_read_seconds": 2.1107902792282403,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:24:14.209221Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC013_AoA_22/boundary_geo_LHC013_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC013_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624561000000000,
+    "extracted_vtu_size_bytes": 21002213616,
+    "geometry_sha256": "ca983d61bc6aba8f50dc077aea59d1a845412ff70713265b61f16129117c5f92",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3598251,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1112565,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2391415,
+      "13": 730883,
+      "14": 1308632,
+      "15": 453132,
+      "16": 950617,
+      "17": 359463,
+      "18": 762741,
+      "19": 306385,
+      "20": 681024,
+      "21": 229822,
+      "22": 371828,
+      "23": 126764,
+      "24": 203588,
+      "25": 70045,
+      "26": 93834,
+      "27": 51982,
+      "28": 123727,
+      "29": 53248,
+      "3": 46454,
+      "30": 115280,
+      "31": 49654,
+      "32": 109457,
+      "33": 39150,
+      "34": 67447,
+      "35": 28100,
+      "36": 62806,
+      "37": 22767,
+      "38": 38147,
+      "39": 15845,
+      "4": 111425,
+      "40": 28890,
+      "41": 10457,
+      "42": 13919,
+      "43": 5736,
+      "44": 7781,
+      "45": 3698,
+      "46": 4279,
+      "47": 2518,
+      "48": 3601,
+      "49": 2169,
+      "5": 942671,
+      "50": 2839,
+      "51": 1741,
+      "52": 2544,
+      "53": 1632,
+      "54": 2201,
+      "55": 1611,
+      "56": 2423,
+      "57": 1707,
+      "58": 2254,
+      "59": 1681,
+      "6": 5161961,
+      "60": 2463,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2019417,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5820141,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1737193,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 46454,
+      "7": 30336816,
+      "9": 111425
+    },
+    "connectivity_max": 136756294,
+    "connectivity_min": 0,
+    "n_cells": 30494695,
+    "n_connectivity_values": 334490902,
+    "n_fan_triangles": 273501512,
+    "n_points": 136756295
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.7893711593485045e-11,
+    "float64_area_closure_relative": 1.794016880807566e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273501512,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1933748.019575078,
+    "surface_area_float64_in2": 1933748.0196290174,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1933748.0196290521,
+    "zero_area_triangles": 232896,
+    "zero_weight_points": 5173
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC013_AoA_6.json b/surface_dual_areas/cases/geo_LHC013_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..1848b79a28ecb9fd2feb8a1df514bb2d8ea774c7
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC013_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC013_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC013_AoA_6/boundary_dual_area_geo_LHC013_AoA_6.npy",
+    "sha256": "fd21ba457e24d9981dfea19483a4d20f3383fbf4e3c961ecaf1c3920d9374ec6",
+    "shape": [
+      133171833
+    ],
+    "size_bytes": 532687460
+  },
+  "runtime": {
+    "accumulation_seconds": 10.060113559942693,
+    "completed_at_utc": "2026-08-07T07:20:03.972049Z",
+    "elapsed_seconds": 19.55222872388549,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.8369613781105727,
+    "geometry_read_seconds": 1.7103919258806854,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:19:44.419727Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC013_AoA_6/boundary_geo_LHC013_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC013_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624495000000000,
+    "extracted_vtu_size_bytes": 20443204264,
+    "geometry_sha256": "9a67e6135660598b63f5efddb18ffeb5c162308a50c1b81a6f9904a8d089eb25",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3010476,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 965460,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2197346,
+      "13": 726417,
+      "14": 1538715,
+      "15": 507165,
+      "16": 1006911,
+      "17": 376165,
+      "18": 771590,
+      "19": 310071,
+      "20": 681345,
+      "21": 229076,
+      "22": 359019,
+      "23": 124138,
+      "24": 195817,
+      "25": 68403,
+      "26": 92148,
+      "27": 51619,
+      "28": 123562,
+      "29": 53205,
+      "3": 46843,
+      "30": 115302,
+      "31": 49667,
+      "32": 109482,
+      "33": 39157,
+      "34": 67470,
+      "35": 28111,
+      "36": 62818,
+      "37": 22765,
+      "38": 38163,
+      "39": 15849,
+      "4": 109248,
+      "40": 28890,
+      "41": 10461,
+      "42": 13933,
+      "43": 5743,
+      "44": 7779,
+      "45": 3698,
+      "46": 4278,
+      "47": 2514,
+      "48": 3603,
+      "49": 2167,
+      "5": 932443,
+      "50": 2838,
+      "51": 1746,
+      "52": 2546,
+      "53": 1631,
+      "54": 2200,
+      "55": 1611,
+      "56": 2425,
+      "57": 1706,
+      "58": 2254,
+      "59": 1682,
+      "6": 5126519,
+      "60": 2463,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1960718,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5529774,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1584501,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 46843,
+      "7": 29198245,
+      "9": 109248
+    },
+    "connectivity_max": 133171832,
+    "connectivity_min": 0,
+    "n_cells": 29354336,
+    "n_connectivity_values": 325041260,
+    "n_fan_triangles": 266332588,
+    "n_points": 133171833
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.84504457371694e-11,
+    "float64_area_closure_relative": 5.05695800518475e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 266332588,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1933748.9105423274,
+    "surface_area_float64_in2": 1933748.9105973435,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1933748.9105972457,
+    "zero_area_triangles": 227087,
+    "zero_weight_points": 4843
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC014_AoA_12.json b/surface_dual_areas/cases/geo_LHC014_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..ec286918ddc40ec6b7e94c4671f27ba2a8cf67a5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC014_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC014_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC014_AoA_12/boundary_dual_area_geo_LHC014_AoA_12.npy",
+    "sha256": "85e33de5a06b9d47b632616deee9293280fabc602dae41cd5e73d4bebc40256a",
+    "shape": [
+      142180932
+    ],
+    "size_bytes": 568723856
+  },
+  "runtime": {
+    "accumulation_seconds": 10.862389554036781,
+    "completed_at_utc": "2026-08-07T07:19:59.448446Z",
+    "elapsed_seconds": 20.44860332692042,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.047075917944312,
+    "geometry_read_seconds": 1.845553832827136,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:19:38.999751Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC014_AoA_12/boundary_geo_LHC014_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC014_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624504000000000,
+    "extracted_vtu_size_bytes": 21837483900,
+    "geometry_sha256": "9dec4e649c14a78da019062001933b6f297bc62c8f92820391b3ff970de9c102",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3600811,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1219779,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2562162,
+      "13": 855858,
+      "14": 1539059,
+      "15": 518328,
+      "16": 963624,
+      "17": 363039,
+      "18": 747824,
+      "19": 300210,
+      "20": 679175,
+      "21": 224076,
+      "22": 369666,
+      "23": 123148,
+      "24": 209848,
+      "25": 70785,
+      "26": 92794,
+      "27": 52048,
+      "28": 123586,
+      "29": 53135,
+      "3": 56546,
+      "30": 115965,
+      "31": 50053,
+      "32": 109795,
+      "33": 39223,
+      "34": 66459,
+      "35": 28209,
+      "36": 62127,
+      "37": 22770,
+      "38": 38031,
+      "39": 16047,
+      "4": 132323,
+      "40": 28939,
+      "41": 10620,
+      "42": 14070,
+      "43": 5754,
+      "44": 7625,
+      "45": 3611,
+      "46": 4132,
+      "47": 2517,
+      "48": 3557,
+      "49": 2121,
+      "5": 949188,
+      "50": 2919,
+      "51": 1785,
+      "52": 2625,
+      "53": 1703,
+      "54": 2343,
+      "55": 1641,
+      "56": 2456,
+      "57": 1718,
+      "58": 2270,
+      "59": 1737,
+      "6": 5232043,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2069484,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6169517,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1837736,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 56546,
+      "7": 31602802,
+      "9": 132323
+    },
+    "connectivity_max": 142180931,
+    "connectivity_min": 0,
+    "n_cells": 31791671,
+    "n_connectivity_values": 347934079,
+    "n_fan_triangles": 284350737,
+    "n_points": 142180932
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4725660125690166e-11,
+    "float64_area_closure_relative": 2.3318412373953858e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284350737,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947044.026103636,
+    "surface_area_float64_in2": 1947044.0261712484,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947044.026171203,
+    "zero_area_triangles": 231787,
+    "zero_weight_points": 5323
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC014_AoA_4.json b/surface_dual_areas/cases/geo_LHC014_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..dbda61c7b6cc866c17addcdf9d5bb19b02fbc0e0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC014_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC014_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC014_AoA_4/boundary_dual_area_geo_LHC014_AoA_4.npy",
+    "sha256": "14efb9eb15c45c41a4e2807aecd5d5e1ac63794aab199b7b13e916ee6e564ac5",
+    "shape": [
+      135273654
+    ],
+    "size_bytes": 541094744
+  },
+  "runtime": {
+    "accumulation_seconds": 12.800426316913217,
+    "completed_at_utc": "2026-08-07T07:24:49.540794Z",
+    "elapsed_seconds": 24.41080025699921,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2786259020213038,
+    "geometry_read_seconds": 3.483082073042169,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:24:25.129903Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC014_AoA_4/boundary_geo_LHC014_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC014_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624564000000000,
+    "extracted_vtu_size_bytes": 20763054280,
+    "geometry_sha256": "5f80eceb400db39ab940ee302156bb97b3204545d409742870cda84f8dedcebb",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2854699,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 984731,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2228963,
+      "13": 811562,
+      "14": 1697292,
+      "15": 565517,
+      "16": 1013482,
+      "17": 381562,
+      "18": 757022,
+      "19": 304806,
+      "20": 686584,
+      "21": 227992,
+      "22": 378987,
+      "23": 126179,
+      "24": 214243,
+      "25": 72034,
+      "26": 93354,
+      "27": 52203,
+      "28": 123623,
+      "29": 53145,
+      "3": 53881,
+      "30": 115981,
+      "31": 50031,
+      "32": 109785,
+      "33": 39233,
+      "34": 66457,
+      "35": 28215,
+      "36": 62134,
+      "37": 22765,
+      "38": 38036,
+      "39": 16043,
+      "4": 123535,
+      "40": 28941,
+      "41": 10621,
+      "42": 14077,
+      "43": 5754,
+      "44": 7626,
+      "45": 3612,
+      "46": 4136,
+      "47": 2516,
+      "48": 3559,
+      "49": 2120,
+      "5": 935545,
+      "50": 2918,
+      "51": 1786,
+      "52": 2625,
+      "53": 1703,
+      "54": 2343,
+      "55": 1641,
+      "56": 2456,
+      "57": 1718,
+      "58": 2270,
+      "59": 1737,
+      "6": 5181009,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1957672,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5571657,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1578397,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53881,
+      "7": 29528156,
+      "9": 123535
+    },
+    "connectivity_max": 135273653,
+    "connectivity_min": 0,
+    "n_cells": 29705572,
+    "n_connectivity_values": 329947325,
+    "n_fan_triangles": 270536181,
+    "n_points": 135273654
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.328815369819594e-11,
+    "float64_area_closure_relative": 9.566523557885403e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 270536181,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947044.9614203162,
+    "surface_area_float64_in2": 1947044.9614851298,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947044.961485128,
+    "zero_area_triangles": 224786,
+    "zero_weight_points": 4802
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC015_AoA_6.json b/surface_dual_areas/cases/geo_LHC015_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..01dff3b5e27f2961cab7ce6863ebe30ff28f3c9e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC015_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC015_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC015_AoA_6/boundary_dual_area_geo_LHC015_AoA_6.npy",
+    "sha256": "16ac9c9be8af8300973b1c2297a4e4dc1e3284f6d02aff887ff3cb69b7f2736f",
+    "shape": [
+      137331506
+    ],
+    "size_bytes": 549326152
+  },
+  "runtime": {
+    "accumulation_seconds": 10.684084913926199,
+    "completed_at_utc": "2026-08-07T07:27:19.661804Z",
+    "elapsed_seconds": 21.598920258926228,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3183946709614247,
+    "geometry_read_seconds": 2.914384013041854,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:26:58.062795Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC015_AoA_6/boundary_geo_LHC015_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC015_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624536000000000,
+    "extracted_vtu_size_bytes": 21082614774,
+    "geometry_sha256": "9b06f6ad6f39de7db6217b9b392c6217c23415b0f9c860a928f22d827761bde1",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2934403,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 937463,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2301033,
+      "13": 778980,
+      "14": 1804674,
+      "15": 566479,
+      "16": 1072728,
+      "17": 388049,
+      "18": 768156,
+      "19": 309442,
+      "20": 689222,
+      "21": 226857,
+      "22": 361456,
+      "23": 121027,
+      "24": 197430,
+      "25": 69041,
+      "26": 88688,
+      "27": 51315,
+      "28": 123414,
+      "29": 53058,
+      "3": 56456,
+      "30": 114627,
+      "31": 49345,
+      "32": 108119,
+      "33": 38999,
+      "34": 66773,
+      "35": 28119,
+      "36": 63199,
+      "37": 22962,
+      "38": 38326,
+      "39": 16029,
+      "4": 131011,
+      "40": 29025,
+      "41": 10568,
+      "42": 13928,
+      "43": 5775,
+      "44": 7743,
+      "45": 3706,
+      "46": 4252,
+      "47": 2531,
+      "48": 3628,
+      "49": 2198,
+      "5": 944663,
+      "50": 2919,
+      "51": 1784,
+      "52": 2647,
+      "53": 1665,
+      "54": 2275,
+      "55": 1646,
+      "56": 2461,
+      "57": 1733,
+      "58": 2254,
+      "59": 1677,
+      "6": 5241690,
+      "60": 2468,
+      "61": 1651,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1981281,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5853223,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1580194,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56456,
+      "7": 30118038,
+      "9": 131011
+    },
+    "connectivity_max": 137331505,
+    "connectivity_min": 0,
+    "n_cells": 30305505,
+    "n_connectivity_values": 335262904,
+    "n_fan_triangles": 274651894,
+    "n_points": 137331506
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.60060678096406e-11,
+    "float64_area_closure_relative": 4.545359819433264e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274651894,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946504.7454992537,
+    "surface_area_float64_in2": 1946504.7455693397,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946504.7455694282,
+    "zero_area_triangles": 225403,
+    "zero_weight_points": 4903
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC016_AoA_10.json b/surface_dual_areas/cases/geo_LHC016_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..00a05a2e0d3ae54c2c7a2cfedcceef25a41eb2eb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC016_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC016_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC016_AoA_10/boundary_dual_area_geo_LHC016_AoA_10.npy",
+    "sha256": "39b237ef95a12b600d287e71631d62d3093d02171c2e18270f1330404b9f2ed4",
+    "shape": [
+      136260866
+    ],
+    "size_bytes": 545043592
+  },
+  "runtime": {
+    "accumulation_seconds": 10.711550574051216,
+    "completed_at_utc": "2026-08-07T07:28:10.389123Z",
+    "elapsed_seconds": 49.66079367394559,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.60144950193353,
+    "geometry_read_seconds": 29.96222315891646,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:27:20.728243Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC016_AoA_10/boundary_geo_LHC016_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC016_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624457000000000,
+    "extracted_vtu_size_bytes": 20921302241,
+    "geometry_sha256": "21618e0188d99419d283313bba4ad65932a8b0ad21583135d1cf448ea89a26a6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3258063,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1054190,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2378308,
+      "13": 768885,
+      "14": 1511401,
+      "15": 498432,
+      "16": 993281,
+      "17": 366360,
+      "18": 760038,
+      "19": 304713,
+      "20": 673579,
+      "21": 228067,
+      "22": 363888,
+      "23": 125639,
+      "24": 202374,
+      "25": 69589,
+      "26": 92349,
+      "27": 51510,
+      "28": 124029,
+      "29": 52943,
+      "3": 51254,
+      "30": 115238,
+      "31": 49529,
+      "32": 109756,
+      "33": 39209,
+      "34": 66951,
+      "35": 28031,
+      "36": 62907,
+      "37": 22756,
+      "38": 38197,
+      "39": 15868,
+      "4": 114712,
+      "40": 29043,
+      "41": 10572,
+      "42": 13995,
+      "43": 5815,
+      "44": 7810,
+      "45": 3747,
+      "46": 4223,
+      "47": 2547,
+      "48": 3627,
+      "49": 2190,
+      "5": 933824,
+      "50": 2866,
+      "51": 1775,
+      "52": 2483,
+      "53": 1619,
+      "54": 2191,
+      "55": 1601,
+      "56": 2423,
+      "57": 1716,
+      "58": 2249,
+      "59": 1678,
+      "6": 5159169,
+      "60": 2465,
+      "61": 1651,
+      "62": 2224,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1978414,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5750650,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1649767,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51254,
+      "7": 30025230,
+      "9": 114712
+    },
+    "connectivity_max": 136260865,
+    "connectivity_min": 0,
+    "n_cells": 30191196,
+    "n_connectivity_values": 332892995,
+    "n_fan_triangles": 272510603,
+    "n_points": 136260866
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.79661996235601e-11,
+    "float64_area_closure_relative": 1.7064798041130207e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272510603,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937435.844141708,
+    "surface_area_float64_in2": 1937435.8441958907,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937435.8441959238,
+    "zero_area_triangles": 234268,
+    "zero_weight_points": 5275
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC016_AoA_4.json b/surface_dual_areas/cases/geo_LHC016_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..06e17b133477c11479bfa691f5d2ca0e2c54f176
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC016_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC016_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC016_AoA_4/boundary_dual_area_geo_LHC016_AoA_4.npy",
+    "sha256": "1efa00db50084d22420deb62282a126ff343459a886e75dc4f92b15fedd5c72f",
+    "shape": [
+      127469904
+    ],
+    "size_bytes": 509879744
+  },
+  "runtime": {
+    "accumulation_seconds": 10.199610976036638,
+    "completed_at_utc": "2026-08-07T07:24:36.478839Z",
+    "elapsed_seconds": 21.06805946608074,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.8873550340067595,
+    "geometry_read_seconds": 1.9857170269824564,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:24:15.410695Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC016_AoA_4/boundary_geo_LHC016_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC016_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624712000000000,
+    "extracted_vtu_size_bytes": 19555699264,
+    "geometry_sha256": "f97b0219fe8baba6bbf4e211bbf1d2976c95a097c058bb7001cc8669744e8605",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2159915,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 765065,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1742151,
+      "13": 707489,
+      "14": 1776852,
+      "15": 562228,
+      "16": 1104089,
+      "17": 390474,
+      "18": 780604,
+      "19": 311103,
+      "20": 684808,
+      "21": 231965,
+      "22": 371552,
+      "23": 127758,
+      "24": 207638,
+      "25": 70638,
+      "26": 93890,
+      "27": 51806,
+      "28": 124283,
+      "29": 53023,
+      "3": 49305,
+      "30": 115250,
+      "31": 49531,
+      "32": 109756,
+      "33": 39211,
+      "34": 66953,
+      "35": 28030,
+      "36": 62903,
+      "37": 22755,
+      "38": 38198,
+      "39": 15866,
+      "4": 111175,
+      "40": 29044,
+      "41": 10572,
+      "42": 13994,
+      "43": 5809,
+      "44": 7813,
+      "45": 3749,
+      "46": 4224,
+      "47": 2546,
+      "48": 3628,
+      "49": 2189,
+      "5": 925081,
+      "50": 2866,
+      "51": 1775,
+      "52": 2483,
+      "53": 1619,
+      "54": 2191,
+      "55": 1601,
+      "56": 2423,
+      "57": 1716,
+      "58": 2249,
+      "59": 1678,
+      "6": 5127311,
+      "60": 2465,
+      "61": 1651,
+      "62": 2224,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1864903,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5178751,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1359937,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49305,
+      "7": 27449092,
+      "9": 111175
+    },
+    "connectivity_max": 127469903,
+    "connectivity_min": 0,
+    "n_cells": 27609572,
+    "n_connectivity_values": 310147823,
+    "n_fan_triangles": 254928679,
+    "n_points": 127469904
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.7629789815514277e-11,
+    "float64_area_closure_relative": 9.61395645868082e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 254928679,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937438.7196206164,
+    "surface_area_float64_in2": 1937438.7196741474,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937438.7196741456,
+    "zero_area_triangles": 218589,
+    "zero_weight_points": 4304
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC016_AoA_6.json b/surface_dual_areas/cases/geo_LHC016_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..5ab3382891ae12591aa42a81c6281ac4c6c10b46
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC016_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC016_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC016_AoA_6/boundary_dual_area_geo_LHC016_AoA_6.npy",
+    "sha256": "8fa120fc5e89965f913f99139b5934420c697e10d86f67795ea2fb8c575ec26c",
+    "shape": [
+      127995094
+    ],
+    "size_bytes": 511980504
+  },
+  "runtime": {
+    "accumulation_seconds": 10.105050166836008,
+    "completed_at_utc": "2026-08-07T07:28:24.793042Z",
+    "elapsed_seconds": 22.18038102891296,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9285237840376794,
+    "geometry_read_seconds": 4.760182536905631,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:28:02.612579Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC016_AoA_6/boundary_geo_LHC016_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC016_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624517000000000,
+    "extracted_vtu_size_bytes": 19636885559,
+    "geometry_sha256": "853f1b293d2fab4077d5fb6be027177ab1d380b172f45270e1dc95ef34028e10",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2171865,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 767107,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1777294,
+      "13": 720729,
+      "14": 1820158,
+      "15": 574418,
+      "16": 1101921,
+      "17": 389409,
+      "18": 772586,
+      "19": 308224,
+      "20": 678738,
+      "21": 230267,
+      "22": 368331,
+      "23": 127000,
+      "24": 205984,
+      "25": 70326,
+      "26": 93564,
+      "27": 51791,
+      "28": 124220,
+      "29": 52999,
+      "3": 47725,
+      "30": 115246,
+      "31": 49525,
+      "32": 109756,
+      "33": 39205,
+      "34": 66943,
+      "35": 28034,
+      "36": 62930,
+      "37": 22754,
+      "38": 38195,
+      "39": 15860,
+      "4": 110488,
+      "40": 29034,
+      "41": 10571,
+      "42": 13993,
+      "43": 5803,
+      "44": 7813,
+      "45": 3749,
+      "46": 4220,
+      "47": 2548,
+      "48": 3627,
+      "49": 2188,
+      "5": 927760,
+      "50": 2865,
+      "51": 1775,
+      "52": 2483,
+      "53": 1619,
+      "54": 2191,
+      "55": 1601,
+      "56": 2423,
+      "57": 1716,
+      "58": 2249,
+      "59": 1678,
+      "6": 5141322,
+      "60": 2465,
+      "61": 1651,
+      "62": 2224,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1870597,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5207118,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1360208,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 47725,
+      "7": 27589686,
+      "9": 110488
+    },
+    "connectivity_max": 127995093,
+    "connectivity_min": 0,
+    "n_cells": 27747899,
+    "n_connectivity_values": 311474857,
+    "n_fan_triangles": 255979059,
+    "n_points": 127995094
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.7799597033898224e-11,
+    "float64_area_closure_relative": 1.0214828999128286e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 255979059,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937438.6699686935,
+    "surface_area_float64_in2": 1937438.6700225535,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937438.6700225733,
+    "zero_area_triangles": 218017,
+    "zero_weight_points": 4268
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC017_AoA_12.json b/surface_dual_areas/cases/geo_LHC017_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..0ab076c656e6c3b3dea3e03c20f5ba7edc5f8b93
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC017_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC017_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC017_AoA_12/boundary_dual_area_geo_LHC017_AoA_12.npy",
+    "sha256": "58e331e9e40d578067fef72f12a5234beaed198cada9913ab1962076ae54ec56",
+    "shape": [
+      143861697
+    ],
+    "size_bytes": 575446916
+  },
+  "runtime": {
+    "accumulation_seconds": 11.127458021976054,
+    "completed_at_utc": "2026-08-07T07:31:43.775180Z",
+    "elapsed_seconds": 51.54183930391446,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2023957460187376,
+    "geometry_read_seconds": 32.53228421788663,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:30:52.233241Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC017_AoA_12/boundary_geo_LHC017_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC017_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624610000000000,
+    "extracted_vtu_size_bytes": 22104315801,
+    "geometry_sha256": "28ad43c7e7dadeb46b20ddd4d25efc4d96efc8ec2f265b8eadab7ec21db7d503",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4347341,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1245514,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2814665,
+      "13": 773858,
+      "14": 1281433,
+      "15": 435760,
+      "16": 908946,
+      "17": 348345,
+      "18": 745660,
+      "19": 301394,
+      "20": 664130,
+      "21": 224599,
+      "22": 361024,
+      "23": 122844,
+      "24": 197308,
+      "25": 68098,
+      "26": 92702,
+      "27": 51749,
+      "28": 124447,
+      "29": 53346,
+      "3": 54154,
+      "30": 115400,
+      "31": 49565,
+      "32": 107917,
+      "33": 38698,
+      "34": 66193,
+      "35": 27838,
+      "36": 62409,
+      "37": 22970,
+      "38": 38823,
+      "39": 16369,
+      "4": 121263,
+      "40": 29366,
+      "41": 10784,
+      "42": 14227,
+      "43": 5883,
+      "44": 7652,
+      "45": 3621,
+      "46": 4292,
+      "47": 2554,
+      "48": 3532,
+      "49": 2150,
+      "5": 934321,
+      "50": 2913,
+      "51": 1848,
+      "52": 2727,
+      "53": 1771,
+      "54": 2457,
+      "55": 1704,
+      "56": 2566,
+      "57": 1710,
+      "58": 2298,
+      "59": 1694,
+      "6": 5266177,
+      "60": 2448,
+      "61": 1666,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1370,
+      "66": 1769,
+      "67": 1096,
+      "68": 1505,
+      "69": 880,
+      "7": 2048140,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6381973,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1870817,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54154,
+      "7": 32339399,
+      "9": 121263
+    },
+    "connectivity_max": 143861696,
+    "connectivity_min": 0,
+    "n_cells": 32514816,
+    "n_connectivity_values": 352741906,
+    "n_fan_triangles": 287712274,
+    "n_points": 143861697
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4709835127695785e-11,
+    "float64_area_closure_relative": 1.5378003171731892e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 287712274,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937983.8886653385,
+    "surface_area_float64_in2": 1937983.8887326056,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937983.8887326354,
+    "zero_area_triangles": 241629,
+    "zero_weight_points": 5910
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC017_AoA_6.json b/surface_dual_areas/cases/geo_LHC017_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..a0e2c4046b79532e458284ba2fd2ed10af471b25
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC017_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC017_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC017_AoA_6/boundary_dual_area_geo_LHC017_AoA_6.npy",
+    "sha256": "5ecf08f62dbb2000434fc3a519ab7c7ecd0433e2d4e6999f9e090e15de152f26",
+    "shape": [
+      140556128
+    ],
+    "size_bytes": 562224640
+  },
+  "runtime": {
+    "accumulation_seconds": 10.717667979886755,
+    "completed_at_utc": "2026-08-07T07:31:09.712724Z",
+    "elapsed_seconds": 68.70998425409198,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1696786019019783,
+    "geometry_read_seconds": 4.1063735170755535,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:30:01.002637Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC017_AoA_6/boundary_geo_LHC017_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC017_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624560000000000,
+    "extracted_vtu_size_bytes": 21589040614,
+    "geometry_sha256": "44b9994a3962c4d848e9f214275064de84a0823c142b392412a9a0e2574bbbd9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3780491,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1104430,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2613130,
+      "13": 777108,
+      "14": 1511687,
+      "15": 495942,
+      "16": 984610,
+      "17": 366367,
+      "18": 747607,
+      "19": 301262,
+      "20": 657867,
+      "21": 221084,
+      "22": 347380,
+      "23": 118691,
+      "24": 189762,
+      "25": 66612,
+      "26": 91882,
+      "27": 51594,
+      "28": 124431,
+      "29": 53343,
+      "3": 51456,
+      "30": 115405,
+      "31": 49567,
+      "32": 107917,
+      "33": 38705,
+      "34": 66192,
+      "35": 27833,
+      "36": 62414,
+      "37": 22969,
+      "38": 38822,
+      "39": 16368,
+      "4": 117798,
+      "40": 29362,
+      "41": 10783,
+      "42": 14233,
+      "43": 5879,
+      "44": 7653,
+      "45": 3623,
+      "46": 4293,
+      "47": 2553,
+      "48": 3532,
+      "49": 2149,
+      "5": 930041,
+      "50": 2914,
+      "51": 1848,
+      "52": 2727,
+      "53": 1771,
+      "54": 2458,
+      "55": 1704,
+      "56": 2566,
+      "57": 1710,
+      "58": 2298,
+      "59": 1695,
+      "6": 5264714,
+      "60": 2448,
+      "61": 1666,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 1996125,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6119275,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1713269,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51456,
+      "7": 31303523,
+      "9": 117798
+    },
+    "connectivity_max": 140556127,
+    "connectivity_min": 0,
+    "n_cells": 31472777,
+    "n_connectivity_values": 344046690,
+    "n_fan_triangles": 281101136,
+    "n_points": 140556128
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5022673013537106e-11,
+    "float64_area_closure_relative": 2.679135850085682e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281101136,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937984.3516085234,
+    "surface_area_float64_in2": 1937984.3516763968,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937984.3516764487,
+    "zero_area_triangles": 235096,
+    "zero_weight_points": 5445
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC019_AoA_4.json b/surface_dual_areas/cases/geo_LHC019_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..7379d32f7647afb3ca93dccecf8e0ebf3ebac306
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC019_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC019_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC019_AoA_4/boundary_dual_area_geo_LHC019_AoA_4.npy",
+    "sha256": "21c75bdf696028338a3df79e8c43233336bd42bd0e17f488f23744c62815c144",
+    "shape": [
+      125892775
+    ],
+    "size_bytes": 503571228
+  },
+  "runtime": {
+    "accumulation_seconds": 9.611060880124569,
+    "completed_at_utc": "2026-08-07T07:21:51.588385Z",
+    "elapsed_seconds": 18.81932189804502,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.7174991311039776,
+    "geometry_read_seconds": 1.9359778461512178,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:21:32.768974Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC019_AoA_4/boundary_geo_LHC019_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC019_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624424000000000,
+    "extracted_vtu_size_bytes": 19311915109,
+    "geometry_sha256": "cd77a337fec3f73b94afc94263e9ef6f058e4308190a771d582e8244162375c5",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2008478,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 751923,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1639152,
+      "13": 699005,
+      "14": 1795489,
+      "15": 567805,
+      "16": 1097668,
+      "17": 393132,
+      "18": 780452,
+      "19": 313742,
+      "20": 689556,
+      "21": 232619,
+      "22": 368265,
+      "23": 126254,
+      "24": 208278,
+      "25": 69977,
+      "26": 95245,
+      "27": 51841,
+      "28": 124248,
+      "29": 53117,
+      "3": 45806,
+      "30": 114968,
+      "31": 49600,
+      "32": 108715,
+      "33": 39039,
+      "34": 65994,
+      "35": 28198,
+      "36": 62374,
+      "37": 22893,
+      "38": 38625,
+      "39": 16061,
+      "4": 105969,
+      "40": 29156,
+      "41": 10578,
+      "42": 14095,
+      "43": 5694,
+      "44": 7600,
+      "45": 3644,
+      "46": 4200,
+      "47": 2490,
+      "48": 3491,
+      "49": 2069,
+      "5": 923657,
+      "50": 2797,
+      "51": 1742,
+      "52": 2517,
+      "53": 1616,
+      "54": 2258,
+      "55": 1623,
+      "56": 2434,
+      "57": 1701,
+      "58": 2256,
+      "59": 1715,
+      "6": 5133197,
+      "60": 2501,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1853477,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5048768,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1344440,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 45806,
+      "7": 27043030,
+      "9": 105969
+    },
+    "connectivity_max": 125892774,
+    "connectivity_min": 0,
+    "n_cells": 27194805,
+    "n_connectivity_values": 306164045,
+    "n_fan_triangles": 251774435,
+    "n_points": 125892775
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.590937228582425e-11,
+    "float64_area_closure_relative": 3.8472996352125405e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 251774435,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936574.0397406511,
+    "surface_area_float64_in2": 1936574.0398101923,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936574.0398101998,
+    "zero_area_triangles": 215834,
+    "zero_weight_points": 4076
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC019_AoA_8.json b/surface_dual_areas/cases/geo_LHC019_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..293487e21161b7b89aee050fa735c82cea43b717
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC019_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC019_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC019_AoA_8/boundary_dual_area_geo_LHC019_AoA_8.npy",
+    "sha256": "d86c18427b3242cec66e319287e5456115164319e98e7a0f9b32a1fa8ae8c75a",
+    "shape": [
+      134563162
+    ],
+    "size_bytes": 538252776
+  },
+  "runtime": {
+    "accumulation_seconds": 10.14491924084723,
+    "completed_at_utc": "2026-08-07T07:21:27.560670Z",
+    "elapsed_seconds": 19.801279391162097,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.8745437029283494,
+    "geometry_read_seconds": 2.303729796083644,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:21:07.759302Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC019_AoA_8/boundary_geo_LHC019_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC019_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624693000000000,
+    "extracted_vtu_size_bytes": 20658853210,
+    "geometry_sha256": "23cf782879dc575072b9b2f404859493b8ba7974533f7111e69b6c0ead0e4510",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3114663,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1045870,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2296489,
+      "13": 751473,
+      "14": 1502183,
+      "15": 492224,
+      "16": 981723,
+      "17": 369559,
+      "18": 762680,
+      "19": 309197,
+      "20": 681579,
+      "21": 229867,
+      "22": 361961,
+      "23": 124336,
+      "24": 203306,
+      "25": 69337,
+      "26": 93571,
+      "27": 51704,
+      "28": 124020,
+      "29": 53077,
+      "3": 49219,
+      "30": 114967,
+      "31": 49599,
+      "32": 108726,
+      "33": 39034,
+      "34": 65998,
+      "35": 28201,
+      "36": 62385,
+      "37": 22889,
+      "38": 38624,
+      "39": 16060,
+      "4": 110255,
+      "40": 29159,
+      "41": 10572,
+      "42": 14096,
+      "43": 5694,
+      "44": 7605,
+      "45": 3644,
+      "46": 4201,
+      "47": 2492,
+      "48": 3490,
+      "49": 2068,
+      "5": 930466,
+      "50": 2796,
+      "51": 1742,
+      "52": 2519,
+      "53": 1617,
+      "54": 2256,
+      "55": 1622,
+      "56": 2434,
+      "57": 1701,
+      "58": 2256,
+      "59": 1715,
+      "6": 5150897,
+      "60": 2501,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1963605,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5607713,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1639400,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49219,
+      "7": 29584164,
+      "9": 110255
+    },
+    "connectivity_max": 134563161,
+    "connectivity_min": 0,
+    "n_cells": 29743638,
+    "n_connectivity_values": 328602485,
+    "n_fan_triangles": 269115209,
+    "n_points": 134563162
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.521847485960396e-11,
+    "float64_area_closure_relative": 2.6450225204358966e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 269115209,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936571.0955688152,
+    "surface_area_float64_in2": 1936571.0956370183,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936571.0956370234,
+    "zero_area_triangles": 231997,
+    "zero_weight_points": 5050
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC020_AoA_10.json b/surface_dual_areas/cases/geo_LHC020_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..3104ffade7e4774cb8b5addbc04ddcbfe8e2d856
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC020_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC020_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC020_AoA_10/boundary_dual_area_geo_LHC020_AoA_10.npy",
+    "sha256": "6641bcd155f05f338491b2cd5958218f6c98f521f6691e6aaa33160b768fb172",
+    "shape": [
+      146828787
+    ],
+    "size_bytes": 587315276
+  },
+  "runtime": {
+    "accumulation_seconds": 11.117381626972929,
+    "completed_at_utc": "2026-08-07T07:22:15.980313Z",
+    "elapsed_seconds": 22.53648044797592,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2114407669287175,
+    "geometry_read_seconds": 2.890422121854499,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:21:53.443743Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC020_AoA_10/boundary_geo_LHC020_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC020_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624711000000000,
+    "extracted_vtu_size_bytes": 22558740395,
+    "geometry_sha256": "11f819a412451b75234bd9cf21be01921474662bef15166ea28ee1dc9d7dd566",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4158439,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1245327,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2983137,
+      "13": 846339,
+      "14": 1510951,
+      "15": 494329,
+      "16": 988715,
+      "17": 368637,
+      "18": 752433,
+      "19": 303371,
+      "20": 665391,
+      "21": 218836,
+      "22": 334374,
+      "23": 115252,
+      "24": 184098,
+      "25": 66827,
+      "26": 88163,
+      "27": 51072,
+      "28": 123096,
+      "29": 53162,
+      "3": 59037,
+      "30": 115930,
+      "31": 49493,
+      "32": 108276,
+      "33": 38474,
+      "34": 66229,
+      "35": 27786,
+      "36": 61918,
+      "37": 22867,
+      "38": 38780,
+      "39": 16331,
+      "4": 131476,
+      "40": 29818,
+      "41": 10888,
+      "42": 14508,
+      "43": 5940,
+      "44": 7755,
+      "45": 3672,
+      "46": 4162,
+      "47": 2445,
+      "48": 3520,
+      "49": 2119,
+      "5": 954222,
+      "50": 2862,
+      "51": 1863,
+      "52": 2752,
+      "53": 1765,
+      "54": 2531,
+      "55": 1737,
+      "56": 2564,
+      "57": 1781,
+      "58": 2286,
+      "59": 1753,
+      "6": 5296446,
+      "60": 2507,
+      "61": 1630,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2072972,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6528363,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1856292,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59037,
+      "7": 32936113,
+      "9": 131476
+    },
+    "connectivity_max": 146828786,
+    "connectivity_min": 0,
+    "n_cells": 33126626,
+    "n_connectivity_values": 359899709,
+    "n_fan_triangles": 293646457,
+    "n_points": 146828787
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.3163977137627594e-11,
+    "float64_area_closure_relative": 2.9801276326824543e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293646457,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945380.782739401,
+    "surface_area_float64_in2": 1945380.7828233715,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945380.7828234294,
+    "zero_area_triangles": 241995,
+    "zero_weight_points": 6117
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC020_AoA_16.json b/surface_dual_areas/cases/geo_LHC020_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ee9e161ef948b0dbc76177ec4d35d17e6dbb0c2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC020_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC020_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC020_AoA_16/boundary_dual_area_geo_LHC020_AoA_16.npy",
+    "sha256": "eb484bf6b9e317f3e4524735787eee6801fd9e158e1316cfd4629aa5ed0484da",
+    "shape": [
+      147603783
+    ],
+    "size_bytes": 590415260
+  },
+  "runtime": {
+    "accumulation_seconds": 11.645509297959507,
+    "completed_at_utc": "2026-08-07T07:22:27.177257Z",
+    "elapsed_seconds": 22.504973283037543,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1564270628150553,
+    "geometry_read_seconds": 2.097272406099364,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:22:04.672183Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC020_AoA_16/boundary_geo_LHC020_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC020_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624449000000000,
+    "extracted_vtu_size_bytes": 22679865178,
+    "geometry_sha256": "d575fae519a11764eb51874af9ecbd9e46ac313a42db54ee2913dcfe01e793f7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4465289,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1272448,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3055835,
+      "13": 827612,
+      "14": 1366722,
+      "15": 476164,
+      "16": 912825,
+      "17": 363777,
+      "18": 754363,
+      "19": 306858,
+      "20": 673187,
+      "21": 222142,
+      "22": 347152,
+      "23": 117332,
+      "24": 193922,
+      "25": 67748,
+      "26": 89625,
+      "27": 51257,
+      "28": 123176,
+      "29": 53161,
+      "3": 59463,
+      "30": 115930,
+      "31": 49493,
+      "32": 108275,
+      "33": 38476,
+      "34": 66230,
+      "35": 27787,
+      "36": 61919,
+      "37": 22867,
+      "38": 38779,
+      "39": 16330,
+      "4": 131945,
+      "40": 29818,
+      "41": 10888,
+      "42": 14508,
+      "43": 5940,
+      "44": 7755,
+      "45": 3673,
+      "46": 4163,
+      "47": 2446,
+      "48": 3520,
+      "49": 2118,
+      "5": 946525,
+      "50": 2862,
+      "51": 1863,
+      "52": 2753,
+      "53": 1765,
+      "54": 2529,
+      "55": 1737,
+      "56": 2564,
+      "57": 1781,
+      "58": 2286,
+      "59": 1752,
+      "6": 5251242,
+      "60": 2507,
+      "61": 1630,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 2070271,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6613162,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1894566,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59463,
+      "7": 33192233,
+      "9": 131945
+    },
+    "connectivity_max": 147603782,
+    "connectivity_min": 0,
+    "n_cells": 33383641,
+    "n_connectivity_values": 361963731,
+    "n_fan_triangles": 295196449,
+    "n_points": 147603783
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.2941231533421237e-11,
+    "float64_area_closure_relative": 3.075873704068201e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295196449,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945381.4159317715,
+    "surface_area_float64_in2": 1945381.4160153086,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945381.4160153684,
+    "zero_area_triangles": 243054,
+    "zero_weight_points": 6213
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC020_AoA_18.json b/surface_dual_areas/cases/geo_LHC020_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..24d7f22ba057c0bd128b1aeb537fa7b0770fddea
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC020_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC020_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC020_AoA_18/boundary_dual_area_geo_LHC020_AoA_18.npy",
+    "sha256": "cd98270bb842d085d8d4ac6056a4d557dcc71b355510257b8e76ba83596bf024",
+    "shape": [
+      148300344
+    ],
+    "size_bytes": 593201504
+  },
+  "runtime": {
+    "accumulation_seconds": 11.364618737949058,
+    "completed_at_utc": "2026-08-07T07:34:26.672517Z",
+    "elapsed_seconds": 53.74089624895714,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.373498692177236,
+    "geometry_read_seconds": 33.9200999638997,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:33:32.931530Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC020_AoA_18/boundary_geo_LHC020_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC020_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624480000000000,
+    "extracted_vtu_size_bytes": 22788522781,
+    "geometry_sha256": "d3c94ebe73d946c4de23a305e077bd5830b04126167b2273db90345a883094a7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4576764,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1307309,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3095882,
+      "13": 830928,
+      "14": 1313207,
+      "15": 466497,
+      "16": 894726,
+      "17": 360692,
+      "18": 753382,
+      "19": 307226,
+      "20": 674657,
+      "21": 222438,
+      "22": 350784,
+      "23": 117629,
+      "24": 195905,
+      "25": 67899,
+      "26": 89909,
+      "27": 51279,
+      "28": 123197,
+      "29": 53165,
+      "3": 60555,
+      "30": 115929,
+      "31": 49493,
+      "32": 108276,
+      "33": 38477,
+      "34": 66228,
+      "35": 27786,
+      "36": 61919,
+      "37": 22867,
+      "38": 38780,
+      "39": 16331,
+      "4": 134397,
+      "40": 29818,
+      "41": 10888,
+      "42": 14508,
+      "43": 5940,
+      "44": 7755,
+      "45": 3672,
+      "46": 4162,
+      "47": 2445,
+      "48": 3520,
+      "49": 2119,
+      "5": 948823,
+      "50": 2862,
+      "51": 1863,
+      "52": 2752,
+      "53": 1765,
+      "54": 2531,
+      "55": 1737,
+      "56": 2564,
+      "57": 1781,
+      "58": 2286,
+      "59": 1752,
+      "6": 5251077,
+      "60": 2507,
+      "61": 1630,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 2084519,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6664124,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1933463,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60555,
+      "7": 33411352,
+      "9": 134397
+    },
+    "connectivity_max": 148300343,
+    "connectivity_min": 0,
+    "n_cells": 33606304,
+    "n_connectivity_values": 363802179,
+    "n_fan_triangles": 296589571,
+    "n_points": 148300344
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.33224306397973e-11,
+    "float64_area_closure_relative": 2.262024176024159e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296589571,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945381.137615435,
+    "surface_area_float64_in2": 1945381.1376997137,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945381.1376997577,
+    "zero_area_triangles": 243956,
+    "zero_weight_points": 6275
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC020_AoA_20.json b/surface_dual_areas/cases/geo_LHC020_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..3fdfea75953e918aacfe9bc61ea8a98c1a9b2dbf
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC020_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC020_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC020_AoA_20/boundary_dual_area_geo_LHC020_AoA_20.npy",
+    "sha256": "85d7eae253e134dae0536ba363cec09371a72c12f722522a7c3e6fc26cf40161",
+    "shape": [
+      148275787
+    ],
+    "size_bytes": 593103276
+  },
+  "runtime": {
+    "accumulation_seconds": 11.515912350034341,
+    "completed_at_utc": "2026-08-07T07:31:13.459438Z",
+    "elapsed_seconds": 22.628014859976247,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.505992989987135,
+    "geometry_read_seconds": 2.0908653850201517,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:30:50.831327Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC020_AoA_20/boundary_geo_LHC020_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC020_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624653000000000,
+    "extracted_vtu_size_bytes": 22785042212,
+    "geometry_sha256": "ba8c2ef0c3f5ea9b6f01b9a214646e1c4eabc77603d834af1e29bd2a404ab02e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4600382,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1322202,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3109701,
+      "13": 830301,
+      "14": 1266230,
+      "15": 457030,
+      "16": 880359,
+      "17": 357832,
+      "18": 752853,
+      "19": 307500,
+      "20": 677542,
+      "21": 223513,
+      "22": 356948,
+      "23": 118750,
+      "24": 199505,
+      "25": 68391,
+      "26": 90424,
+      "27": 51381,
+      "28": 123260,
+      "29": 53182,
+      "3": 60794,
+      "30": 115923,
+      "31": 49496,
+      "32": 108276,
+      "33": 38477,
+      "34": 66228,
+      "35": 27786,
+      "36": 61919,
+      "37": 22867,
+      "38": 38779,
+      "39": 16331,
+      "4": 134696,
+      "40": 29819,
+      "41": 10887,
+      "42": 14508,
+      "43": 5941,
+      "44": 7754,
+      "45": 3673,
+      "46": 4162,
+      "47": 2445,
+      "48": 3520,
+      "49": 2119,
+      "5": 947960,
+      "50": 2863,
+      "51": 1862,
+      "52": 2752,
+      "53": 1765,
+      "54": 2531,
+      "55": 1737,
+      "56": 2564,
+      "57": 1782,
+      "58": 2286,
+      "59": 1752,
+      "6": 5241053,
+      "60": 2507,
+      "61": 1630,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2087428,
+      "70": 1013,
+      "71": 565,
+      "72": 670,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6670694,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1946680,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60794,
+      "7": 33416969,
+      "9": 134696
+    },
+    "connectivity_max": 148275786,
+    "connectivity_min": 0,
+    "n_cells": 33612459,
+    "n_connectivity_values": 363765374,
+    "n_fan_triangles": 296540456,
+    "n_points": 148275787
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.377136309564223e-11,
+    "float64_area_closure_relative": 1.0292808055848607e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296540456,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945381.2064413817,
+    "surface_area_float64_in2": 1945381.2065265337,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945381.2065265537,
+    "zero_area_triangles": 243554,
+    "zero_weight_points": 6200
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC021_AoA_14.json b/surface_dual_areas/cases/geo_LHC021_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..75a00993812a663d36137bb3b1b8d60396295f2d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC021_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC021_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC021_AoA_14/boundary_dual_area_geo_LHC021_AoA_14.npy",
+    "sha256": "71bff268e4467110b45fa2b25a424504d9c3f159b0c1c38eca3a3d1e807ccea8",
+    "shape": [
+      142778296
+    ],
+    "size_bytes": 571113312
+  },
+  "runtime": {
+    "accumulation_seconds": 10.839010613970459,
+    "completed_at_utc": "2026-08-07T07:22:38.375833Z",
+    "elapsed_seconds": 21.244644702179357,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.040771988919005,
+    "geometry_read_seconds": 2.5702914351131767,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:22:17.131091Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC021_AoA_14/boundary_geo_LHC021_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC021_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624398000000000,
+    "extracted_vtu_size_bytes": 21936185775,
+    "geometry_sha256": "03babef43f11ffa4c51817695c97d195dd6a3d6a2759bbd36676c7f835153ac3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4274372,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1228559,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2762891,
+      "13": 762729,
+      "14": 1283510,
+      "15": 433766,
+      "16": 904149,
+      "17": 345952,
+      "18": 748015,
+      "19": 303059,
+      "20": 671671,
+      "21": 226863,
+      "22": 360234,
+      "23": 123265,
+      "24": 199043,
+      "25": 68553,
+      "26": 92310,
+      "27": 51504,
+      "28": 123976,
+      "29": 53138,
+      "3": 53938,
+      "30": 115718,
+      "31": 49750,
+      "32": 108612,
+      "33": 38718,
+      "34": 66045,
+      "35": 27925,
+      "36": 61772,
+      "37": 22928,
+      "38": 38260,
+      "39": 16233,
+      "4": 121400,
+      "40": 29141,
+      "41": 10734,
+      "42": 14248,
+      "43": 5841,
+      "44": 7635,
+      "45": 3640,
+      "46": 4141,
+      "47": 2496,
+      "48": 3503,
+      "49": 2139,
+      "5": 935237,
+      "50": 2924,
+      "51": 1803,
+      "52": 2750,
+      "53": 1764,
+      "54": 2487,
+      "55": 1685,
+      "56": 2508,
+      "57": 1738,
+      "58": 2289,
+      "59": 1743,
+      "6": 5221332,
+      "60": 2508,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2034760,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6297335,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1847555,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53938,
+      "7": 32028008,
+      "9": 121400
+    },
+    "connectivity_max": 142778295,
+    "connectivity_min": 0,
+    "n_cells": 32203346,
+    "n_connectivity_values": 349952173,
+    "n_fan_triangles": 285545481,
+    "n_points": 142778296
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.007553714333401e-11,
+    "float64_area_closure_relative": 8.769498923395228e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285545481,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938153.7228857798,
+    "surface_area_float64_in2": 1938153.7229440708,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938153.7229440538,
+    "zero_area_triangles": 240032,
+    "zero_weight_points": 5728
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC021_AoA_16.json b/surface_dual_areas/cases/geo_LHC021_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..3bd2857ef56f207b9ee9d8304fb9802c0c23857f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC021_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC021_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC021_AoA_16/boundary_dual_area_geo_LHC021_AoA_16.npy",
+    "sha256": "9ceb56729526e70dc05da039960f56ade0bdacb575f02297655e50c395625078",
+    "shape": [
+      141884948
+    ],
+    "size_bytes": 567539920
+  },
+  "runtime": {
+    "accumulation_seconds": 10.658724062843248,
+    "completed_at_utc": "2026-08-07T07:22:13.065094Z",
+    "elapsed_seconds": 21.08087537297979,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2662745111156255,
+    "geometry_read_seconds": 2.185790847055614,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:21:51.984126Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC021_AoA_16/boundary_geo_LHC021_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC021_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624558000000000,
+    "extracted_vtu_size_bytes": 21797355896,
+    "geometry_sha256": "22547bd572b0dddf14574cf95551407069c804799a5f22329577b90bf4ff7525",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4132871,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1210218,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2745038,
+      "13": 763398,
+      "14": 1294914,
+      "15": 439330,
+      "16": 903808,
+      "17": 346052,
+      "18": 744314,
+      "19": 301847,
+      "20": 671522,
+      "21": 226929,
+      "22": 364534,
+      "23": 123729,
+      "24": 201940,
+      "25": 69031,
+      "26": 92932,
+      "27": 51745,
+      "28": 124150,
+      "29": 53184,
+      "3": 52049,
+      "30": 115734,
+      "31": 49750,
+      "32": 108609,
+      "33": 38721,
+      "34": 66044,
+      "35": 27929,
+      "36": 61772,
+      "37": 22926,
+      "38": 38258,
+      "39": 16235,
+      "4": 118580,
+      "40": 29143,
+      "41": 10732,
+      "42": 14248,
+      "43": 5841,
+      "44": 7635,
+      "45": 3640,
+      "46": 4141,
+      "47": 2498,
+      "48": 3504,
+      "49": 2139,
+      "5": 933306,
+      "50": 2923,
+      "51": 1803,
+      "52": 2751,
+      "53": 1764,
+      "54": 2485,
+      "55": 1685,
+      "56": 2508,
+      "57": 1738,
+      "58": 2289,
+      "59": 1743,
+      "6": 5220665,
+      "60": 2508,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2027670,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6227846,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1822921,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52049,
+      "7": 31768142,
+      "9": 118580
+    },
+    "connectivity_max": 141884947,
+    "connectivity_min": 0,
+    "n_cells": 31938771,
+    "n_connectivity_values": 347636327,
+    "n_fan_triangles": 283758785,
+    "n_points": 141884948
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.995852204127652e-11,
+    "float64_area_closure_relative": 2.8110440756659233e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283758785,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938154.2639265328,
+    "surface_area_float64_in2": 1938154.263984597,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938154.2639846515,
+    "zero_area_triangles": 238015,
+    "zero_weight_points": 5590
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC022_AoA_16.json b/surface_dual_areas/cases/geo_LHC022_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..b4b2b1459e77422599a3d134730e28fa4deddca3
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC022_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC022_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC022_AoA_16/boundary_dual_area_geo_LHC022_AoA_16.npy",
+    "sha256": "62336d15199e36c81b14f1a5f7b043b0e276f09159c63528701035ee73c0dd6f",
+    "shape": [
+      139684091
+    ],
+    "size_bytes": 558736492
+  },
+  "runtime": {
+    "accumulation_seconds": 10.638313068076968,
+    "completed_at_utc": "2026-08-07T07:23:00.936886Z",
+    "elapsed_seconds": 20.990094627952203,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.071286452934146,
+    "geometry_read_seconds": 2.6022371950093657,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:22:39.946697Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC022_AoA_16/boundary_geo_LHC022_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC022_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624514000000000,
+    "extracted_vtu_size_bytes": 21454721221,
+    "geometry_sha256": "1da9d2ecdab195b9e19764bd43f460ad1552373bd7f382b3fc3fceacb6fd63c6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3725289,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1203360,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2601587,
+      "13": 799212,
+      "14": 1358708,
+      "15": 476108,
+      "16": 915953,
+      "17": 363642,
+      "18": 748235,
+      "19": 304050,
+      "20": 661815,
+      "21": 224504,
+      "22": 356323,
+      "23": 122048,
+      "24": 207293,
+      "25": 68692,
+      "26": 95468,
+      "27": 51743,
+      "28": 123888,
+      "29": 53005,
+      "3": 53859,
+      "30": 114757,
+      "31": 49434,
+      "32": 108383,
+      "33": 38750,
+      "34": 66388,
+      "35": 27800,
+      "36": 62487,
+      "37": 22856,
+      "38": 38950,
+      "39": 16341,
+      "4": 121197,
+      "40": 30039,
+      "41": 10849,
+      "42": 14598,
+      "43": 5962,
+      "44": 7844,
+      "45": 3674,
+      "46": 4289,
+      "47": 2527,
+      "48": 3540,
+      "49": 2143,
+      "5": 928628,
+      "50": 2917,
+      "51": 1841,
+      "52": 2747,
+      "53": 1777,
+      "54": 2443,
+      "55": 1705,
+      "56": 2584,
+      "57": 1716,
+      "58": 2307,
+      "59": 1704,
+      "6": 5197400,
+      "60": 2448,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2013046,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6016367,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1794814,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53859,
+      "7": 31087404,
+      "9": 121197
+    },
+    "connectivity_max": 139684090,
+    "connectivity_min": 0,
+    "n_cells": 31262460,
+    "n_connectivity_values": 341881983,
+    "n_fan_triangles": 279357063,
+    "n_points": 139684091
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.141520677542328e-11,
+    "float64_area_closure_relative": 3.8305496891419834e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279357063,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938963.8916065076,
+    "surface_area_float64_in2": 1938963.8916868102,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938963.8916868845,
+    "zero_area_triangles": 238019,
+    "zero_weight_points": 5525
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC022_AoA_20.json b/surface_dual_areas/cases/geo_LHC022_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..50dc5fb32651092672e8c58a5ae1caeedddd55f8
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC022_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC022_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC022_AoA_20/boundary_dual_area_geo_LHC022_AoA_20.npy",
+    "sha256": "0b0cfd39c3fc08e54a62d9d563ea1df17a1ecf6cc7261f0b9a82be2f64cfa598",
+    "shape": [
+      140419116
+    ],
+    "size_bytes": 561676592
+  },
+  "runtime": {
+    "accumulation_seconds": 10.615310549037531,
+    "completed_at_utc": "2026-08-07T07:22:35.928233Z",
+    "elapsed_seconds": 21.367701657814905,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.947533499915153,
+    "geometry_read_seconds": 3.0121199199929833,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:22:14.560437Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC022_AoA_20/boundary_geo_LHC022_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC022_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624493000000000,
+    "extracted_vtu_size_bytes": 21569940713,
+    "geometry_sha256": "6da152f5dbdfc1bedb2191e5bf0c012822cc99526747aaee267acc8e1679aa7a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3883396,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1237887,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2638743,
+      "13": 789729,
+      "14": 1260195,
+      "15": 458906,
+      "16": 898660,
+      "17": 359921,
+      "18": 742371,
+      "19": 302570,
+      "20": 659568,
+      "21": 226301,
+      "22": 365353,
+      "23": 125409,
+      "24": 213167,
+      "25": 70877,
+      "26": 96513,
+      "27": 52242,
+      "28": 124098,
+      "29": 53058,
+      "3": 52507,
+      "30": 114784,
+      "31": 49440,
+      "32": 108388,
+      "33": 38743,
+      "34": 66385,
+      "35": 27806,
+      "36": 62487,
+      "37": 22862,
+      "38": 38950,
+      "39": 16337,
+      "4": 120182,
+      "40": 30041,
+      "41": 10850,
+      "42": 14598,
+      "43": 5965,
+      "44": 7846,
+      "45": 3671,
+      "46": 4290,
+      "47": 2527,
+      "48": 3534,
+      "49": 2141,
+      "5": 928533,
+      "50": 2917,
+      "51": 1842,
+      "52": 2748,
+      "53": 1777,
+      "54": 2441,
+      "55": 1705,
+      "56": 2584,
+      "57": 1716,
+      "58": 2307,
+      "59": 1704,
+      "6": 5203603,
+      "60": 2448,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2034004,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6104718,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1841121,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52507,
+      "7": 31347203,
+      "9": 120182
+    },
+    "connectivity_max": 140419115,
+    "connectivity_min": 0,
+    "n_cells": 31519892,
+    "n_connectivity_values": 343866896,
+    "n_fan_triangles": 280827112,
+    "n_points": 140419116
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.190428695855516e-11,
+    "float64_area_closure_relative": 5.391588057538261e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280827112,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938964.1397035625,
+    "surface_area_float64_in2": 1938964.1397848134,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938964.139784918,
+    "zero_area_triangles": 237847,
+    "zero_weight_points": 5538
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC023_AoA_16.json b/surface_dual_areas/cases/geo_LHC023_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..2e938294cd11c276b27016f6f388d0149d560065
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC023_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC023_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC023_AoA_16/boundary_dual_area_geo_LHC023_AoA_16.npy",
+    "sha256": "7b24d6b620eefbbd043f815b18c840fdecc6e4b5d59bd7a3efa7bb7c31ec7425",
+    "shape": [
+      146588507
+    ],
+    "size_bytes": 586354156
+  },
+  "runtime": {
+    "accumulation_seconds": 11.448392199119553,
+    "completed_at_utc": "2026-08-07T07:33:55.940226Z",
+    "elapsed_seconds": 23.426246829796582,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.387163922889158,
+    "geometry_read_seconds": 3.5584793898742646,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:33:32.513895Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC023_AoA_16/boundary_geo_LHC023_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC023_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624468000000000,
+    "extracted_vtu_size_bytes": 22520568522,
+    "geometry_sha256": "f753f36a20ef368a94f9d8372214b19633845e2cbdd297ecad4cf2828a5fff34",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4246052,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1380637,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2815182,
+      "13": 875071,
+      "14": 1387839,
+      "15": 487591,
+      "16": 907211,
+      "17": 359281,
+      "18": 749196,
+      "19": 303285,
+      "20": 677582,
+      "21": 224184,
+      "22": 363072,
+      "23": 121258,
+      "24": 210086,
+      "25": 70408,
+      "26": 92362,
+      "27": 51752,
+      "28": 123614,
+      "29": 52872,
+      "3": 59796,
+      "30": 114593,
+      "31": 49395,
+      "32": 109613,
+      "33": 39079,
+      "34": 67506,
+      "35": 28152,
+      "36": 63708,
+      "37": 23054,
+      "38": 38837,
+      "39": 15932,
+      "4": 133840,
+      "40": 29208,
+      "41": 10646,
+      "42": 14044,
+      "43": 5792,
+      "44": 7778,
+      "45": 3710,
+      "46": 4205,
+      "47": 2488,
+      "48": 3494,
+      "49": 2138,
+      "5": 942285,
+      "50": 2755,
+      "51": 1721,
+      "52": 2478,
+      "53": 1601,
+      "54": 2185,
+      "55": 1617,
+      "56": 2424,
+      "57": 1723,
+      "58": 2259,
+      "59": 1680,
+      "6": 5175468,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 921,
+      "7": 2105963,
+      "70": 991,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6433506,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1995846,
+      "90": 58,
+      "91": 57,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59796,
+      "7": 32828573,
+      "9": 133840
+    },
+    "connectivity_max": 146588506,
+    "connectivity_min": 0,
+    "n_cells": 33022209,
+    "n_connectivity_values": 359210314,
+    "n_fan_triangles": 293165896,
+    "n_points": 146588507
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.522066808633114e-11,
+    "float64_area_closure_relative": 2.619268385007851e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293165896,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946723.415219961,
+    "surface_area_float64_in2": 1946723.4152885259,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946723.4152885769,
+    "zero_area_triangles": 244923,
+    "zero_weight_points": 6038
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC024_AoA_12.json b/surface_dual_areas/cases/geo_LHC024_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..580f4fcd9b4c4dbfc5655d77bb888c8d8ca0f589
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC024_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC024_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC024_AoA_12/boundary_dual_area_geo_LHC024_AoA_12.npy",
+    "sha256": "1f00a61c55c5169a9cf920b27ac66ad89f10563a0cdd2b5af6087fce665f7d00",
+    "shape": [
+      148646538
+    ],
+    "size_bytes": 594586280
+  },
+  "runtime": {
+    "accumulation_seconds": 11.587058841949329,
+    "completed_at_utc": "2026-08-07T07:33:16.766504Z",
+    "elapsed_seconds": 77.63942651008256,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6259751189500093,
+    "geometry_read_seconds": 2.035197164164856,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:31:59.126993Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC024_AoA_12/boundary_geo_LHC024_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC024_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624622000000000,
+    "extracted_vtu_size_bytes": 22842449824,
+    "geometry_sha256": "d6c9c11ac1ced387da52b37b0f5c5cb7c88c13365982a962e428a8b30f1932a3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4269831,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1386210,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3016588,
+      "13": 872475,
+      "14": 1432549,
+      "15": 474792,
+      "16": 947456,
+      "17": 359965,
+      "18": 737731,
+      "19": 298175,
+      "20": 658981,
+      "21": 218359,
+      "22": 348174,
+      "23": 118094,
+      "24": 198224,
+      "25": 69668,
+      "26": 91635,
+      "27": 51998,
+      "28": 123840,
+      "29": 52911,
+      "3": 60197,
+      "30": 113803,
+      "31": 49160,
+      "32": 107446,
+      "33": 38439,
+      "34": 66334,
+      "35": 27845,
+      "36": 62853,
+      "37": 23075,
+      "38": 38898,
+      "39": 16555,
+      "4": 136863,
+      "40": 30061,
+      "41": 10964,
+      "42": 14618,
+      "43": 5985,
+      "44": 7837,
+      "45": 3648,
+      "46": 4371,
+      "47": 2554,
+      "48": 3546,
+      "49": 2125,
+      "5": 966443,
+      "50": 2888,
+      "51": 1876,
+      "52": 2741,
+      "53": 1796,
+      "54": 2439,
+      "55": 1720,
+      "56": 2575,
+      "57": 1731,
+      "58": 2316,
+      "59": 1695,
+      "6": 5345214,
+      "60": 2440,
+      "61": 1665,
+      "62": 2197,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2150080,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6639264,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2013444,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60197,
+      "7": 33516863,
+      "9": 136863
+    },
+    "connectivity_max": 148646537,
+    "connectivity_min": 0,
+    "n_cells": 33713923,
+    "n_connectivity_values": 364709787,
+    "n_fan_triangles": 297281941,
+    "n_points": 148646538
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.7931476521908677e-11,
+    "float64_area_closure_relative": 5.2721199906530244e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 297281941,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947571.641588727,
+    "surface_area_float64_in2": 1947571.6416431256,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947571.6416432282,
+    "zero_area_triangles": 242231,
+    "zero_weight_points": 6143
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC026_AoA_16.json b/surface_dual_areas/cases/geo_LHC026_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..edcc7add8bc55b67b576946127598803c10822f2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC026_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC026_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC026_AoA_16/boundary_dual_area_geo_LHC026_AoA_16.npy",
+    "sha256": "6e5053c0e7dcd7ae7fabf5c65f0a884eb06d3fdcb8153f2e358e929fdcd276e5",
+    "shape": [
+      142311930
+    ],
+    "size_bytes": 569247848
+  },
+  "runtime": {
+    "accumulation_seconds": 11.030567409005016,
+    "completed_at_utc": "2026-08-07T07:24:18.420291Z",
+    "elapsed_seconds": 21.45376038295217,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.057350765215233,
+    "geometry_read_seconds": 2.2897901670075953,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:23:56.966425Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC026_AoA_16/boundary_geo_LHC026_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC026_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624709000000000,
+    "extracted_vtu_size_bytes": 21863264155,
+    "geometry_sha256": "e129a6a777a8a282774953874fdabba25b7ae5c46f200778f7f7ba458ef86e24",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3964174,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1295953,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2719654,
+      "13": 823897,
+      "14": 1341308,
+      "15": 468054,
+      "16": 917682,
+      "17": 358828,
+      "18": 738125,
+      "19": 300368,
+      "20": 654635,
+      "21": 222656,
+      "22": 351949,
+      "23": 121883,
+      "24": 201468,
+      "25": 68065,
+      "26": 94143,
+      "27": 51721,
+      "28": 124631,
+      "29": 52983,
+      "3": 54273,
+      "30": 114029,
+      "31": 48760,
+      "32": 107336,
+      "33": 38324,
+      "34": 66086,
+      "35": 27540,
+      "36": 63309,
+      "37": 22905,
+      "38": 39219,
+      "39": 16418,
+      "4": 123078,
+      "40": 30151,
+      "41": 10949,
+      "42": 14504,
+      "43": 5865,
+      "44": 7599,
+      "45": 3693,
+      "46": 4300,
+      "47": 2515,
+      "48": 3523,
+      "49": 2139,
+      "5": 942064,
+      "50": 2943,
+      "51": 1796,
+      "52": 2718,
+      "53": 1749,
+      "54": 2396,
+      "55": 1701,
+      "56": 2512,
+      "57": 1736,
+      "58": 2290,
+      "59": 1723,
+      "6": 5263403,
+      "60": 2506,
+      "61": 1654,
+      "62": 2230,
+      "63": 1637,
+      "64": 2177,
+      "65": 1376,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2055847,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6177962,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1884732,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54273,
+      "7": 31870023,
+      "9": 123078
+    },
+    "connectivity_max": 142311929,
+    "connectivity_min": 0,
+    "n_cells": 32047374,
+    "n_connectivity_values": 348707478,
+    "n_fan_triangles": 284612730,
+    "n_points": 142311930
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3571806758870185e-11,
+    "float64_area_closure_relative": 2.5827146477298503e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284612730,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938215.9940859831,
+    "surface_area_float64_in2": 1938215.9941510526,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938215.9941511026,
+    "zero_area_triangles": 240119,
+    "zero_weight_points": 5652
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC026_AoA_22.json b/surface_dual_areas/cases/geo_LHC026_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..ed21ac486b9006b8675edcb950fc0700165d3770
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC026_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC026_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC026_AoA_22/boundary_dual_area_geo_LHC026_AoA_22.npy",
+    "sha256": "389021f1e4625cb693e542f21400feedf67ca739f4575fccc972f88ef3a82233",
+    "shape": [
+      142522354
+    ],
+    "size_bytes": 570089544
+  },
+  "runtime": {
+    "accumulation_seconds": 10.895876770839095,
+    "completed_at_utc": "2026-08-07T07:34:17.574499Z",
+    "elapsed_seconds": 21.26726555498317,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4306273150723428,
+    "geometry_read_seconds": 2.126248650951311,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:33:56.307152Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC026_AoA_22/boundary_geo_LHC026_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC026_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624418000000000,
+    "extracted_vtu_size_bytes": 21897600599,
+    "geometry_sha256": "3c5f9c7ca2a7d5bb8d249aeff98421f4dd4a3e226be6c51b26ff00ecf755343b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4011667,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1292062,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2686941,
+      "13": 808157,
+      "14": 1284930,
+      "15": 461757,
+      "16": 919649,
+      "17": 359897,
+      "18": 732431,
+      "19": 297866,
+      "20": 652971,
+      "21": 222229,
+      "22": 359917,
+      "23": 124320,
+      "24": 207412,
+      "25": 70375,
+      "26": 95530,
+      "27": 52384,
+      "28": 124935,
+      "29": 53123,
+      "3": 52278,
+      "30": 114095,
+      "31": 48785,
+      "32": 107358,
+      "33": 38330,
+      "34": 66075,
+      "35": 27541,
+      "36": 63315,
+      "37": 22905,
+      "38": 39208,
+      "39": 16411,
+      "4": 121482,
+      "40": 30137,
+      "41": 10945,
+      "42": 14501,
+      "43": 5864,
+      "44": 7596,
+      "45": 3694,
+      "46": 4302,
+      "47": 2515,
+      "48": 3522,
+      "49": 2139,
+      "5": 947457,
+      "50": 2946,
+      "51": 1794,
+      "52": 2718,
+      "53": 1749,
+      "54": 2395,
+      "55": 1701,
+      "56": 2512,
+      "57": 1737,
+      "58": 2290,
+      "59": 1723,
+      "6": 5300782,
+      "60": 2506,
+      "61": 1654,
+      "62": 2230,
+      "63": 1637,
+      "64": 2177,
+      "65": 1376,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 905,
+      "7": 2084892,
+      "70": 1022,
+      "71": 572,
+      "72": 658,
+      "73": 440,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6270203,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1905563,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52278,
+      "7": 32001362,
+      "9": 121482
+    },
+    "connectivity_max": 142522353,
+    "connectivity_min": 0,
+    "n_cells": 32175122,
+    "n_connectivity_values": 349383821,
+    "n_fan_triangles": 285033577,
+    "n_points": 142522354
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.2650555026180656e-11,
+    "float64_area_closure_relative": 3.6998885026834396e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285033577,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938216.1973540434,
+    "surface_area_float64_in2": 1938216.1974173272,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938216.197417399,
+    "zero_area_triangles": 239265,
+    "zero_weight_points": 5630
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC027_AoA_10.json b/surface_dual_areas/cases/geo_LHC027_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..f55df3c42f31594f3176586a7a66b6076da67b30
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC027_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC027_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC027_AoA_10/boundary_dual_area_geo_LHC027_AoA_10.npy",
+    "sha256": "7d4c2b5a2bb5f128d8c542d4ed63ef89965c18294a7f08f5be0926cbd930855e",
+    "shape": [
+      138529440
+    ],
+    "size_bytes": 554117888
+  },
+  "runtime": {
+    "accumulation_seconds": 10.64357956405729,
+    "completed_at_utc": "2026-08-07T07:32:55.348600Z",
+    "elapsed_seconds": 57.122377288062125,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3760089338757098,
+    "geometry_read_seconds": 32.005762950051576,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:31:58.226140Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC027_AoA_10/boundary_geo_LHC027_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC027_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624404000000000,
+    "extracted_vtu_size_bytes": 21274246868,
+    "geometry_sha256": "fd484fae02287baa4684b2c97d18b874a55645c36ecdc92470831b79ad33c624",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3658708,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1149209,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2544857,
+      "13": 772621,
+      "14": 1465599,
+      "15": 475983,
+      "16": 953782,
+      "17": 359112,
+      "18": 747905,
+      "19": 300957,
+      "20": 662490,
+      "21": 222868,
+      "22": 342268,
+      "23": 120553,
+      "24": 200889,
+      "25": 68429,
+      "26": 94697,
+      "27": 51736,
+      "28": 124129,
+      "29": 52943,
+      "3": 49683,
+      "30": 115514,
+      "31": 49686,
+      "32": 109810,
+      "33": 39004,
+      "34": 67451,
+      "35": 28103,
+      "36": 62405,
+      "37": 22816,
+      "38": 38413,
+      "39": 16296,
+      "4": 111973,
+      "40": 29376,
+      "41": 10756,
+      "42": 14321,
+      "43": 5805,
+      "44": 7773,
+      "45": 3652,
+      "46": 4299,
+      "47": 2551,
+      "48": 3515,
+      "49": 2152,
+      "5": 921303,
+      "50": 2905,
+      "51": 1857,
+      "52": 2722,
+      "53": 1768,
+      "54": 2451,
+      "55": 1709,
+      "56": 2584,
+      "57": 1734,
+      "58": 2303,
+      "59": 1694,
+      "6": 5180875,
+      "60": 2445,
+      "61": 1666,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 1976378,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5849238,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1741540,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49683,
+      "7": 30717367,
+      "9": 111973
+    },
+    "connectivity_max": 138529439,
+    "connectivity_min": 0,
+    "n_cells": 30879023,
+    "n_connectivity_values": 338805797,
+    "n_fan_triangles": 277047751,
+    "n_points": 138529440
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4286294011118346e-11,
+    "float64_area_closure_relative": 4.7469798822960286e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277047751,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937402.4436699727,
+    "surface_area_float64_in2": 1937402.443736399,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937402.443736491,
+    "zero_area_triangles": 235616,
+    "zero_weight_points": 5548
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC027_AoA_16.json b/surface_dual_areas/cases/geo_LHC027_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..043460640a5e1426349bc45ab529243fc00b8097
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC027_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC027_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC027_AoA_16/boundary_dual_area_geo_LHC027_AoA_16.npy",
+    "sha256": "c86a9e9226d2c932d00d157fdde8e29a34ae7fbc69c871bd05696910a490b32e",
+    "shape": [
+      138740693
+    ],
+    "size_bytes": 554962900
+  },
+  "runtime": {
+    "accumulation_seconds": 10.497328951023519,
+    "completed_at_utc": "2026-08-07T07:24:02.463542Z",
+    "elapsed_seconds": 20.567840482108295,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.938350240001455,
+    "geometry_read_seconds": 2.2590399240143597,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:23:41.895590Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC027_AoA_16/boundary_geo_LHC027_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC027_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624435000000000,
+    "extracted_vtu_size_bytes": 21310148562,
+    "geometry_sha256": "73254aa34c2c66ea20e49f83bc0b3f9576cb94aa5588d61bc705d77c2cd978f7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3884141,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1188273,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2528161,
+      "13": 739678,
+      "14": 1241282,
+      "15": 431276,
+      "16": 886147,
+      "17": 347900,
+      "18": 758323,
+      "19": 305392,
+      "20": 680854,
+      "21": 230078,
+      "22": 371108,
+      "23": 126845,
+      "24": 215571,
+      "25": 71156,
+      "26": 96277,
+      "27": 52065,
+      "28": 124254,
+      "29": 52963,
+      "3": 52494,
+      "30": 115517,
+      "31": 49692,
+      "32": 109814,
+      "33": 39003,
+      "34": 67447,
+      "35": 28105,
+      "36": 62414,
+      "37": 22813,
+      "38": 38409,
+      "39": 16296,
+      "4": 117768,
+      "40": 29378,
+      "41": 10757,
+      "42": 14320,
+      "43": 5802,
+      "44": 7774,
+      "45": 3651,
+      "46": 4300,
+      "47": 2549,
+      "48": 3516,
+      "49": 2152,
+      "5": 924998,
+      "50": 2905,
+      "51": 1857,
+      "52": 2722,
+      "53": 1768,
+      "54": 2451,
+      "55": 1709,
+      "56": 2584,
+      "57": 1734,
+      "58": 2303,
+      "59": 1694,
+      "6": 5182227,
+      "60": 2445,
+      "61": 1666,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 1996464,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5978045,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1802424,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52494,
+      "7": 30894211,
+      "9": 117768
+    },
+    "connectivity_max": 138740692,
+    "connectivity_min": 0,
+    "n_cells": 31064473,
+    "n_connectivity_values": 339599203,
+    "n_fan_triangles": 277470257,
+    "n_points": 138740693
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4389400436802965e-11,
+    "float64_area_closure_relative": 4.4585551155672936e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277470257,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937402.735944968,
+    "surface_area_float64_in2": 1937402.736011594,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937402.7360116804,
+    "zero_area_triangles": 236634,
+    "zero_weight_points": 5564
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC028_AoA_18.json b/surface_dual_areas/cases/geo_LHC028_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..86ddf7165c399bd82b60eaca597d727b5c339484
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC028_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC028_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC028_AoA_18/boundary_dual_area_geo_LHC028_AoA_18.npy",
+    "sha256": "6c193fedfe70735a33d5d1fb461dcd9381a45024b2a961228321897a6d868960",
+    "shape": [
+      139184015
+    ],
+    "size_bytes": 556736188
+  },
+  "runtime": {
+    "accumulation_seconds": 10.591216234955937,
+    "completed_at_utc": "2026-08-07T07:24:50.464957Z",
+    "elapsed_seconds": 20.263456349028274,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.935404426883906,
+    "geometry_read_seconds": 2.213591655017808,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:24:30.201410Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC028_AoA_18/boundary_geo_LHC028_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC028_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624517000000000,
+    "extracted_vtu_size_bytes": 21378826301,
+    "geometry_sha256": "c7d0846d1f1fb9ad4b6257b4385b7a70603b51218a0d08b5c67cfed4ba1dd127",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3881200,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1215248,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2594919,
+      "13": 762952,
+      "14": 1217593,
+      "15": 439099,
+      "16": 874419,
+      "17": 354314,
+      "18": 748968,
+      "19": 306233,
+      "20": 667069,
+      "21": 228022,
+      "22": 369701,
+      "23": 125937,
+      "24": 221292,
+      "25": 71776,
+      "26": 98350,
+      "27": 52266,
+      "28": 124954,
+      "29": 53186,
+      "3": 51348,
+      "30": 114713,
+      "31": 49241,
+      "32": 107704,
+      "33": 38371,
+      "34": 65845,
+      "35": 27946,
+      "36": 62794,
+      "37": 22876,
+      "38": 39276,
+      "39": 16259,
+      "4": 116261,
+      "40": 29996,
+      "41": 10863,
+      "42": 14341,
+      "43": 5878,
+      "44": 7810,
+      "45": 3702,
+      "46": 4286,
+      "47": 2488,
+      "48": 3591,
+      "49": 2207,
+      "5": 923724,
+      "50": 2954,
+      "51": 1819,
+      "52": 2764,
+      "53": 1752,
+      "54": 2408,
+      "55": 1718,
+      "56": 2524,
+      "57": 1764,
+      "58": 2281,
+      "59": 1692,
+      "6": 5182045,
+      "60": 2462,
+      "61": 1655,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2008714,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6003378,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1819129,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51348,
+      "7": 31019507,
+      "9": 116261
+    },
+    "connectivity_max": 139184014,
+    "connectivity_min": 0,
+    "n_cells": 31187116,
+    "n_connectivity_values": 340731134,
+    "n_fan_triangles": 278356902,
+    "n_points": 139184015
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.749207412371346e-11,
+    "float64_area_closure_relative": 1.2018500903569918e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278356902,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937268.5954200947,
+    "surface_area_float64_in2": 1937268.595492727,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937268.5954927502,
+    "zero_area_triangles": 236996,
+    "zero_weight_points": 5572
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC028_AoA_6.json b/surface_dual_areas/cases/geo_LHC028_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..00fb15635519b8e8c82081df024d08eaba676279
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC028_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC028_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC028_AoA_6/boundary_dual_area_geo_LHC028_AoA_6.npy",
+    "sha256": "ecb9f0ed187f3af47a30f40e1d95fa72a3309620d1af48239d08bb748f3bb5af",
+    "shape": [
+      133795192
+    ],
+    "size_bytes": 535180896
+  },
+  "runtime": {
+    "accumulation_seconds": 10.32344628800638,
+    "completed_at_utc": "2026-08-07T07:35:24.910912Z",
+    "elapsed_seconds": 66.40027786395513,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.064454363891855,
+    "geometry_read_seconds": 1.8360272769350559,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:34:18.510535Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC028_AoA_6/boundary_geo_LHC028_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC028_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624593000000000,
+    "extracted_vtu_size_bytes": 20539168396,
+    "geometry_sha256": "c1205a985010224d3491cb1007201e2c33e36037260260f29e49c8875a13e745",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2942508,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 999249,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2196155,
+      "13": 755736,
+      "14": 1603273,
+      "15": 519905,
+      "16": 1035407,
+      "17": 381852,
+      "18": 762283,
+      "19": 307711,
+      "20": 661487,
+      "21": 224445,
+      "22": 346205,
+      "23": 121450,
+      "24": 201793,
+      "25": 68964,
+      "26": 94962,
+      "27": 51745,
+      "28": 124825,
+      "29": 53166,
+      "3": 49937,
+      "30": 114711,
+      "31": 49234,
+      "32": 107703,
+      "33": 38379,
+      "34": 65843,
+      "35": 27945,
+      "36": 62796,
+      "37": 22875,
+      "38": 39275,
+      "39": 16260,
+      "4": 111634,
+      "40": 29996,
+      "41": 10863,
+      "42": 14341,
+      "43": 5878,
+      "44": 7810,
+      "45": 3702,
+      "46": 4286,
+      "47": 2488,
+      "48": 3591,
+      "49": 2207,
+      "5": 922878,
+      "50": 2954,
+      "51": 1819,
+      "52": 2764,
+      "53": 1752,
+      "54": 2408,
+      "55": 1718,
+      "56": 2524,
+      "57": 1764,
+      "58": 2281,
+      "59": 1692,
+      "6": 5186254,
+      "60": 2462,
+      "61": 1655,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1934961,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5578755,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1590077,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49937,
+      "7": 29341061,
+      "9": 111634
+    },
+    "connectivity_max": 133795191,
+    "connectivity_min": 0,
+    "n_cells": 29502632,
+    "n_connectivity_values": 326584520,
+    "n_fan_triangles": 267579256,
+    "n_points": 133795192
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.623180175430402e-11,
+    "float64_area_closure_relative": 1.7306635394984458e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 267579256,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937269.25654532,
+    "surface_area_float64_in2": 1937269.2566155107,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937269.2566155442,
+    "zero_area_triangles": 228766,
+    "zero_weight_points": 5073
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC029_AoA_22.json b/surface_dual_areas/cases/geo_LHC029_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..75cc9bb3d11395f928f73732432eec0dcf668dc3
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC029_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC029_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC029_AoA_22/boundary_dual_area_geo_LHC029_AoA_22.npy",
+    "sha256": "148769b99e31a29c133b14baec24e2a0d9220190721aaf86a6b7efb8ef294e16",
+    "shape": [
+      148676988
+    ],
+    "size_bytes": 594708080
+  },
+  "runtime": {
+    "accumulation_seconds": 11.385298724053428,
+    "completed_at_utc": "2026-08-07T07:25:13.500690Z",
+    "elapsed_seconds": 21.99430417199619,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.143317969981581,
+    "geometry_read_seconds": 1.9205756201408803,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:24:51.506294Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC029_AoA_22/boundary_geo_LHC029_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC029_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624503000000000,
+    "extracted_vtu_size_bytes": 22846456952,
+    "geometry_sha256": "e1ef34eb1760f2d7ba5d1ee1768810696bb03fbf51b7a351732182826ba54a4b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4594794,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1447042,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2956060,
+      "13": 841719,
+      "14": 1287404,
+      "15": 431804,
+      "16": 886134,
+      "17": 339531,
+      "18": 740866,
+      "19": 297067,
+      "20": 675280,
+      "21": 224675,
+      "22": 375368,
+      "23": 126060,
+      "24": 213523,
+      "25": 72873,
+      "26": 92936,
+      "27": 52597,
+      "28": 124446,
+      "29": 53249,
+      "3": 61321,
+      "30": 115144,
+      "31": 49411,
+      "32": 108562,
+      "33": 38849,
+      "34": 66376,
+      "35": 28107,
+      "36": 62256,
+      "37": 23007,
+      "38": 38349,
+      "39": 16214,
+      "4": 138906,
+      "40": 29168,
+      "41": 10633,
+      "42": 14216,
+      "43": 5869,
+      "44": 7744,
+      "45": 3616,
+      "46": 4302,
+      "47": 2574,
+      "48": 3514,
+      "49": 2110,
+      "5": 938417,
+      "50": 2879,
+      "51": 1862,
+      "52": 2707,
+      "53": 1739,
+      "54": 2391,
+      "55": 1665,
+      "56": 2542,
+      "57": 1696,
+      "58": 2292,
+      "59": 1684,
+      "6": 5186291,
+      "60": 2441,
+      "61": 1666,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1370,
+      "66": 1770,
+      "67": 1096,
+      "68": 1503,
+      "69": 880,
+      "7": 2105177,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6689894,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 2066157,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61321,
+      "7": 33493712,
+      "9": 138906
+    },
+    "connectivity_max": 148676987,
+    "connectivity_min": 0,
+    "n_cells": 33693939,
+    "n_connectivity_values": 364730735,
+    "n_fan_triangles": 297342857,
+    "n_points": 148676988
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.372020423671249e-11,
+    "float64_area_closure_relative": 4.0757571058345323e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 297342857,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947987.7583686819,
+    "surface_area_float64_in2": 1947987.7584538483,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947987.7584539277,
+    "zero_area_triangles": 242110,
+    "zero_weight_points": 6063
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC030_AoA_16.json b/surface_dual_areas/cases/geo_LHC030_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..517189569315eb03c23af45220eb0641bf8ab3cb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC030_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC030_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC030_AoA_16/boundary_dual_area_geo_LHC030_AoA_16.npy",
+    "sha256": "508e5712f41e25a917f4810fc4c4c7e709935ad3042cfad22f9b84617aa2c9d2",
+    "shape": [
+      141233001
+    ],
+    "size_bytes": 564932132
+  },
+  "runtime": {
+    "accumulation_seconds": 10.818944714032114,
+    "completed_at_utc": "2026-08-07T07:42:28.986353Z",
+    "elapsed_seconds": 20.61357673094608,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.210422873031348,
+    "geometry_read_seconds": 1.8977398620918393,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:42:08.372688Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC030_AoA_16/boundary_geo_LHC030_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC030_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624633000000000,
+    "extracted_vtu_size_bytes": 21695020427,
+    "geometry_sha256": "5b5065a870febbdf6d7210220d67c8a49d2eebb2e2c8ee4d54f0ce34b505eec9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4034672,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1191299,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2730980,
+      "13": 748585,
+      "14": 1308661,
+      "15": 431756,
+      "16": 907657,
+      "17": 345207,
+      "18": 746571,
+      "19": 302291,
+      "20": 671620,
+      "21": 228024,
+      "22": 365734,
+      "23": 126449,
+      "24": 210360,
+      "25": 71337,
+      "26": 94229,
+      "27": 52034,
+      "28": 124367,
+      "29": 52994,
+      "3": 54019,
+      "30": 115235,
+      "31": 49685,
+      "32": 110373,
+      "33": 39106,
+      "34": 66994,
+      "35": 27969,
+      "36": 61867,
+      "37": 22989,
+      "38": 38069,
+      "39": 16203,
+      "4": 118273,
+      "40": 29081,
+      "41": 10678,
+      "42": 14176,
+      "43": 5804,
+      "44": 7629,
+      "45": 3585,
+      "46": 4125,
+      "47": 2506,
+      "48": 3536,
+      "49": 2089,
+      "5": 932583,
+      "50": 2904,
+      "51": 1836,
+      "52": 2761,
+      "53": 1739,
+      "54": 2438,
+      "55": 1699,
+      "56": 2505,
+      "57": 1727,
+      "58": 2270,
+      "59": 1736,
+      "6": 5170516,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2039041,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6150854,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1818395,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 54019,
+      "7": 31532590,
+      "9": 118273
+    },
+    "connectivity_max": 141233000,
+    "connectivity_min": 0,
+    "n_cells": 31704882,
+    "n_connectivity_values": 345864644,
+    "n_fan_triangles": 282454880,
+    "n_points": 141233001
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5982245508131976e-11,
+    "float64_area_closure_relative": 1.6087567350179622e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282454880,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939342.6967158935,
+    "surface_area_float64_in2": 1939342.6967856754,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939342.6967857066,
+    "zero_area_triangles": 238974,
+    "zero_weight_points": 5683
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC030_AoA_18.json b/surface_dual_areas/cases/geo_LHC030_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..99e2790d00b0dd21fcc80abdc10a38851cb622d6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC030_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC030_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC030_AoA_18/boundary_dual_area_geo_LHC030_AoA_18.npy",
+    "sha256": "d59ad20fee0542ebb054c913e04a9463c26452896626f318c7c870bd01288799",
+    "shape": [
+      140924006
+    ],
+    "size_bytes": 563696152
+  },
+  "runtime": {
+    "accumulation_seconds": 11.474663578905165,
+    "completed_at_utc": "2026-08-07T07:38:23.831492Z",
+    "elapsed_seconds": 61.254997161915526,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.729696075897664,
+    "geometry_read_seconds": 40.968974431976676,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:37:22.576396Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC030_AoA_18/boundary_geo_LHC030_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC030_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624399000000000,
+    "extracted_vtu_size_bytes": 21646740667,
+    "geometry_sha256": "0ded209eab289915ec556b7a92cd3439b3220f02851c4d441077bd204f81ce5b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4038102,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1181318,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2706970,
+      "13": 745015,
+      "14": 1309398,
+      "15": 435281,
+      "16": 906904,
+      "17": 346518,
+      "18": 750349,
+      "19": 303442,
+      "20": 673642,
+      "21": 228182,
+      "22": 364737,
+      "23": 126249,
+      "24": 209975,
+      "25": 71210,
+      "26": 94255,
+      "27": 52047,
+      "28": 124374,
+      "29": 52992,
+      "3": 54128,
+      "30": 115239,
+      "31": 49687,
+      "32": 110368,
+      "33": 39103,
+      "34": 66995,
+      "35": 27973,
+      "36": 61867,
+      "37": 22986,
+      "38": 38074,
+      "39": 16205,
+      "4": 118717,
+      "40": 29077,
+      "41": 10681,
+      "42": 14171,
+      "43": 5802,
+      "44": 7632,
+      "45": 3586,
+      "46": 4124,
+      "47": 2506,
+      "48": 3536,
+      "49": 2089,
+      "5": 930527,
+      "50": 2904,
+      "51": 1836,
+      "52": 2761,
+      "53": 1739,
+      "54": 2438,
+      "55": 1699,
+      "56": 2505,
+      "57": 1727,
+      "58": 2270,
+      "59": 1736,
+      "6": 5150283,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2028577,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6116336,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1807038,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 54128,
+      "7": 31430097,
+      "9": 118717
+    },
+    "connectivity_max": 140924005,
+    "connectivity_min": 0,
+    "n_cells": 31602942,
+    "n_connectivity_values": 345042774,
+    "n_fan_triangles": 281836890,
+    "n_points": 140924006
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.615223709956565e-11,
+    "float64_area_closure_relative": 4.934319887596091e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281836890,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939343.1459284844,
+    "surface_area_float64_in2": 1939343.145998596,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939343.1459986917,
+    "zero_area_triangles": 238965,
+    "zero_weight_points": 5727
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC031_AoA_20.json b/surface_dual_areas/cases/geo_LHC031_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..e14dca079c8e5a089e528d4a5f4d5f1fb4a5d7b7
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC031_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC031_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC031_AoA_20/boundary_dual_area_geo_LHC031_AoA_20.npy",
+    "sha256": "f042ad8d4b65c0cc3605d6eed4249aebc58c02b875de2c764b181c091efeed31",
+    "shape": [
+      140817642
+    ],
+    "size_bytes": 563270696
+  },
+  "runtime": {
+    "accumulation_seconds": 10.910978042054921,
+    "completed_at_utc": "2026-08-07T07:42:51.001569Z",
+    "elapsed_seconds": 21.087467161938548,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.266065434087068,
+    "geometry_read_seconds": 2.2183274989947677,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:42:29.914009Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC031_AoA_20/boundary_geo_LHC031_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC031_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624441000000000,
+    "extracted_vtu_size_bytes": 21630399863,
+    "geometry_sha256": "cf817be1e3dac4cb63e8071c4245a8db86dc01432b83881ffa86905ea8e2338c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3932861,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1204477,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2696372,
+      "13": 788436,
+      "14": 1355365,
+      "15": 465735,
+      "16": 914081,
+      "17": 350256,
+      "18": 738414,
+      "19": 297253,
+      "20": 658405,
+      "21": 224335,
+      "22": 362440,
+      "23": 124955,
+      "24": 205298,
+      "25": 69791,
+      "26": 94441,
+      "27": 52289,
+      "28": 125037,
+      "29": 53358,
+      "3": 51817,
+      "30": 115018,
+      "31": 49560,
+      "32": 108624,
+      "33": 38915,
+      "34": 67467,
+      "35": 28283,
+      "36": 62397,
+      "37": 22790,
+      "38": 38085,
+      "39": 16002,
+      "4": 119215,
+      "40": 28910,
+      "41": 10510,
+      "42": 14160,
+      "43": 5722,
+      "44": 7627,
+      "45": 3607,
+      "46": 4194,
+      "47": 2491,
+      "48": 3478,
+      "49": 2081,
+      "5": 942254,
+      "50": 2838,
+      "51": 1758,
+      "52": 2621,
+      "53": 1691,
+      "54": 2365,
+      "55": 1654,
+      "56": 2463,
+      "57": 1729,
+      "58": 2266,
+      "59": 1735,
+      "6": 5173443,
+      "60": 2507,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 2033433,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6061340,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1809785,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51817,
+      "7": 31407954,
+      "9": 119215
+    },
+    "connectivity_max": 140817641,
+    "connectivity_min": 0,
+    "n_cells": 31578986,
+    "n_connectivity_values": 344782130,
+    "n_fan_triangles": 281624158,
+    "n_points": 140817642
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.648177550150481e-11,
+    "float64_area_closure_relative": 7.452595151558967e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281624158,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936976.2629590314,
+    "surface_area_float64_in2": 1936976.2630296957,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936976.26302984,
+    "zero_area_triangles": 238068,
+    "zero_weight_points": 5582
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC032_AoA_4.json b/surface_dual_areas/cases/geo_LHC032_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..ec93fe4123915e4d45dd4dd61e5d778fd91f9192
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC032_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC032_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC032_AoA_4/boundary_dual_area_geo_LHC032_AoA_4.npy",
+    "sha256": "b05c2f76ccf013d7772f0507eb066feef9b5fbf56bd97412b2c08a54d40cc5d3",
+    "shape": [
+      129174758
+    ],
+    "size_bytes": 516699160
+  },
+  "runtime": {
+    "accumulation_seconds": 9.98738367902115,
+    "completed_at_utc": "2026-08-07T07:41:44.168518Z",
+    "elapsed_seconds": 19.69980823714286,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.217098376946524,
+    "geometry_read_seconds": 1.8694491221103817,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:41:24.468617Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC032_AoA_4/boundary_geo_LHC032_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC032_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624451000000000,
+    "extracted_vtu_size_bytes": 19822559603,
+    "geometry_sha256": "aedeb0f92940b45189b2551b30d41b70bd2c74431b57a9c001693a0ddfc3de98",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2363768,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 841488,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1846130,
+      "13": 704132,
+      "14": 1772738,
+      "15": 532841,
+      "16": 1070358,
+      "17": 378574,
+      "18": 759598,
+      "19": 305973,
+      "20": 671309,
+      "21": 229311,
+      "22": 364654,
+      "23": 126845,
+      "24": 211746,
+      "25": 70980,
+      "26": 96437,
+      "27": 52397,
+      "28": 125133,
+      "29": 53363,
+      "3": 45965,
+      "30": 114816,
+      "31": 49575,
+      "32": 108451,
+      "33": 38873,
+      "34": 66324,
+      "35": 27983,
+      "36": 62345,
+      "37": 22845,
+      "38": 38032,
+      "39": 16290,
+      "4": 106369,
+      "40": 29014,
+      "41": 10578,
+      "42": 14032,
+      "43": 5797,
+      "44": 7702,
+      "45": 3598,
+      "46": 4245,
+      "47": 2560,
+      "48": 3561,
+      "49": 2142,
+      "5": 919274,
+      "50": 2867,
+      "51": 1867,
+      "52": 2714,
+      "53": 1748,
+      "54": 2399,
+      "55": 1682,
+      "56": 2530,
+      "57": 1706,
+      "58": 2289,
+      "59": 1695,
+      "6": 5196774,
+      "60": 2446,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 1890027,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5340343,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1441588,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 45965,
+      "7": 28038913,
+      "9": 106369
+    },
+    "connectivity_max": 129174757,
+    "connectivity_min": 0,
+    "n_cells": 28191247,
+    "n_connectivity_values": 314720890,
+    "n_fan_triangles": 258338396,
+    "n_points": 129174758
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.033927710165585e-11,
+    "float64_area_closure_relative": 4.446864971304786e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 258338396,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937260.0406178066,
+    "surface_area_float64_in2": 1937260.0406765817,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937260.040676573,
+    "zero_area_triangles": 218087,
+    "zero_weight_points": 4288
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC032_AoA_6.json b/surface_dual_areas/cases/geo_LHC032_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..610b116471275bd61283399d4bbd33038d78ea60
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC032_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC032_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC032_AoA_6/boundary_dual_area_geo_LHC032_AoA_6.npy",
+    "sha256": "63f9923502af3de15ce14d69d2ec434bcdeabbd92474ea55e464eaf2bfcf18f8",
+    "shape": [
+      135666916
+    ],
+    "size_bytes": 542667792
+  },
+  "runtime": {
+    "accumulation_seconds": 12.330587850883603,
+    "completed_at_utc": "2026-08-07T07:38:18.689959Z",
+    "elapsed_seconds": 28.558320922078565,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4570900150574744,
+    "geometry_read_seconds": 6.195190557977185,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:37:50.131561Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC032_AoA_6/boundary_geo_LHC032_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC032_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624494000000000,
+    "extracted_vtu_size_bytes": 20831141187,
+    "geometry_sha256": "2e3b45224d56bb7d83f71147ae532a33fed6be874683f95455482adaf8dd5179",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3208812,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1063187,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2340933,
+      "13": 743856,
+      "14": 1528986,
+      "15": 474421,
+      "16": 984701,
+      "17": 361118,
+      "18": 750455,
+      "19": 303268,
+      "20": 668096,
+      "21": 227617,
+      "22": 359177,
+      "23": 125615,
+      "24": 207700,
+      "25": 70505,
+      "26": 95218,
+      "27": 52284,
+      "28": 124950,
+      "29": 53349,
+      "3": 48764,
+      "30": 114808,
+      "31": 49568,
+      "32": 108452,
+      "33": 38871,
+      "34": 66329,
+      "35": 27984,
+      "36": 62348,
+      "37": 22845,
+      "38": 38033,
+      "39": 16289,
+      "4": 109507,
+      "40": 29018,
+      "41": 10578,
+      "42": 14029,
+      "43": 5797,
+      "44": 7702,
+      "45": 3598,
+      "46": 4245,
+      "47": 2560,
+      "48": 3561,
+      "49": 2142,
+      "5": 923002,
+      "50": 2867,
+      "51": 1867,
+      "52": 2714,
+      "53": 1748,
+      "54": 2399,
+      "55": 1682,
+      "56": 2530,
+      "57": 1706,
+      "58": 2289,
+      "59": 1695,
+      "6": 5204918,
+      "60": 2446,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 1971893,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5763179,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1662298,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 48764,
+      "7": 29942664,
+      "9": 109507
+    },
+    "connectivity_max": 135666915,
+    "connectivity_min": 0,
+    "n_cells": 30100935,
+    "n_connectivity_values": 331524582,
+    "n_fan_triangles": 271322712,
+    "n_points": 135666916
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.088844371306927e-11,
+    "float64_area_closure_relative": 2.764270894067038e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 271322712,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937257.6021283825,
+    "surface_area_float64_in2": 1937257.6021882214,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937257.602188275,
+    "zero_area_triangles": 230712,
+    "zero_weight_points": 5051
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC033_AoA_22.json b/surface_dual_areas/cases/geo_LHC033_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..00ea0ad91df20ef33407027335fa5ba3f6b9680c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC033_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC033_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC033_AoA_22/boundary_dual_area_geo_LHC033_AoA_22.npy",
+    "sha256": "bba77ab5cfdd1eacad379f18baae5b230e42f2b766390d55e9743e8fb12b55ba",
+    "shape": [
+      145848136
+    ],
+    "size_bytes": 583392672
+  },
+  "runtime": {
+    "accumulation_seconds": 11.417245676042512,
+    "completed_at_utc": "2026-08-07T07:43:19.553061Z",
+    "elapsed_seconds": 22.16849388112314,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4052849360741675,
+    "geometry_read_seconds": 2.3356587060261518,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:42:57.384483Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC033_AoA_22/boundary_geo_LHC033_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC033_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624544000000000,
+    "extracted_vtu_size_bytes": 22408668644,
+    "geometry_sha256": "fb7ccc3b56973f73f4c16db40c2da8b35eb91c2cbd381661da7a3dc466ba4c06",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4200093,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1343716,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2843145,
+      "13": 829093,
+      "14": 1328022,
+      "15": 455088,
+      "16": 902522,
+      "17": 353852,
+      "18": 760407,
+      "19": 306308,
+      "20": 687228,
+      "21": 226277,
+      "22": 364794,
+      "23": 121872,
+      "24": 209496,
+      "25": 70135,
+      "26": 93192,
+      "27": 52136,
+      "28": 124124,
+      "29": 53208,
+      "3": 58865,
+      "30": 115080,
+      "31": 49571,
+      "32": 108741,
+      "33": 38852,
+      "34": 66529,
+      "35": 28033,
+      "36": 62554,
+      "37": 22901,
+      "38": 38187,
+      "39": 15991,
+      "4": 132014,
+      "40": 28937,
+      "41": 10630,
+      "42": 14050,
+      "43": 5778,
+      "44": 7689,
+      "45": 3595,
+      "46": 4244,
+      "47": 2508,
+      "48": 3458,
+      "49": 2066,
+      "5": 948483,
+      "50": 2749,
+      "51": 1759,
+      "52": 2482,
+      "53": 1650,
+      "54": 2227,
+      "55": 1621,
+      "56": 2472,
+      "57": 1687,
+      "58": 2277,
+      "59": 1692,
+      "6": 5237832,
+      "60": 2449,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1370,
+      "66": 1769,
+      "67": 1096,
+      "68": 1505,
+      "69": 880,
+      "7": 2095089,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6496683,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1962655,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58865,
+      "7": 32738336,
+      "9": 132014
+    },
+    "connectivity_max": 145848135,
+    "connectivity_min": 0,
+    "n_cells": 32929215,
+    "n_connectivity_values": 357543569,
+    "n_fan_triangles": 291685139,
+    "n_points": 145848136
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.166441214807506e-11,
+    "float64_area_closure_relative": 4.2024191910729594e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 291685139,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944678.8195881445,
+    "surface_area_float64_in2": 1944678.8196691684,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944678.8196692502,
+    "zero_area_triangles": 241546,
+    "zero_weight_points": 5989
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC034_AoA_16.json b/surface_dual_areas/cases/geo_LHC034_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d201a270871d527f338b75762aaee8b4e68a28f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC034_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC034_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC034_AoA_16/boundary_dual_area_geo_LHC034_AoA_16.npy",
+    "sha256": "dc3c262cd111cf25832ad822ac696ed27add1df4782e416edc054d5d58447ae8",
+    "shape": [
+      148072106
+    ],
+    "size_bytes": 592288552
+  },
+  "runtime": {
+    "accumulation_seconds": 11.326526680029929,
+    "completed_at_utc": "2026-08-07T07:26:40.986084Z",
+    "elapsed_seconds": 21.986355433007702,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.142954669194296,
+    "geometry_read_seconds": 2.718336960999295,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:26:18.999635Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC034_AoA_16/boundary_geo_LHC034_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC034_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624375000000000,
+    "extracted_vtu_size_bytes": 22752240567,
+    "geometry_sha256": "8e11c60c5993b0968fe20b562bf3c5a42f0f3264d4db159eb432e666a4008197",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4380037,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1363046,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2968051,
+      "13": 831813,
+      "14": 1323859,
+      "15": 452569,
+      "16": 937881,
+      "17": 359082,
+      "18": 761738,
+      "19": 305567,
+      "20": 678510,
+      "21": 225031,
+      "22": 365107,
+      "23": 120736,
+      "24": 203725,
+      "25": 69847,
+      "26": 90135,
+      "27": 51821,
+      "28": 123376,
+      "29": 52943,
+      "3": 60176,
+      "30": 114900,
+      "31": 49472,
+      "32": 107862,
+      "33": 38752,
+      "34": 66274,
+      "35": 28020,
+      "36": 62234,
+      "37": 23073,
+      "38": 38917,
+      "39": 16438,
+      "4": 135770,
+      "40": 29718,
+      "41": 10856,
+      "42": 14367,
+      "43": 5879,
+      "44": 7675,
+      "45": 3627,
+      "46": 4141,
+      "47": 2507,
+      "48": 3516,
+      "49": 2128,
+      "5": 953942,
+      "50": 2943,
+      "51": 1876,
+      "52": 2742,
+      "53": 1795,
+      "54": 2456,
+      "55": 1734,
+      "56": 2521,
+      "57": 1763,
+      "58": 2281,
+      "59": 1747,
+      "6": 5244110,
+      "60": 2508,
+      "61": 1627,
+      "62": 2259,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2158301,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6572434,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2041304,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60176,
+      "7": 33310240,
+      "9": 135770
+    },
+    "connectivity_max": 148072105,
+    "connectivity_min": 0,
+    "n_cells": 33506186,
+    "n_connectivity_values": 363145462,
+    "n_fan_triangles": 296133090,
+    "n_points": 148072106
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.294028474097085e-11,
+    "float64_area_closure_relative": 1.434846240937317e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296133090,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947224.4788412277,
+    "surface_area_float64_in2": 1947224.478924842,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947224.47892487,
+    "zero_area_triangles": 242735,
+    "zero_weight_points": 6254
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC034_AoA_20.json b/surface_dual_areas/cases/geo_LHC034_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..a5e76fb63dd499a57765a4256a94c00d0bc0c00c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC034_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC034_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC034_AoA_20/boundary_dual_area_geo_LHC034_AoA_20.npy",
+    "sha256": "2c67073508605907d6ab348c94fd2538464d2f424967bb8cdaabff3a0b810c30",
+    "shape": [
+      149083173
+    ],
+    "size_bytes": 596332820
+  },
+  "runtime": {
+    "accumulation_seconds": 11.475673833163455,
+    "completed_at_utc": "2026-08-07T07:26:12.672045Z",
+    "elapsed_seconds": 22.348890519933775,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.143457927973941,
+    "geometry_read_seconds": 2.677675582934171,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:25:50.323064Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC034_AoA_20/boundary_geo_LHC034_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC034_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624519000000000,
+    "extracted_vtu_size_bytes": 22910354658,
+    "geometry_sha256": "2e801e0afd994876914493cd927bdcdd4de9c01114b4a56f731cf76da8562daa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4548434,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1411337,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3046056,
+      "13": 833647,
+      "14": 1226813,
+      "15": 431678,
+      "16": 901858,
+      "17": 351287,
+      "18": 759696,
+      "19": 305402,
+      "20": 682356,
+      "21": 226937,
+      "22": 373870,
+      "23": 123034,
+      "24": 207810,
+      "25": 70817,
+      "26": 90621,
+      "27": 51945,
+      "28": 123447,
+      "29": 52951,
+      "3": 61599,
+      "30": 114902,
+      "31": 49470,
+      "32": 107865,
+      "33": 38754,
+      "34": 66274,
+      "35": 28020,
+      "36": 62233,
+      "37": 23071,
+      "38": 38916,
+      "39": 16439,
+      "4": 138685,
+      "40": 29718,
+      "41": 10855,
+      "42": 14367,
+      "43": 5879,
+      "44": 7675,
+      "45": 3627,
+      "46": 4141,
+      "47": 2507,
+      "48": 3516,
+      "49": 2128,
+      "5": 960470,
+      "50": 2943,
+      "51": 1876,
+      "52": 2742,
+      "53": 1795,
+      "54": 2456,
+      "55": 1734,
+      "56": 2521,
+      "57": 1763,
+      "58": 2281,
+      "59": 1747,
+      "6": 5254361,
+      "60": 2508,
+      "61": 1627,
+      "62": 2259,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2181401,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6658724,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2094721,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 61599,
+      "7": 33644949,
+      "9": 138685
+    },
+    "connectivity_max": 149083172,
+    "connectivity_min": 0,
+    "n_cells": 33845233,
+    "n_connectivity_values": 365845690,
+    "n_fan_triangles": 298155224,
+    "n_points": 149083173
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.276954057027193e-11,
+    "float64_area_closure_relative": 5.356759616621467e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 298155224,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947224.363565151,
+    "surface_area_float64_in2": 1947224.363648433,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947224.3636483287,
+    "zero_area_triangles": 244083,
+    "zero_weight_points": 6312
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC034_AoA_6.json b/surface_dual_areas/cases/geo_LHC034_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..a445f336ee84fd4b48fe9a598ec6b04533d49861
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC034_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC034_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC034_AoA_6/boundary_dual_area_geo_LHC034_AoA_6.npy",
+    "sha256": "38eaf536b81366d651c769d317dcade1276f35426e0edc427aa641a3eb06307c",
+    "shape": [
+      137333416
+    ],
+    "size_bytes": 549333792
+  },
+  "runtime": {
+    "accumulation_seconds": 10.64816654799506,
+    "completed_at_utc": "2026-08-07T07:41:42.374919Z",
+    "elapsed_seconds": 20.821188285015523,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.78192275413312,
+    "geometry_read_seconds": 1.828599451808259,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:41:21.553620Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC034_AoA_6/boundary_geo_LHC034_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC034_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624576000000000,
+    "extracted_vtu_size_bytes": 21081049597,
+    "geometry_sha256": "c4151056b0d0f30b255a5e1da4fef8c2c2a6062387e7fd5c7bd5e5505692a66e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2814571,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 894729,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2251783,
+      "13": 799012,
+      "14": 1932266,
+      "15": 608505,
+      "16": 1137885,
+      "17": 403749,
+      "18": 764199,
+      "19": 305409,
+      "20": 666987,
+      "21": 221089,
+      "22": 345641,
+      "23": 117674,
+      "24": 192134,
+      "25": 68251,
+      "26": 89047,
+      "27": 51615,
+      "28": 123371,
+      "29": 52922,
+      "3": 56022,
+      "30": 114904,
+      "31": 49479,
+      "32": 107867,
+      "33": 38750,
+      "34": 66271,
+      "35": 28025,
+      "36": 62227,
+      "37": 23073,
+      "38": 38916,
+      "39": 16439,
+      "4": 131869,
+      "40": 29719,
+      "41": 10855,
+      "42": 14367,
+      "43": 5879,
+      "44": 7675,
+      "45": 3627,
+      "46": 4141,
+      "47": 2507,
+      "48": 3516,
+      "49": 2128,
+      "5": 953119,
+      "50": 2943,
+      "51": 1876,
+      "52": 2742,
+      "53": 1795,
+      "54": 2456,
+      "55": 1734,
+      "56": 2521,
+      "57": 1763,
+      "58": 2281,
+      "59": 1747,
+      "6": 5247614,
+      "60": 2508,
+      "61": 1627,
+      "62": 2259,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1984720,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5793571,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1548554,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 56022,
+      "7": 30043701,
+      "9": 131869
+    },
+    "connectivity_max": 137333415,
+    "connectivity_min": 0,
+    "n_cells": 30231592,
+    "n_connectivity_values": 335118894,
+    "n_fan_triangles": 274655710,
+    "n_points": 137333416
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.228079471942386e-11,
+    "float64_area_closure_relative": 2.1522663782561082e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274655710,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947227.177793954,
+    "surface_area_float64_in2": 1947227.1778762843,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947227.1778762802,
+    "zero_area_triangles": 222791,
+    "zero_weight_points": 5047
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC035_AoA_4.json b/surface_dual_areas/cases/geo_LHC035_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..8c59fab27e0a60dff98a41fff0f4347800c7d183
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC035_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC035_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC035_AoA_4/boundary_dual_area_geo_LHC035_AoA_4.npy",
+    "sha256": "4c22bf5ee65cb8edf6bfbbc615e35775b9e62ac375a65ac34f57942a90dfddb9",
+    "shape": [
+      127641338
+    ],
+    "size_bytes": 510565480
+  },
+  "runtime": {
+    "accumulation_seconds": 9.70674853399396,
+    "completed_at_utc": "2026-08-07T07:26:50.095719Z",
+    "elapsed_seconds": 19.51679845387116,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.7645059060305357,
+    "geometry_read_seconds": 2.227458877954632,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:26:30.578828Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC035_AoA_4/boundary_geo_LHC035_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC035_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624542000000000,
+    "extracted_vtu_size_bytes": 19582705172,
+    "geometry_sha256": "76ccb246e5ce1d06441165801c697cf5644c860abfc23de9058aeac9ee1c9928",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2169506,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 769526,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1733080,
+      "13": 712180,
+      "14": 1856242,
+      "15": 574039,
+      "16": 1117091,
+      "17": 393320,
+      "18": 769018,
+      "19": 306831,
+      "20": 666103,
+      "21": 224950,
+      "22": 352315,
+      "23": 124227,
+      "24": 205460,
+      "25": 72337,
+      "26": 94972,
+      "27": 53211,
+      "28": 125209,
+      "29": 53477,
+      "3": 48171,
+      "30": 114369,
+      "31": 49272,
+      "32": 107743,
+      "33": 38504,
+      "34": 66591,
+      "35": 27950,
+      "36": 62209,
+      "37": 22946,
+      "38": 38696,
+      "39": 16438,
+      "4": 108835,
+      "40": 29647,
+      "41": 10788,
+      "42": 14330,
+      "43": 5913,
+      "44": 7740,
+      "45": 3645,
+      "46": 4282,
+      "47": 2559,
+      "48": 3544,
+      "49": 2163,
+      "5": 923314,
+      "50": 2904,
+      "51": 1890,
+      "52": 2739,
+      "53": 1792,
+      "54": 2420,
+      "55": 1709,
+      "56": 2560,
+      "57": 1742,
+      "58": 2302,
+      "59": 1709,
+      "6": 5147040,
+      "60": 2454,
+      "61": 1667,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 1865825,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5165892,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1368770,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 48171,
+      "7": 27517914,
+      "9": 108835
+    },
+    "connectivity_max": 127641337,
+    "connectivity_min": 0,
+    "n_cells": 27674920,
+    "n_connectivity_values": 310621384,
+    "n_fan_triangles": 255271544,
+    "n_points": 127641338
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.855682151226378e-11,
+    "float64_area_closure_relative": 6.005754147561796e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 255271544,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938396.393893484,
+    "surface_area_float64_in2": 1938396.3939682224,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938396.393968234,
+    "zero_area_triangles": 214664,
+    "zero_weight_points": 4263
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC036_AoA_10.json b/surface_dual_areas/cases/geo_LHC036_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..9c408811828b4f7ff13bd8b594b1775151050402
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC036_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC036_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC036_AoA_10/boundary_dual_area_geo_LHC036_AoA_10.npy",
+    "sha256": "f264bc4ad7199581f8c458eb3769e24acf033e0a3c3a56083ec1d84c033357b7",
+    "shape": [
+      147991909
+    ],
+    "size_bytes": 591967764
+  },
+  "runtime": {
+    "accumulation_seconds": 11.471771236043423,
+    "completed_at_utc": "2026-08-07T07:45:29.377400Z",
+    "elapsed_seconds": 22.059965359978378,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2863058680668473,
+    "geometry_read_seconds": 1.9712698960211128,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:45:07.317359Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC036_AoA_10/boundary_geo_LHC036_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC036_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624501000000000,
+    "extracted_vtu_size_bytes": 22740898623,
+    "geometry_sha256": "b3e74d926a5da1a5fd926901b7188a3c1e78fa5412b1c9e9a7bbad28268e313d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4108099,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1339248,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2951460,
+      "13": 863541,
+      "14": 1481308,
+      "15": 486402,
+      "16": 980380,
+      "17": 368939,
+      "18": 748067,
+      "19": 301891,
+      "20": 662455,
+      "21": 219472,
+      "22": 342934,
+      "23": 117540,
+      "24": 195410,
+      "25": 68385,
+      "26": 90529,
+      "27": 51840,
+      "28": 123739,
+      "29": 53068,
+      "3": 60377,
+      "30": 114532,
+      "31": 49335,
+      "32": 108093,
+      "33": 38690,
+      "34": 66008,
+      "35": 27800,
+      "36": 62073,
+      "37": 22837,
+      "38": 38855,
+      "39": 16426,
+      "4": 137064,
+      "40": 30074,
+      "41": 10981,
+      "42": 14696,
+      "43": 6005,
+      "44": 7866,
+      "45": 3672,
+      "46": 4310,
+      "47": 2527,
+      "48": 3514,
+      "49": 2158,
+      "5": 971590,
+      "50": 2927,
+      "51": 1862,
+      "52": 2764,
+      "53": 1805,
+      "54": 2433,
+      "55": 1711,
+      "56": 2568,
+      "57": 1732,
+      "58": 2316,
+      "59": 1693,
+      "6": 5405062,
+      "60": 2443,
+      "61": 1665,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2148845,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6596115,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1978385,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60377,
+      "7": 33329837,
+      "9": 137064
+    },
+    "connectivity_max": 147991908,
+    "connectivity_min": 0,
+    "n_cells": 33527278,
+    "n_connectivity_values": 363027241,
+    "n_fan_triangles": 295972685,
+    "n_points": 147991909
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.497132037172078e-11,
+    "float64_area_closure_relative": 4.9981748078857735e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295972685,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947174.974559997,
+    "surface_area_float64_in2": 1947174.9746280923,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947174.9746281896,
+    "zero_area_triangles": 241235,
+    "zero_weight_points": 6037
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC036_AoA_20.json b/surface_dual_areas/cases/geo_LHC036_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..71bc249cc2670e4466593d9330b1126a9151ec82
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC036_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC036_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC036_AoA_20/boundary_dual_area_geo_LHC036_AoA_20.npy",
+    "sha256": "875d1bacffdaa322c10c2710d1eb4e6f37f8571258cd6a7aedc2d711eb4e3a83",
+    "shape": [
+      150625088
+    ],
+    "size_bytes": 602500480
+  },
+  "runtime": {
+    "accumulation_seconds": 12.866371087031439,
+    "completed_at_utc": "2026-08-07T07:44:43.793175Z",
+    "elapsed_seconds": 26.462997992988676,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.829661909956485,
+    "geometry_read_seconds": 3.3554648391436785,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:44:17.330099Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC036_AoA_20/boundary_geo_LHC036_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC036_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624378000000000,
+    "extracted_vtu_size_bytes": 23149959190,
+    "geometry_sha256": "3da27ade69a247b28b60cd7db5061099dd6beb01ac953a8f4d5e19392425ed7b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4653290,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1470948,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3102533,
+      "13": 859082,
+      "14": 1274840,
+      "15": 442927,
+      "16": 900927,
+      "17": 357605,
+      "18": 753767,
+      "19": 306460,
+      "20": 672146,
+      "21": 223320,
+      "22": 349001,
+      "23": 119163,
+      "24": 199856,
+      "25": 69121,
+      "26": 91232,
+      "27": 51992,
+      "28": 123798,
+      "29": 53079,
+      "3": 61620,
+      "30": 114524,
+      "31": 49334,
+      "32": 108090,
+      "33": 38689,
+      "34": 66002,
+      "35": 27809,
+      "36": 62069,
+      "37": 22833,
+      "38": 38858,
+      "39": 16426,
+      "4": 139635,
+      "40": 30085,
+      "41": 10980,
+      "42": 14692,
+      "43": 6008,
+      "44": 7867,
+      "45": 3670,
+      "46": 4310,
+      "47": 2527,
+      "48": 3514,
+      "49": 2158,
+      "5": 960495,
+      "50": 2927,
+      "51": 1862,
+      "52": 2764,
+      "53": 1805,
+      "54": 2433,
+      "55": 1711,
+      "56": 2568,
+      "57": 1732,
+      "58": 2316,
+      "59": 1693,
+      "6": 5296718,
+      "60": 2443,
+      "61": 1665,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2183385,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6777502,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2131713,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61620,
+      "7": 34100026,
+      "9": 139635
+    },
+    "connectivity_max": 150625087,
+    "connectivity_min": 0,
+    "n_cells": 34301281,
+    "n_connectivity_values": 369841605,
+    "n_fan_triangles": 301239043,
+    "n_points": 150625088
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4604226662698066e-11,
+    "float64_area_closure_relative": 2.929551976130031e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 301239043,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947175.1366084034,
+    "surface_area_float64_in2": 1947175.136675784,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947175.136675841,
+    "zero_area_triangles": 245118,
+    "zero_weight_points": 6378
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC036_AoA_4.json b/surface_dual_areas/cases/geo_LHC036_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..8b50e34e4ffee783139e04f33eb7d2a9fbeb3b05
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC036_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC036_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC036_AoA_4/boundary_dual_area_geo_LHC036_AoA_4.npy",
+    "sha256": "c1e61ffd4a0bfe70422505e3d88d7a11006ca68bc87f0d71468ebac74bb2deac",
+    "shape": [
+      140385699
+    ],
+    "size_bytes": 561542924
+  },
+  "runtime": {
+    "accumulation_seconds": 10.806198691017926,
+    "completed_at_utc": "2026-08-07T07:26:34.908427Z",
+    "elapsed_seconds": 21.19707473111339,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.967741362983361,
+    "geometry_read_seconds": 1.8415996751282364,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:26:13.711255Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC036_AoA_4/boundary_geo_LHC036_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC036_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624431000000000,
+    "extracted_vtu_size_bytes": 21558950268,
+    "geometry_sha256": "2e136b268a6c41427bbf5744b1955e971130583d74ab0b82cf8721ca57147074",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3168025,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1029300,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2429850,
+      "13": 821074,
+      "14": 1751296,
+      "15": 573276,
+      "16": 1070050,
+      "17": 396695,
+      "18": 759478,
+      "19": 306415,
+      "20": 666060,
+      "21": 221295,
+      "22": 346301,
+      "23": 118901,
+      "24": 197167,
+      "25": 68961,
+      "26": 90863,
+      "27": 51924,
+      "28": 123811,
+      "29": 53091,
+      "3": 58986,
+      "30": 114525,
+      "31": 49334,
+      "32": 108091,
+      "33": 38688,
+      "34": 66011,
+      "35": 27804,
+      "36": 62074,
+      "37": 22840,
+      "38": 38853,
+      "39": 16423,
+      "4": 134801,
+      "40": 30075,
+      "41": 10980,
+      "42": 14696,
+      "43": 6006,
+      "44": 7866,
+      "45": 3673,
+      "46": 4311,
+      "47": 2528,
+      "48": 3514,
+      "49": 2157,
+      "5": 967909,
+      "50": 2927,
+      "51": 1862,
+      "52": 2765,
+      "53": 1805,
+      "54": 2431,
+      "55": 1711,
+      "56": 2568,
+      "57": 1732,
+      "58": 2316,
+      "59": 1693,
+      "6": 5394196,
+      "60": 2443,
+      "61": 1665,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2034245,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6103595,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1665413,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58986,
+      "7": 31084320,
+      "9": 134801
+    },
+    "connectivity_max": 140385698,
+    "connectivity_min": 0,
+    "n_cells": 31278107,
+    "n_connectivity_values": 343316479,
+    "n_fan_triangles": 280760265,
+    "n_points": 140385699
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5184962503874967e-11,
+    "float64_area_closure_relative": 3.5872031480158263e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280760265,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947176.9568539385,
+    "surface_area_float64_in2": 1947176.9569224499,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947176.9569224492,
+    "zero_area_triangles": 228155,
+    "zero_weight_points": 5176
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC036_AoA_8.json b/surface_dual_areas/cases/geo_LHC036_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..35e8ecff933f89f51ca5bae5d5669231cc99ea90
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC036_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC036_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC036_AoA_8/boundary_dual_area_geo_LHC036_AoA_8.npy",
+    "sha256": "1f9016af505776100c288ae7b3d3b6d9d411643ce8e9e8da98fd7266a0936019",
+    "shape": [
+      145395071
+    ],
+    "size_bytes": 581580412
+  },
+  "runtime": {
+    "accumulation_seconds": 11.160066369920969,
+    "completed_at_utc": "2026-08-07T07:27:12.184264Z",
+    "elapsed_seconds": 21.017802227986977,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1079461940098554,
+    "geometry_read_seconds": 1.965326827019453,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:26:51.166370Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC036_AoA_8/boundary_geo_LHC036_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC036_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624720000000000,
+    "extracted_vtu_size_bytes": 22337189374,
+    "geometry_sha256": "3adbc0d014d016de778b4b07ca7e143693469513b9760414d7c1a2f98c4b99be",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3779681,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1227287,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2793329,
+      "13": 847058,
+      "14": 1568599,
+      "15": 513859,
+      "16": 1012089,
+      "17": 378142,
+      "18": 752417,
+      "19": 303450,
+      "20": 664025,
+      "21": 220231,
+      "22": 344226,
+      "23": 117999,
+      "24": 196079,
+      "25": 68569,
+      "26": 90641,
+      "27": 51872,
+      "28": 123757,
+      "29": 53069,
+      "3": 57682,
+      "30": 114522,
+      "31": 49336,
+      "32": 108099,
+      "33": 38690,
+      "34": 65999,
+      "35": 27813,
+      "36": 62068,
+      "37": 22832,
+      "38": 38855,
+      "39": 16426,
+      "4": 134853,
+      "40": 30081,
+      "41": 10978,
+      "42": 14694,
+      "43": 6006,
+      "44": 7866,
+      "45": 3672,
+      "46": 4310,
+      "47": 2528,
+      "48": 3514,
+      "49": 2157,
+      "5": 968190,
+      "50": 2927,
+      "51": 1862,
+      "52": 2764,
+      "53": 1805,
+      "54": 2433,
+      "55": 1711,
+      "56": 2568,
+      "57": 1732,
+      "58": 2316,
+      "59": 1693,
+      "6": 5394089,
+      "60": 2443,
+      "61": 1665,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2108810,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6442137,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1864922,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57682,
+      "7": 32559654,
+      "9": 134853
+    },
+    "connectivity_max": 145395070,
+    "connectivity_min": 0,
+    "n_cells": 32752189,
+    "n_connectivity_values": 356283387,
+    "n_fan_triangles": 290779009,
+    "n_points": 145395071
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.574985389120776e-11,
+    "float64_area_closure_relative": 5.5721263481937854e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290779009,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947175.515393591,
+    "surface_area_float64_in2": 1947175.5154632023,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947175.5154633108,
+    "zero_area_triangles": 236287,
+    "zero_weight_points": 5791
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC037_AoA_8.json b/surface_dual_areas/cases/geo_LHC037_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..b4faea00794698c5b39258b967b76d06f58dc9e7
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC037_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC037_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC037_AoA_8/boundary_dual_area_geo_LHC037_AoA_8.npy",
+    "sha256": "468c13133b53b39a616786b38806c9d2596367594c56875063d03506af17b42c",
+    "shape": [
+      139176787
+    ],
+    "size_bytes": 556707276
+  },
+  "runtime": {
+    "accumulation_seconds": 10.685372728155926,
+    "completed_at_utc": "2026-08-07T07:26:56.152546Z",
+    "elapsed_seconds": 20.045986000914127,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1003685139585286,
+    "geometry_read_seconds": 1.7677759579382837,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:26:36.106451Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC037_AoA_8/boundary_geo_LHC037_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC037_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624463000000000,
+    "extracted_vtu_size_bytes": 21374493768,
+    "geometry_sha256": "7f7706e6e19ff2862d7c22f238ef584e47029e78e032d34dd426fc00388507dd",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3809985,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1143313,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2591409,
+      "13": 767244,
+      "14": 1413425,
+      "15": 475313,
+      "16": 937694,
+      "17": 359084,
+      "18": 755035,
+      "19": 304920,
+      "20": 670377,
+      "21": 224532,
+      "22": 352163,
+      "23": 121398,
+      "24": 194175,
+      "25": 67634,
+      "26": 92875,
+      "27": 51483,
+      "28": 123936,
+      "29": 53377,
+      "3": 49086,
+      "30": 115284,
+      "31": 49515,
+      "32": 108427,
+      "33": 38930,
+      "34": 67305,
+      "35": 28232,
+      "36": 63737,
+      "37": 23164,
+      "38": 38767,
+      "39": 16138,
+      "4": 113396,
+      "40": 29223,
+      "41": 10627,
+      "42": 14003,
+      "43": 5832,
+      "44": 7814,
+      "45": 3734,
+      "46": 4296,
+      "47": 2548,
+      "48": 3639,
+      "49": 2153,
+      "5": 919081,
+      "50": 2812,
+      "51": 1760,
+      "52": 2523,
+      "53": 1630,
+      "54": 2218,
+      "55": 1629,
+      "56": 2410,
+      "57": 1716,
+      "58": 2246,
+      "59": 1677,
+      "6": 5156875,
+      "60": 2461,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1977029,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5926794,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1727827,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49086,
+      "7": 30894117,
+      "9": 113396
+    },
+    "connectivity_max": 139176786,
+    "connectivity_min": 0,
+    "n_cells": 31056599,
+    "n_connectivity_values": 340455661,
+    "n_fan_triangles": 278342463,
+    "n_points": 139176787
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.465505431133713e-11,
+    "float64_area_closure_relative": 6.675443608582453e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278342463,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935766.5917105977,
+    "surface_area_float64_in2": 1935766.5917776818,
+    "weight_max_in2": 1.1008609652596335,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935766.591777811,
+    "zero_area_triangles": 239014,
+    "zero_weight_points": 5645
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC038_AoA_12.json b/surface_dual_areas/cases/geo_LHC038_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..266a25135ae6c37992cbc43516fd52a55116460d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC038_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC038_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC038_AoA_12/boundary_dual_area_geo_LHC038_AoA_12.npy",
+    "sha256": "6f66c8121143b6adc85caf7ea66692e8599fa3ba52ba5d89c949513b60e7bbe4",
+    "shape": [
+      138914607
+    ],
+    "size_bytes": 555658556
+  },
+  "runtime": {
+    "accumulation_seconds": 10.73061027401127,
+    "completed_at_utc": "2026-08-07T07:27:17.965749Z",
+    "elapsed_seconds": 20.553891557035968,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9247246289160103,
+    "geometry_read_seconds": 1.823887717910111,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:26:57.411765Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC038_AoA_12/boundary_geo_LHC038_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC038_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624662000000000,
+    "extracted_vtu_size_bytes": 21333502609,
+    "geometry_sha256": "be722a4b9b41ca3084054bcdbdba8ffbfa977f509d8a967a80ea3dc0be9ffe5c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3671973,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1171484,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2568167,
+      "13": 786462,
+      "14": 1398025,
+      "15": 474249,
+      "16": 938419,
+      "17": 359970,
+      "18": 757351,
+      "19": 306416,
+      "20": 677646,
+      "21": 227523,
+      "22": 361734,
+      "23": 122868,
+      "24": 196796,
+      "25": 67269,
+      "26": 92664,
+      "27": 51514,
+      "28": 124208,
+      "29": 53076,
+      "3": 52033,
+      "30": 115442,
+      "31": 49628,
+      "32": 109325,
+      "33": 39137,
+      "34": 66856,
+      "35": 28295,
+      "36": 62412,
+      "37": 22914,
+      "38": 37821,
+      "39": 16017,
+      "4": 116918,
+      "40": 29121,
+      "41": 10618,
+      "42": 14221,
+      "43": 5756,
+      "44": 7736,
+      "45": 3649,
+      "46": 4168,
+      "47": 2521,
+      "48": 3542,
+      "49": 2067,
+      "5": 925005,
+      "50": 2791,
+      "51": 1759,
+      "52": 2531,
+      "53": 1654,
+      "54": 2241,
+      "55": 1629,
+      "56": 2414,
+      "57": 1719,
+      "58": 2266,
+      "59": 1736,
+      "6": 5141236,
+      "60": 2504,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1990060,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5910845,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1750112,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52033,
+      "7": 30800113,
+      "9": 116918
+    },
+    "connectivity_max": 138914606,
+    "connectivity_min": 0,
+    "n_cells": 30969064,
+    "n_connectivity_values": 339756213,
+    "n_fan_triangles": 277818085,
+    "n_points": 138914607
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.541925227686727e-11,
+    "float64_area_closure_relative": 1.8026777239330928e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277818085,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937373.279936291,
+    "surface_area_float64_in2": 1937373.2800049114,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937373.2800049148,
+    "zero_area_triangles": 240283,
+    "zero_weight_points": 5683
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC038_AoA_16.json b/surface_dual_areas/cases/geo_LHC038_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..9816cb679211637b1cf3581aaeb5864671d664d7
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC038_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC038_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC038_AoA_16/boundary_dual_area_geo_LHC038_AoA_16.npy",
+    "sha256": "2713e5e48d539e7c9bdb9c396ed4e8f7f8769bc923ace126ad25c48127a47136",
+    "shape": [
+      139332270
+    ],
+    "size_bytes": 557329208
+  },
+  "runtime": {
+    "accumulation_seconds": 10.686698578996584,
+    "completed_at_utc": "2026-08-07T07:27:58.601795Z",
+    "elapsed_seconds": 21.660609625047073,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.278606710024178,
+    "geometry_read_seconds": 2.2886605449020863,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:27:36.941071Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC038_AoA_16/boundary_geo_LHC038_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC038_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624378000000000,
+    "extracted_vtu_size_bytes": 21398581883,
+    "geometry_sha256": "0f506e2906057c624b429ccacdf80ee3b837fd56ba48bec783c35d518658e128",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3768891,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1173229,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2583376,
+      "13": 782379,
+      "14": 1380534,
+      "15": 472989,
+      "16": 931106,
+      "17": 358937,
+      "18": 756055,
+      "19": 306073,
+      "20": 677348,
+      "21": 227840,
+      "22": 362243,
+      "23": 122974,
+      "24": 197461,
+      "25": 67371,
+      "26": 92804,
+      "27": 51532,
+      "28": 124245,
+      "29": 53101,
+      "3": 53400,
+      "30": 115442,
+      "31": 49614,
+      "32": 109327,
+      "33": 39135,
+      "34": 66831,
+      "35": 28304,
+      "36": 62386,
+      "37": 22910,
+      "38": 37829,
+      "39": 16010,
+      "4": 120390,
+      "40": 29128,
+      "41": 10623,
+      "42": 14224,
+      "43": 5754,
+      "44": 7732,
+      "45": 3648,
+      "46": 4172,
+      "47": 2518,
+      "48": 3543,
+      "49": 2067,
+      "5": 928163,
+      "50": 2792,
+      "51": 1759,
+      "52": 2531,
+      "53": 1654,
+      "54": 2240,
+      "55": 1630,
+      "56": 2414,
+      "57": 1719,
+      "58": 2266,
+      "59": 1736,
+      "6": 5137349,
+      "60": 2504,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1992056,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5942370,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1760461,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53400,
+      "7": 30925880,
+      "9": 120390
+    },
+    "connectivity_max": 139332269,
+    "connectivity_min": 0,
+    "n_cells": 31099670,
+    "n_connectivity_values": 340852751,
+    "n_fan_triangles": 278653411,
+    "n_points": 139332270
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.466597429587512e-11,
+    "float64_area_closure_relative": 7.81160368458015e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278653411,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937373.226812683,
+    "surface_area_float64_in2": 1937373.226879844,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937373.226879859,
+    "zero_area_triangles": 239577,
+    "zero_weight_points": 5606
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC038_AoA_20.json b/surface_dual_areas/cases/geo_LHC038_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..6eb460550115bd5d768f16735ddb4a02c47a6f11
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC038_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC038_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC038_AoA_20/boundary_dual_area_geo_LHC038_AoA_20.npy",
+    "sha256": "b2ce5f0b9eccda9684b516aa938f30df630bf07af6ad383e76902bc702dd5c72",
+    "shape": [
+      141467703
+    ],
+    "size_bytes": 565870940
+  },
+  "runtime": {
+    "accumulation_seconds": 14.82680105487816,
+    "completed_at_utc": "2026-08-07T07:44:11.652249Z",
+    "elapsed_seconds": 74.32339335908182,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.595723396865651,
+    "geometry_read_seconds": 50.76374705112539,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:42:57.328781Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC038_AoA_20/boundary_geo_LHC038_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC038_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624441000000000,
+    "extracted_vtu_size_bytes": 21730852467,
+    "geometry_sha256": "6afe45e7a89e8db87caaecbb6cf0a3ec048369423182e5678ed06b829ae108ca",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4055265,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1238359,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2710990,
+      "13": 793086,
+      "14": 1330045,
+      "15": 463609,
+      "16": 906371,
+      "17": 353185,
+      "18": 745398,
+      "19": 302209,
+      "20": 666867,
+      "21": 225552,
+      "22": 358429,
+      "23": 122760,
+      "24": 199038,
+      "25": 68145,
+      "26": 93437,
+      "27": 51914,
+      "28": 124401,
+      "29": 53165,
+      "3": 51936,
+      "30": 115462,
+      "31": 49639,
+      "32": 109330,
+      "33": 39131,
+      "34": 66840,
+      "35": 28303,
+      "36": 62376,
+      "37": 22909,
+      "38": 37823,
+      "39": 16002,
+      "4": 120228,
+      "40": 29125,
+      "41": 10622,
+      "42": 14212,
+      "43": 5755,
+      "44": 7730,
+      "45": 3645,
+      "46": 4170,
+      "47": 2521,
+      "48": 3542,
+      "49": 2068,
+      "5": 933173,
+      "50": 2791,
+      "51": 1758,
+      "52": 2532,
+      "53": 1654,
+      "54": 2237,
+      "55": 1628,
+      "56": 2414,
+      "57": 1720,
+      "58": 2266,
+      "59": 1736,
+      "6": 5174198,
+      "60": 2504,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2018654,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6082782,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1830538,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51936,
+      "7": 31576566,
+      "9": 120228
+    },
+    "connectivity_max": 141467702,
+    "connectivity_min": 0,
+    "n_cells": 31748730,
+    "n_connectivity_values": 346421737,
+    "n_fan_triangles": 282924277,
+    "n_points": 141467703
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.459831567805169e-11,
+    "float64_area_closure_relative": 2.8722667422928655e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282924277,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937373.1210955777,
+    "surface_area_float64_in2": 1937373.1211626076,
+    "weight_max_in2": 1.1002392926736668,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937373.1211626632,
+    "zero_area_triangles": 242749,
+    "zero_weight_points": 5831
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC039_AoA_12.json b/surface_dual_areas/cases/geo_LHC039_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ad4d743936ef909ce6ea3f8209dfbfa59ab7cee
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC039_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC039_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC039_AoA_12/boundary_dual_area_geo_LHC039_AoA_12.npy",
+    "sha256": "2a94de7005adce310a788f692bcd510fde535e887e6d5f47114b2728d096c11c",
+    "shape": [
+      137305318
+    ],
+    "size_bytes": 549221400
+  },
+  "runtime": {
+    "accumulation_seconds": 10.406275792978704,
+    "completed_at_utc": "2026-08-07T07:28:06.435066Z",
+    "elapsed_seconds": 20.473804346984252,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.8891454748809338,
+    "geometry_read_seconds": 2.551159613998607,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:27:45.961168Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC039_AoA_12/boundary_geo_LHC039_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC039_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624686000000000,
+    "extracted_vtu_size_bytes": 21084118668,
+    "geometry_sha256": "3b6563119d9c8603bf58582c62b9bb61e7cfee98f892c7d80e7169181fb1e353",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3621846,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1113299,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2511957,
+      "13": 752819,
+      "14": 1386697,
+      "15": 463550,
+      "16": 927307,
+      "17": 354548,
+      "18": 751321,
+      "19": 304143,
+      "20": 671063,
+      "21": 229673,
+      "22": 367414,
+      "23": 127403,
+      "24": 208018,
+      "25": 71121,
+      "26": 95894,
+      "27": 52659,
+      "28": 125350,
+      "29": 53563,
+      "3": 49637,
+      "30": 115086,
+      "31": 49487,
+      "32": 107787,
+      "33": 38751,
+      "34": 66224,
+      "35": 28076,
+      "36": 62764,
+      "37": 22968,
+      "38": 38781,
+      "39": 16152,
+      "4": 110737,
+      "40": 29275,
+      "41": 10682,
+      "42": 14086,
+      "43": 5742,
+      "44": 7625,
+      "45": 3670,
+      "46": 4292,
+      "47": 2568,
+      "48": 3508,
+      "49": 2108,
+      "5": 916221,
+      "50": 2852,
+      "51": 1754,
+      "52": 2555,
+      "53": 1648,
+      "54": 2207,
+      "55": 1626,
+      "56": 2446,
+      "57": 1707,
+      "58": 2255,
+      "59": 1716,
+      "6": 5122832,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1376,
+      "66": 1817,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1960876,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5798827,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 1698419,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49637,
+      "7": 30360321,
+      "9": 110737
+    },
+    "connectivity_max": 137305317,
+    "connectivity_min": 0,
+    "n_cells": 30520695,
+    "n_connectivity_values": 335640904,
+    "n_fan_triangles": 274599514,
+    "n_points": 137305318
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.88446238463466e-11,
+    "float64_area_closure_relative": 8.258342771602701e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274599514,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936885.6029325672,
+    "surface_area_float64_in2": 1936885.6030078048,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936885.6030079648,
+    "zero_area_triangles": 235794,
+    "zero_weight_points": 5333
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC039_AoA_18.json b/surface_dual_areas/cases/geo_LHC039_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd815b6d069fcf96e218870b3e57b938d2dd3ff3
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC039_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC039_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC039_AoA_18/boundary_dual_area_geo_LHC039_AoA_18.npy",
+    "sha256": "b3c852ff1c8a4d60324d433ed54f06b7d338d56b30faae6046174af10a3f4cb6",
+    "shape": [
+      138855839
+    ],
+    "size_bytes": 555423484
+  },
+  "runtime": {
+    "accumulation_seconds": 10.465319087030366,
+    "completed_at_utc": "2026-08-07T07:27:58.932389Z",
+    "elapsed_seconds": 19.87092174286954,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9345044831279665,
+    "geometry_read_seconds": 1.871660318924114,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:27:39.061375Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC039_AoA_18/boundary_geo_LHC039_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC039_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624490000000000,
+    "extracted_vtu_size_bytes": 21326191426,
+    "geometry_sha256": "fd78272313d4541f943bb177687d34867dfe9da551cdcc62d899c26dbd444d93",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3917565,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1155658,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2550221,
+      "13": 735606,
+      "14": 1294360,
+      "15": 438470,
+      "16": 901205,
+      "17": 350238,
+      "18": 760455,
+      "19": 307748,
+      "20": 678257,
+      "21": 232216,
+      "22": 369332,
+      "23": 128093,
+      "24": 208054,
+      "25": 71128,
+      "26": 95982,
+      "27": 52710,
+      "28": 125344,
+      "29": 53569,
+      "3": 52721,
+      "30": 115064,
+      "31": 49481,
+      "32": 107777,
+      "33": 38737,
+      "34": 66204,
+      "35": 28070,
+      "36": 62751,
+      "37": 22965,
+      "38": 38783,
+      "39": 16157,
+      "4": 116643,
+      "40": 29273,
+      "41": 10679,
+      "42": 14081,
+      "43": 5743,
+      "44": 7622,
+      "45": 3669,
+      "46": 4286,
+      "47": 2566,
+      "48": 3509,
+      "49": 2107,
+      "5": 919673,
+      "50": 2854,
+      "51": 1753,
+      "52": 2555,
+      "53": 1648,
+      "54": 2206,
+      "55": 1626,
+      "56": 2447,
+      "57": 1707,
+      "58": 2254,
+      "59": 1716,
+      "6": 5128224,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1376,
+      "66": 1817,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1984388,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5959336,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 1763932,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52721,
+      "7": 30855157,
+      "9": 116643
+    },
+    "connectivity_max": 138855838,
+    "connectivity_min": 0,
+    "n_cells": 31024521,
+    "n_connectivity_values": 339749598,
+    "n_fan_triangles": 277700556,
+    "n_points": 138855839
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9256702651733955e-11,
+    "float64_area_closure_relative": 5.421416137970614e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277700556,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936885.4485883438,
+    "surface_area_float64_in2": 1936885.4486643795,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936885.4486642745,
+    "zero_area_triangles": 238670,
+    "zero_weight_points": 5458
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC039_AoA_4.json b/surface_dual_areas/cases/geo_LHC039_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..db6eb38606d87f224bb50019fa2d3055695b8698
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC039_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC039_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC039_AoA_4/boundary_dual_area_geo_LHC039_AoA_4.npy",
+    "sha256": "ac885ba0f1c8a9688e585426c5ab009897b147d0c033e36793d9960fce0f8654",
+    "shape": [
+      126278762
+    ],
+    "size_bytes": 505115176
+  },
+  "runtime": {
+    "accumulation_seconds": 9.771949802991003,
+    "completed_at_utc": "2026-08-07T07:47:25.962436Z",
+    "elapsed_seconds": 46.40356640005484,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9978809151798487,
+    "geometry_read_seconds": 27.98224199609831,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:46:39.558785Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC039_AoA_4/boundary_geo_LHC039_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC039_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624516000000000,
+    "extracted_vtu_size_bytes": 19371118071,
+    "geometry_sha256": "620e582bb7ac117786a4e8da827457e5e376cc9e622a87b1b1d76884f63179aa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2088441,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 742722,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1702175,
+      "13": 695691,
+      "14": 1801996,
+      "15": 559278,
+      "16": 1092975,
+      "17": 385784,
+      "18": 770135,
+      "19": 308854,
+      "20": 677546,
+      "21": 232329,
+      "22": 372415,
+      "23": 128979,
+      "24": 211294,
+      "25": 71902,
+      "26": 96911,
+      "27": 52880,
+      "28": 125645,
+      "29": 53603,
+      "3": 46556,
+      "30": 115074,
+      "31": 49494,
+      "32": 107791,
+      "33": 38748,
+      "34": 66218,
+      "35": 28059,
+      "36": 62765,
+      "37": 22971,
+      "38": 38778,
+      "39": 16161,
+      "4": 106740,
+      "40": 29277,
+      "41": 10681,
+      "42": 14086,
+      "43": 5739,
+      "44": 7623,
+      "45": 3672,
+      "46": 4291,
+      "47": 2569,
+      "48": 3510,
+      "49": 2106,
+      "5": 912573,
+      "50": 2853,
+      "51": 1754,
+      "52": 2555,
+      "53": 1648,
+      "54": 2207,
+      "55": 1626,
+      "56": 2446,
+      "57": 1707,
+      "58": 2255,
+      "59": 1716,
+      "6": 5122944,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1376,
+      "66": 1817,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1830688,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5088969,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 1324375,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 46556,
+      "7": 27124587,
+      "9": 106740
+    },
+    "connectivity_max": 126278761,
+    "connectivity_min": 0,
+    "n_cells": 27277883,
+    "n_connectivity_values": 307102167,
+    "n_fan_triangles": 252546401,
+    "n_points": 126278762
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.973795005327934e-11,
+    "float64_area_closure_relative": 5.42140678334084e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 252546401,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936888.790680527,
+    "surface_area_float64_in2": 1936888.790757495,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936888.79075739,
+    "zero_area_triangles": 216181,
+    "zero_weight_points": 4127
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC041_AoA_10.json b/surface_dual_areas/cases/geo_LHC041_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..1332db3f3cdd3eb9dbd7a0f386e9fa178f867edf
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC041_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC041_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC041_AoA_10/boundary_dual_area_geo_LHC041_AoA_10.npy",
+    "sha256": "c27f78cb4fff8d522f9b992f35d3bf8908627cf8c21291e6d2b7cf0af3d2fd1f",
+    "shape": [
+      141123491
+    ],
+    "size_bytes": 564494092
+  },
+  "runtime": {
+    "accumulation_seconds": 10.765726735116914,
+    "completed_at_utc": "2026-08-07T07:46:06.279278Z",
+    "elapsed_seconds": 51.92306610709056,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.242561795981601,
+    "geometry_read_seconds": 32.93119551311247,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:45:14.356123Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC041_AoA_10/boundary_geo_LHC041_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC041_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624573000000000,
+    "extracted_vtu_size_bytes": 21677413518,
+    "geometry_sha256": "e65b37bc5870478586a0f366c62cb1da915ee2bcfefde6e454800e24c4803023",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3784614,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1211640,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2663465,
+      "13": 823399,
+      "14": 1470278,
+      "15": 493141,
+      "16": 960448,
+      "17": 360174,
+      "18": 741525,
+      "19": 295449,
+      "20": 650440,
+      "21": 217940,
+      "22": 341989,
+      "23": 118146,
+      "24": 194020,
+      "25": 66817,
+      "26": 93971,
+      "27": 51581,
+      "28": 124224,
+      "29": 53444,
+      "3": 53732,
+      "30": 115658,
+      "31": 49691,
+      "32": 108737,
+      "33": 38654,
+      "34": 66071,
+      "35": 27822,
+      "36": 62272,
+      "37": 22979,
+      "38": 38953,
+      "39": 16394,
+      "4": 120998,
+      "40": 29758,
+      "41": 10954,
+      "42": 14407,
+      "43": 5856,
+      "44": 7661,
+      "45": 3675,
+      "46": 4148,
+      "47": 2498,
+      "48": 3501,
+      "49": 2130,
+      "5": 951531,
+      "50": 2952,
+      "51": 1874,
+      "52": 2782,
+      "53": 1800,
+      "54": 2470,
+      "55": 1728,
+      "56": 2527,
+      "57": 1757,
+      "58": 2287,
+      "59": 1742,
+      "6": 5239678,
+      "60": 2506,
+      "61": 1627,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 2051278,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6028588,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1809601,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53732,
+      "7": 31474179,
+      "9": 120998
+    },
+    "connectivity_max": 141123490,
+    "connectivity_min": 0,
+    "n_cells": 31648909,
+    "n_connectivity_values": 345533665,
+    "n_fan_triangles": 282235847,
+    "n_points": 141123491
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.504563233282061e-11,
+    "float64_area_closure_relative": 1.8490632691130138e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282235847,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939139.6562995506,
+    "surface_area_float64_in2": 1939139.656367509,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939139.6563675448,
+    "zero_area_triangles": 237236,
+    "zero_weight_points": 5498
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC041_AoA_14.json b/surface_dual_areas/cases/geo_LHC041_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..50545edef1fbe3196c92db1b00a6c377676ddac9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC041_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC041_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC041_AoA_14/boundary_dual_area_geo_LHC041_AoA_14.npy",
+    "sha256": "fb3dd4cb60c141655be53bf89922506eada1b9b3be4ff08e199e2eda5a23e539",
+    "shape": [
+      141150201
+    ],
+    "size_bytes": 564600932
+  },
+  "runtime": {
+    "accumulation_seconds": 10.973253909032792,
+    "completed_at_utc": "2026-08-07T07:46:32.822641Z",
+    "elapsed_seconds": 21.420548828085884,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3286236790008843,
+    "geometry_read_seconds": 2.233217569999397,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:46:11.402002Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC041_AoA_14/boundary_geo_LHC041_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC041_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624512000000000,
+    "extracted_vtu_size_bytes": 21682728448,
+    "geometry_sha256": "88eac90079fb6f9bbfb06828473eebc803996c424dcd7683c7b7aeba7fe68cb8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3883462,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1221716,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2650594,
+      "13": 809636,
+      "14": 1382933,
+      "15": 479537,
+      "16": 926610,
+      "17": 357157,
+      "18": 745030,
+      "19": 297283,
+      "20": 656762,
+      "21": 220217,
+      "22": 353424,
+      "23": 119968,
+      "24": 201921,
+      "25": 67646,
+      "26": 94932,
+      "27": 51738,
+      "28": 124315,
+      "29": 53460,
+      "3": 54541,
+      "30": 115662,
+      "31": 49693,
+      "32": 108737,
+      "33": 38655,
+      "34": 66069,
+      "35": 27821,
+      "36": 62271,
+      "37": 22980,
+      "38": 38954,
+      "39": 16394,
+      "4": 123431,
+      "40": 29759,
+      "41": 10953,
+      "42": 14407,
+      "43": 5856,
+      "44": 7661,
+      "45": 3674,
+      "46": 4147,
+      "47": 2497,
+      "48": 3501,
+      "49": 2131,
+      "5": 948702,
+      "50": 2951,
+      "51": 1874,
+      "52": 2782,
+      "53": 1800,
+      "54": 2472,
+      "55": 1728,
+      "56": 2527,
+      "57": 1757,
+      "58": 2287,
+      "59": 1743,
+      "6": 5234234,
+      "60": 2506,
+      "61": 1627,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2051042,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6087557,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1828733,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 54541,
+      "7": 31525411,
+      "9": 123431
+    },
+    "connectivity_max": 141150200,
+    "connectivity_min": 0,
+    "n_cells": 31703383,
+    "n_connectivity_values": 345696033,
+    "n_fan_triangles": 282289267,
+    "n_points": 141150201
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.372066653177308e-11,
+    "float64_area_closure_relative": 2.7015531646212644e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282289267,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939139.8809543087,
+    "surface_area_float64_in2": 1939139.8810196978,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939139.8810197501,
+    "zero_area_triangles": 238365,
+    "zero_weight_points": 5567
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC042_AoA_4.json b/surface_dual_areas/cases/geo_LHC042_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..bde70e7c1331b0b325146a668d7dfacbe8490cdf
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC042_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC042_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC042_AoA_4/boundary_dual_area_geo_LHC042_AoA_4.npy",
+    "sha256": "79bbe4dc6515ecc4c736a7671afd7adf8c66a7c115ca635e7d480dcb0539ec2e",
+    "shape": [
+      137810418
+    ],
+    "size_bytes": 551241800
+  },
+  "runtime": {
+    "accumulation_seconds": 10.371544477064162,
+    "completed_at_utc": "2026-08-07T07:28:24.312542Z",
+    "elapsed_seconds": 21.264727561967447,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9243778069503605,
+    "geometry_read_seconds": 3.121477758977562,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:28:03.047688Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC042_AoA_4/boundary_geo_LHC042_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC042_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624699000000000,
+    "extracted_vtu_size_bytes": 21156968202,
+    "geometry_sha256": "e57a556dca689384b894328fdc2fb712d52403abc69d4ab4d6cb805b2e76f817",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2933793,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 930095,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2317670,
+      "13": 797217,
+      "14": 1856061,
+      "15": 591142,
+      "16": 1107039,
+      "17": 397459,
+      "18": 755296,
+      "19": 302349,
+      "20": 662389,
+      "21": 221240,
+      "22": 345376,
+      "23": 119722,
+      "24": 196655,
+      "25": 69668,
+      "26": 90518,
+      "27": 51521,
+      "28": 123603,
+      "29": 52797,
+      "3": 57581,
+      "30": 115136,
+      "31": 49559,
+      "32": 109491,
+      "33": 38918,
+      "34": 66648,
+      "35": 28040,
+      "36": 62876,
+      "37": 22806,
+      "38": 38682,
+      "39": 16232,
+      "4": 128470,
+      "40": 29349,
+      "41": 10699,
+      "42": 14291,
+      "43": 5852,
+      "44": 7750,
+      "45": 3603,
+      "46": 4304,
+      "47": 2536,
+      "48": 3544,
+      "49": 2152,
+      "5": 954445,
+      "50": 2923,
+      "51": 1854,
+      "52": 2724,
+      "53": 1761,
+      "54": 2423,
+      "55": 1715,
+      "56": 2548,
+      "57": 1716,
+      "58": 2312,
+      "59": 1702,
+      "6": 5282461,
+      "60": 2442,
+      "61": 1664,
+      "62": 2196,
+      "63": 1586,
+      "64": 2151,
+      "65": 1369,
+      "66": 1771,
+      "67": 1094,
+      "68": 1503,
+      "69": 880,
+      "7": 2001065,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5832477,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1589363,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57581,
+      "7": 30258434,
+      "9": 128470
+    },
+    "connectivity_max": 137810417,
+    "connectivity_min": 0,
+    "n_cells": 30444485,
+    "n_connectivity_values": 336498682,
+    "n_fan_triangles": 275609712,
+    "n_points": 137810418
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.068547085817554e-11,
+    "float64_area_closure_relative": 8.856688112258677e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275609712,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945362.3534329718,
+    "surface_area_float64_in2": 1945362.3535121197,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945362.353512137,
+    "zero_area_triangles": 224987,
+    "zero_weight_points": 5035
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC042_AoA_6.json b/surface_dual_areas/cases/geo_LHC042_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..911eb07d9a0b95fc86f2ae89e87b3ab150027d66
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC042_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC042_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC042_AoA_6/boundary_dual_area_geo_LHC042_AoA_6.npy",
+    "sha256": "0c9e8c598627ccb188cfdf57c556d2ac62f341ea0a2b3999bcdfaf90e483d2e5",
+    "shape": [
+      137936186
+    ],
+    "size_bytes": 551744872
+  },
+  "runtime": {
+    "accumulation_seconds": 10.40053934394382,
+    "completed_at_utc": "2026-08-07T07:28:41.909470Z",
+    "elapsed_seconds": 20.125610823044553,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.8916551279835403,
+    "geometry_read_seconds": 2.3281878461129963,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:28:21.783769Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC042_AoA_6/boundary_geo_LHC042_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC042_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624599000000000,
+    "extracted_vtu_size_bytes": 21176555041,
+    "geometry_sha256": "32086227fa0d7a6eeeaa707332b699d1a6df50bb0c7814c53c4d9ec01a528133",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2960463,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 928071,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2308881,
+      "13": 794463,
+      "14": 1861136,
+      "15": 591941,
+      "16": 1107146,
+      "17": 397119,
+      "18": 755397,
+      "19": 302052,
+      "20": 662299,
+      "21": 221050,
+      "22": 344863,
+      "23": 119679,
+      "24": 196505,
+      "25": 69672,
+      "26": 90510,
+      "27": 51515,
+      "28": 123608,
+      "29": 52803,
+      "3": 55197,
+      "30": 115147,
+      "31": 49558,
+      "32": 109490,
+      "33": 38923,
+      "34": 66649,
+      "35": 28039,
+      "36": 62875,
+      "37": 22807,
+      "38": 38682,
+      "39": 16230,
+      "4": 127733,
+      "40": 29349,
+      "41": 10698,
+      "42": 14292,
+      "43": 5850,
+      "44": 7748,
+      "45": 3604,
+      "46": 4304,
+      "47": 2535,
+      "48": 3543,
+      "49": 2155,
+      "5": 955436,
+      "50": 2924,
+      "51": 1854,
+      "52": 2724,
+      "53": 1761,
+      "54": 2423,
+      "55": 1715,
+      "56": 2548,
+      "57": 1716,
+      "58": 2312,
+      "59": 1702,
+      "6": 5287342,
+      "60": 2442,
+      "61": 1664,
+      "62": 2196,
+      "63": 1586,
+      "64": 2151,
+      "65": 1369,
+      "66": 1771,
+      "67": 1094,
+      "68": 1503,
+      "69": 880,
+      "7": 2003299,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5847193,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1591015,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 55197,
+      "7": 30300482,
+      "9": 127733
+    },
+    "connectivity_max": 137936185,
+    "connectivity_min": 0,
+    "n_cells": 30483412,
+    "n_connectivity_values": 336828072,
+    "n_fan_triangles": 275861248,
+    "n_points": 137936186
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.1205021858121905e-11,
+    "float64_area_closure_relative": 1.1968497020765688e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275861248,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945362.4230369774,
+    "surface_area_float64_in2": 1945362.4231171361,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945362.4231171338,
+    "zero_area_triangles": 224384,
+    "zero_weight_points": 4942
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC043_AoA_10.json b/surface_dual_areas/cases/geo_LHC043_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..fc5bab73d534d8eb1ccbaa54dc8d562f47a1ba1c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC043_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC043_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC043_AoA_10/boundary_dual_area_geo_LHC043_AoA_10.npy",
+    "sha256": "0faf714fb2bedee2f43e70a42d317bb92f11810a78db10db45ca315062c0e33e",
+    "shape": [
+      140614027
+    ],
+    "size_bytes": 562456236
+  },
+  "runtime": {
+    "accumulation_seconds": 10.60256248083897,
+    "completed_at_utc": "2026-08-07T07:29:03.461444Z",
+    "elapsed_seconds": 20.491342353168875,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.95734384492971,
+    "geometry_read_seconds": 2.1665304671041667,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:28:42.970007Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC043_AoA_10/boundary_geo_LHC043_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC043_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624535000000000,
+    "extracted_vtu_size_bytes": 21593191964,
+    "geometry_sha256": "36c6d6dbfef28fe6a0347af99afb3bddbb0c1628fbd7d07532c13c268ab30ae0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3306482,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1113103,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2546081,
+      "13": 815370,
+      "14": 1603984,
+      "15": 526365,
+      "16": 1018488,
+      "17": 380149,
+      "18": 770753,
+      "19": 310096,
+      "20": 691202,
+      "21": 228258,
+      "22": 364175,
+      "23": 121070,
+      "24": 198395,
+      "25": 68933,
+      "26": 89020,
+      "27": 51546,
+      "28": 123391,
+      "29": 53098,
+      "3": 57255,
+      "30": 114651,
+      "31": 49525,
+      "32": 108626,
+      "33": 39162,
+      "34": 66871,
+      "35": 28214,
+      "36": 62041,
+      "37": 22765,
+      "38": 37953,
+      "39": 15917,
+      "4": 133558,
+      "40": 28886,
+      "41": 10530,
+      "42": 14063,
+      "43": 5750,
+      "44": 7730,
+      "45": 3609,
+      "46": 4121,
+      "47": 2515,
+      "48": 3556,
+      "49": 2090,
+      "5": 945421,
+      "50": 2839,
+      "51": 1759,
+      "52": 2553,
+      "53": 1650,
+      "54": 2242,
+      "55": 1613,
+      "56": 2426,
+      "57": 1702,
+      "58": 2265,
+      "59": 1737,
+      "6": 5231217,
+      "60": 2506,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2040964,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6095442,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1739833,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 57255,
+      "7": 31105254,
+      "9": 133558
+    },
+    "connectivity_max": 140614026,
+    "connectivity_min": 0,
+    "n_cells": 31296067,
+    "n_connectivity_values": 343809074,
+    "n_fan_triangles": 281216940,
+    "n_points": 140614027
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9405767101415983e-11,
+    "float64_area_closure_relative": 4.823388452761099e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281216940,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945328.4824094884,
+    "surface_area_float64_in2": 1945328.4824861456,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945328.4824860517,
+    "zero_area_triangles": 235923,
+    "zero_weight_points": 5559
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC043_AoA_14.json b/surface_dual_areas/cases/geo_LHC043_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..00b0756b7b6312ebb7676fae79ec182ca705092b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC043_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC043_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC043_AoA_14/boundary_dual_area_geo_LHC043_AoA_14.npy",
+    "sha256": "a03be2fa2dc424fd45b80a53ddf58d8f82abfe54417ebb9d78c6d23a72bea0a7",
+    "shape": [
+      145048267
+    ],
+    "size_bytes": 580193196
+  },
+  "runtime": {
+    "accumulation_seconds": 11.113611099077389,
+    "completed_at_utc": "2026-08-07T07:49:32.187554Z",
+    "elapsed_seconds": 21.612892493139952,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4243360720574856,
+    "geometry_read_seconds": 2.1381586140487343,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:49:10.574582Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC043_AoA_14/boundary_geo_LHC043_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC043_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624506000000000,
+    "extracted_vtu_size_bytes": 22282557817,
+    "geometry_sha256": "97bb22603b9b542ab3dc27b3d03cc6b5df6194e858841cc679747535f8e4dddd",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3904210,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1292289,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2799930,
+      "13": 838920,
+      "14": 1450922,
+      "15": 483141,
+      "16": 957655,
+      "17": 366268,
+      "18": 764178,
+      "19": 308548,
+      "20": 688667,
+      "21": 227446,
+      "22": 362487,
+      "23": 120435,
+      "24": 197716,
+      "25": 68789,
+      "26": 88963,
+      "27": 51499,
+      "28": 123352,
+      "29": 53083,
+      "3": 58728,
+      "30": 114623,
+      "31": 49514,
+      "32": 108612,
+      "33": 39154,
+      "34": 66861,
+      "35": 28206,
+      "36": 62014,
+      "37": 22747,
+      "38": 37943,
+      "39": 15905,
+      "4": 135850,
+      "40": 28868,
+      "41": 10530,
+      "42": 14052,
+      "43": 5747,
+      "44": 7731,
+      "45": 3610,
+      "46": 4121,
+      "47": 2512,
+      "48": 3554,
+      "49": 2093,
+      "5": 949217,
+      "50": 2840,
+      "51": 1756,
+      "52": 2553,
+      "53": 1650,
+      "54": 2242,
+      "55": 1613,
+      "56": 2426,
+      "57": 1702,
+      "58": 2265,
+      "59": 1737,
+      "6": 5244059,
+      "60": 2506,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 2108763,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 436,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6371939,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1930708,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 58728,
+      "7": 32425422,
+      "9": 135850
+    },
+    "connectivity_max": 145048266,
+    "connectivity_min": 0,
+    "n_cells": 32620000,
+    "n_connectivity_values": 355325421,
+    "n_fan_triangles": 290085421,
+    "n_points": 145048267
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9566046107058036e-11,
+    "float64_area_closure_relative": 4.93110905293679e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290085421,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945327.5957153833,
+    "surface_area_float64_in2": 1945327.5957923522,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945327.5957922563,
+    "zero_area_triangles": 242370,
+    "zero_weight_points": 5985
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC043_AoA_16.json b/surface_dual_areas/cases/geo_LHC043_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..127c14025796c79ea58cfe11659532cd138b8f2b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC043_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC043_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC043_AoA_16/boundary_dual_area_geo_LHC043_AoA_16.npy",
+    "sha256": "9c70546aa3be405d29672af3b391533cecdd066a43a28a0014a47dc3932bd49c",
+    "shape": [
+      146686848
+    ],
+    "size_bytes": 586747520
+  },
+  "runtime": {
+    "accumulation_seconds": 11.395380420144647,
+    "completed_at_utc": "2026-08-07T07:47:03.489701Z",
+    "elapsed_seconds": 53.96044575306587,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.641928610857576,
+    "geometry_read_seconds": 33.80272009805776,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:46:09.529160Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC043_AoA_16/boundary_geo_LHC043_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC043_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624533000000000,
+    "extracted_vtu_size_bytes": 22537086947,
+    "geometry_sha256": "83b0cf3cf5638532e3ee3d4560abdebd25845c6068f5e99a676d0dc37369b9a4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4137500,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1351863,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2901754,
+      "13": 847444,
+      "14": 1392896,
+      "15": 470423,
+      "16": 935767,
+      "17": 362084,
+      "18": 762138,
+      "19": 307826,
+      "20": 686820,
+      "21": 226794,
+      "22": 361103,
+      "23": 120071,
+      "24": 196994,
+      "25": 68635,
+      "26": 88862,
+      "27": 51457,
+      "28": 123327,
+      "29": 53077,
+      "3": 59021,
+      "30": 114637,
+      "31": 49517,
+      "32": 108603,
+      "33": 39148,
+      "34": 66867,
+      "35": 28209,
+      "36": 62011,
+      "37": 22750,
+      "38": 37941,
+      "39": 15904,
+      "4": 136633,
+      "40": 28870,
+      "41": 10528,
+      "42": 14057,
+      "43": 5746,
+      "44": 7727,
+      "45": 3611,
+      "46": 4124,
+      "47": 2512,
+      "48": 3554,
+      "49": 2093,
+      "5": 948638,
+      "50": 2839,
+      "51": 1758,
+      "52": 2554,
+      "53": 1649,
+      "54": 2241,
+      "55": 1613,
+      "56": 2425,
+      "57": 1702,
+      "58": 2265,
+      "59": 1737,
+      "6": 5240270,
+      "60": 2506,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2128825,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6473977,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1994318,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59021,
+      "7": 32905112,
+      "9": 136633
+    },
+    "connectivity_max": 146686847,
+    "connectivity_min": 0,
+    "n_cells": 33100766,
+    "n_connectivity_values": 359564114,
+    "n_fan_triangles": 293362582,
+    "n_points": 146686848
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.952236608031491e-11,
+    "float64_area_closure_relative": 1.196871304072962e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293362582,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945327.3117363844,
+    "surface_area_float64_in2": 1945327.3118132683,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945327.3118132707,
+    "zero_area_triangles": 244128,
+    "zero_weight_points": 6079
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC043_AoA_20.json b/surface_dual_areas/cases/geo_LHC043_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..f66ad4e5549a60bae473ce5551f4d3f291a50f42
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC043_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC043_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC043_AoA_20/boundary_dual_area_geo_LHC043_AoA_20.npy",
+    "sha256": "79fc9f9d697b33904d8f1c23460f3c409c3c1aea4ea087a6d463e0c63458d57c",
+    "shape": [
+      148234148
+    ],
+    "size_bytes": 592936720
+  },
+  "runtime": {
+    "accumulation_seconds": 11.49400218296796,
+    "completed_at_utc": "2026-08-07T07:49:11.198567Z",
+    "elapsed_seconds": 22.531361384084448,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.437044481979683,
+    "geometry_read_seconds": 2.211777992080897,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:48:48.667113Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC043_AoA_20/boundary_geo_LHC043_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC043_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624655000000000,
+    "extracted_vtu_size_bytes": 22777824472,
+    "geometry_sha256": "52ce048dda39bf46c5a062722f7258023cdaaddb5ea0ac9c0329101dc6ac9284",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4378157,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1405021,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2966477,
+      "13": 848741,
+      "14": 1331580,
+      "15": 457141,
+      "16": 918455,
+      "17": 359163,
+      "18": 761761,
+      "19": 308226,
+      "20": 687690,
+      "21": 226532,
+      "22": 359930,
+      "23": 119453,
+      "24": 196327,
+      "25": 68409,
+      "26": 88807,
+      "27": 51451,
+      "28": 123318,
+      "29": 53096,
+      "3": 60342,
+      "30": 114636,
+      "31": 49518,
+      "32": 108607,
+      "33": 39150,
+      "34": 66880,
+      "35": 28217,
+      "36": 62043,
+      "37": 22748,
+      "38": 37949,
+      "39": 15912,
+      "4": 138929,
+      "40": 28882,
+      "41": 10535,
+      "42": 14063,
+      "43": 5750,
+      "44": 7724,
+      "45": 3610,
+      "46": 4122,
+      "47": 2518,
+      "48": 3553,
+      "49": 2088,
+      "5": 950345,
+      "50": 2840,
+      "51": 1759,
+      "52": 2553,
+      "53": 1649,
+      "54": 2244,
+      "55": 1612,
+      "56": 2425,
+      "57": 1702,
+      "58": 2265,
+      "59": 1737,
+      "6": 5236809,
+      "60": 2506,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2151683,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6591175,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2058885,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60342,
+      "7": 33370980,
+      "9": 138929
+    },
+    "connectivity_max": 148234147,
+    "connectivity_min": 0,
+    "n_cells": 33570251,
+    "n_connectivity_values": 363597684,
+    "n_fan_triangles": 296457182,
+    "n_points": 148234148
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.908694958875845e-11,
+    "float64_area_closure_relative": 4.7156735761264846e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296457182,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945327.0485144886,
+    "surface_area_float64_in2": 1945327.0485905255,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945327.0485904338,
+    "zero_area_triangles": 246495,
+    "zero_weight_points": 6242
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC044_AoA_18.json b/surface_dual_areas/cases/geo_LHC044_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3811b07145b66607c35e3f74dfa6af31ceecccb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC044_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC044_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC044_AoA_18/boundary_dual_area_geo_LHC044_AoA_18.npy",
+    "sha256": "b78174a60632a456613fbce77abf9f626efa2502ee0bee2a75804b3a4b240ac5",
+    "shape": [
+      147705765
+    ],
+    "size_bytes": 590823188
+  },
+  "runtime": {
+    "accumulation_seconds": 11.33796025486663,
+    "completed_at_utc": "2026-08-07T07:49:55.287015Z",
+    "elapsed_seconds": 22.03115128003992,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3133474430069327,
+    "geometry_read_seconds": 2.3814905050676316,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:49:33.255769Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC044_AoA_18/boundary_geo_LHC044_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC044_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624506000000000,
+    "extracted_vtu_size_bytes": 22697485344,
+    "geometry_sha256": "07c59cf766a40d98ba2565175adcfd83da94c1b23e9d0ff66244b0add9615efa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4543406,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1349449,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2998044,
+      "13": 798878,
+      "14": 1234789,
+      "15": 432033,
+      "16": 891963,
+      "17": 358782,
+      "18": 762641,
+      "19": 313683,
+      "20": 685097,
+      "21": 228251,
+      "22": 350719,
+      "23": 122426,
+      "24": 201637,
+      "25": 70778,
+      "26": 91673,
+      "27": 52150,
+      "28": 123246,
+      "29": 52977,
+      "3": 59494,
+      "30": 114598,
+      "31": 49215,
+      "32": 108119,
+      "33": 38480,
+      "34": 65940,
+      "35": 27765,
+      "36": 62895,
+      "37": 23000,
+      "38": 39580,
+      "39": 16654,
+      "4": 136433,
+      "40": 30517,
+      "41": 11068,
+      "42": 14513,
+      "43": 6010,
+      "44": 7932,
+      "45": 3767,
+      "46": 4235,
+      "47": 2499,
+      "48": 3606,
+      "49": 2224,
+      "5": 945495,
+      "50": 2888,
+      "51": 1860,
+      "52": 2776,
+      "53": 1751,
+      "54": 2441,
+      "55": 1734,
+      "56": 2539,
+      "57": 1783,
+      "58": 2279,
+      "59": 1698,
+      "6": 5228212,
+      "60": 2470,
+      "61": 1654,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2138323,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6610984,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2025626,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59494,
+      "7": 33288792,
+      "9": 136433
+    },
+    "connectivity_max": 147705764,
+    "connectivity_min": 0,
+    "n_cells": 33484719,
+    "n_connectivity_values": 362369836,
+    "n_fan_triangles": 295400398,
+    "n_points": 147705765
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.670713870345023e-11,
+    "float64_area_closure_relative": 4.639888523379221e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295400398,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946992.6762074914,
+    "surface_area_float64_in2": 1946992.67627896,
+    "weight_max_in2": 1.101064467658409,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946992.6762790503,
+    "zero_area_triangles": 241404,
+    "zero_weight_points": 6215
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC046_AoA_18.json b/surface_dual_areas/cases/geo_LHC046_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..ee1445e40a11ec999fbf9c0eea354217509e4e07
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC046_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC046_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC046_AoA_18/boundary_dual_area_geo_LHC046_AoA_18.npy",
+    "sha256": "3ff52322bc5586cd8980d22b6485ed416598726858096ead8ef00dceaa075cdf",
+    "shape": [
+      148845539
+    ],
+    "size_bytes": 595382284
+  },
+  "runtime": {
+    "accumulation_seconds": 11.16966336616315,
+    "completed_at_utc": "2026-08-07T07:30:20.622503Z",
+    "elapsed_seconds": 22.44421923207119,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3174598289187998,
+    "geometry_read_seconds": 3.08327119005844,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:29:58.178185Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC046_AoA_18/boundary_geo_LHC046_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC046_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624557000000000,
+    "extracted_vtu_size_bytes": 22871890473,
+    "geometry_sha256": "b3e3293612bd5255566bcd10c7b1656fd7a96e9458c0f1caa858d60a81ad32af",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4482843,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1369552,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3053999,
+      "13": 844063,
+      "14": 1325525,
+      "15": 465418,
+      "16": 920036,
+      "17": 366077,
+      "18": 756570,
+      "19": 307572,
+      "20": 664395,
+      "21": 224315,
+      "22": 361231,
+      "23": 119916,
+      "24": 196028,
+      "25": 68142,
+      "26": 89969,
+      "27": 51327,
+      "28": 124255,
+      "29": 52806,
+      "3": 60684,
+      "30": 114730,
+      "31": 49109,
+      "32": 108572,
+      "33": 38432,
+      "34": 66684,
+      "35": 27906,
+      "36": 62823,
+      "37": 23105,
+      "38": 38849,
+      "39": 16378,
+      "4": 137480,
+      "40": 29874,
+      "41": 10950,
+      "42": 14578,
+      "43": 5997,
+      "44": 7690,
+      "45": 3685,
+      "46": 4185,
+      "47": 2466,
+      "48": 3496,
+      "49": 2114,
+      "5": 951850,
+      "50": 2903,
+      "51": 1839,
+      "52": 2783,
+      "53": 1787,
+      "54": 2461,
+      "55": 1714,
+      "56": 2532,
+      "57": 1766,
+      "58": 2300,
+      "59": 1745,
+      "6": 5223153,
+      "60": 2512,
+      "61": 1626,
+      "62": 2260,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2156002,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6624013,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2039725,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60684,
+      "7": 33515300,
+      "9": 137480
+    },
+    "connectivity_max": 148845538,
+    "connectivity_min": 0,
+    "n_cells": 33713464,
+    "n_connectivity_values": 365106868,
+    "n_fan_triangles": 297679940,
+    "n_points": 148845539
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.145979742061856e-11,
+    "float64_area_closure_relative": 3.742851874943356e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 297679940,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947071.214559958,
+    "surface_area_float64_in2": 1947071.2146406833,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947071.2146406104,
+    "zero_area_triangles": 244686,
+    "zero_weight_points": 6223
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC047_AoA_12.json b/surface_dual_areas/cases/geo_LHC047_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..248521b2691c14d494496bd366a371b86e0d3b66
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC047_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC047_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC047_AoA_12/boundary_dual_area_geo_LHC047_AoA_12.npy",
+    "sha256": "ddb1deb34b9857db8e7fc95b094f3facf024dff4069a41217650705d59150ba4",
+    "shape": [
+      145299184
+    ],
+    "size_bytes": 581196864
+  },
+  "runtime": {
+    "accumulation_seconds": 11.252830761950463,
+    "completed_at_utc": "2026-08-07T07:50:54.500013Z",
+    "elapsed_seconds": 21.610435436014086,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3622612399049103,
+    "geometry_read_seconds": 2.1785904630087316,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:50:32.889498Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC047_AoA_12/boundary_geo_LHC047_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC047_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624540000000000,
+    "extracted_vtu_size_bytes": 22318489993,
+    "geometry_sha256": "e2648b11aef8302811633bee47c447441d4dd12de879edb854442a7aeeb1496f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3837539,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1275964,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2801912,
+      "13": 869929,
+      "14": 1606181,
+      "15": 515949,
+      "16": 1008501,
+      "17": 370808,
+      "18": 743043,
+      "19": 298226,
+      "20": 663884,
+      "21": 218328,
+      "22": 349817,
+      "23": 117888,
+      "24": 196962,
+      "25": 67892,
+      "26": 90401,
+      "27": 51495,
+      "28": 123581,
+      "29": 52844,
+      "3": 58901,
+      "30": 114337,
+      "31": 49243,
+      "32": 108391,
+      "33": 38679,
+      "34": 66744,
+      "35": 27788,
+      "36": 62209,
+      "37": 22768,
+      "38": 38562,
+      "39": 16219,
+      "4": 134487,
+      "40": 29394,
+      "41": 10720,
+      "42": 14393,
+      "43": 5852,
+      "44": 7666,
+      "45": 3642,
+      "46": 4178,
+      "47": 2531,
+      "48": 3512,
+      "49": 2118,
+      "5": 945355,
+      "50": 2850,
+      "51": 1810,
+      "52": 2675,
+      "53": 1728,
+      "54": 2362,
+      "55": 1683,
+      "56": 2489,
+      "57": 1754,
+      "58": 2273,
+      "59": 1742,
+      "6": 5196634,
+      "60": 2507,
+      "61": 1627,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2089515,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6309057,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1903396,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 58901,
+      "7": 32378472,
+      "9": 134487
+    },
+    "connectivity_max": 145299183,
+    "connectivity_min": 0,
+    "n_cells": 32571860,
+    "n_connectivity_values": 355730970,
+    "n_fan_triangles": 290587250,
+    "n_points": 145299184
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.681315340617597e-11,
+    "float64_area_closure_relative": 5.5506894549709163e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290587250,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946306.3017274223,
+    "surface_area_float64_in2": 1946306.301799072,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946306.30179918,
+    "zero_area_triangles": 238201,
+    "zero_weight_points": 5840
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC047_AoA_14.json b/surface_dual_areas/cases/geo_LHC047_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..759c4467f1911a88e96440d77e8e0fc3eac72602
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC047_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC047_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC047_AoA_14/boundary_dual_area_geo_LHC047_AoA_14.npy",
+    "sha256": "3fcc80484aaa2d0b0b6dbbfb8face06d4e42a66cbccfd7daae66fcbc32c6c0f5",
+    "shape": [
+      147154629
+    ],
+    "size_bytes": 588618644
+  },
+  "runtime": {
+    "accumulation_seconds": 12.398811056977138,
+    "completed_at_utc": "2026-08-07T07:49:31.476080Z",
+    "elapsed_seconds": 23.47761601000093,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2882036441005766,
+    "geometry_read_seconds": 2.8723640150856227,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:49:07.998352Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC047_AoA_14/boundary_geo_LHC047_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC047_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624524000000000,
+    "extracted_vtu_size_bytes": 22606996603,
+    "geometry_sha256": "f1c40625e6ad70cd273a4b043a64b13b40d96725de5ca5ac0cd81b394ae99122",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4089074,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1348684,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2918429,
+      "13": 881263,
+      "14": 1530578,
+      "15": 499276,
+      "16": 976701,
+      "17": 365872,
+      "18": 742139,
+      "19": 298068,
+      "20": 663686,
+      "21": 217920,
+      "22": 349603,
+      "23": 117555,
+      "24": 196946,
+      "25": 67721,
+      "26": 90429,
+      "27": 51453,
+      "28": 123588,
+      "29": 52839,
+      "3": 59060,
+      "30": 114335,
+      "31": 49242,
+      "32": 108389,
+      "33": 38681,
+      "34": 66743,
+      "35": 27788,
+      "36": 62212,
+      "37": 22769,
+      "38": 38560,
+      "39": 16217,
+      "4": 135270,
+      "40": 29395,
+      "41": 10719,
+      "42": 14394,
+      "43": 5852,
+      "44": 7664,
+      "45": 3643,
+      "46": 4180,
+      "47": 2532,
+      "48": 3512,
+      "49": 2116,
+      "5": 945835,
+      "50": 2850,
+      "51": 1811,
+      "52": 2676,
+      "53": 1728,
+      "54": 2360,
+      "55": 1683,
+      "56": 2489,
+      "57": 1754,
+      "58": 2273,
+      "59": 1742,
+      "6": 5203906,
+      "60": 2507,
+      "61": 1627,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2116899,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6431197,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1980531,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59060,
+      "7": 32933560,
+      "9": 135270
+    },
+    "connectivity_max": 147154628,
+    "connectivity_min": 0,
+    "n_cells": 33127890,
+    "n_connectivity_values": 360553920,
+    "n_fan_triangles": 294298140,
+    "n_points": 147154629
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.70534919101606e-11,
+    "float64_area_closure_relative": 5.514802568132199e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294298140,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946305.8812060044,
+    "surface_area_float64_in2": 1946305.8812781218,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946305.8812782292,
+    "zero_area_triangles": 240696,
+    "zero_weight_points": 6008
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC047_AoA_16.json b/surface_dual_areas/cases/geo_LHC047_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..71a5e294c20ca0abbce2069c879673b8b2a9217c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC047_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC047_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC047_AoA_16/boundary_dual_area_geo_LHC047_AoA_16.npy",
+    "sha256": "3c31f277b10bc205b36913d2208e54844654f234ffd6f9f9a8b7d9aac2f52ac8",
+    "shape": [
+      148139639
+    ],
+    "size_bytes": 592558684
+  },
+  "runtime": {
+    "accumulation_seconds": 11.371036316035315,
+    "completed_at_utc": "2026-08-07T07:50:50.026844Z",
+    "elapsed_seconds": 22.10250590601936,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.721334684174508,
+    "geometry_read_seconds": 1.9812196679413319,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:50:27.924254Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC047_AoA_16/boundary_geo_LHC047_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC047_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624421000000000,
+    "extracted_vtu_size_bytes": 22760585533,
+    "geometry_sha256": "6cae9fc87414a626e02438c4839300444b340ab13e471af874fb3e75bfabc4dc",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4274571,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1394639,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2976553,
+      "13": 883971,
+      "14": 1440744,
+      "15": 486354,
+      "16": 943002,
+      "17": 362290,
+      "18": 743276,
+      "19": 298255,
+      "20": 666381,
+      "21": 218311,
+      "22": 355422,
+      "23": 117945,
+      "24": 201476,
+      "25": 68056,
+      "26": 90911,
+      "27": 51484,
+      "28": 123600,
+      "29": 52839,
+      "3": 59290,
+      "30": 114339,
+      "31": 49246,
+      "32": 108397,
+      "33": 38672,
+      "34": 66740,
+      "35": 27801,
+      "36": 62222,
+      "37": 22766,
+      "38": 38564,
+      "39": 16218,
+      "4": 135555,
+      "40": 29391,
+      "41": 10719,
+      "42": 14395,
+      "43": 5853,
+      "44": 7666,
+      "45": 3640,
+      "46": 4178,
+      "47": 2531,
+      "48": 3512,
+      "49": 2117,
+      "5": 944255,
+      "50": 2849,
+      "51": 1812,
+      "52": 2676,
+      "53": 1728,
+      "54": 2362,
+      "55": 1683,
+      "56": 2489,
+      "57": 1754,
+      "58": 2273,
+      "59": 1742,
+      "6": 5199434,
+      "60": 2507,
+      "61": 1627,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2131995,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6515858,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2030327,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59290,
+      "7": 33245343,
+      "9": 135555
+    },
+    "connectivity_max": 148139638,
+    "connectivity_min": 0,
+    "n_cells": 33440188,
+    "n_connectivity_values": 363148536,
+    "n_fan_triangles": 296268160,
+    "n_points": 148139639
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.7882269510519014e-11,
+    "float64_area_closure_relative": 2.105434500853048e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296268160,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946305.7751227021,
+    "surface_area_float64_in2": 1946305.7751964326,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946305.7751964736,
+    "zero_area_triangles": 242090,
+    "zero_weight_points": 6093
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC047_AoA_6.json b/surface_dual_areas/cases/geo_LHC047_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..c61612ab4043206f9f8b5917ea65b43ff86428ca
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC047_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC047_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC047_AoA_6/boundary_dual_area_geo_LHC047_AoA_6.npy",
+    "sha256": "09afc47ddcd70fa8f600c7540da3ffc43196beacd7f1b12cd51a4c626a8cb3e4",
+    "shape": [
+      137187698
+    ],
+    "size_bytes": 548750920
+  },
+  "runtime": {
+    "accumulation_seconds": 11.162345391931012,
+    "completed_at_utc": "2026-08-07T07:50:39.119525Z",
+    "elapsed_seconds": 20.67158593609929,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1416804660111666,
+    "geometry_read_seconds": 1.8569938491564244,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:50:18.447831Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC047_AoA_6/boundary_geo_LHC047_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC047_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624679000000000,
+    "extracted_vtu_size_bytes": 21057573740,
+    "geometry_sha256": "5ec338db6a93b8b6149bcc62c4eb89baad95a6a4277b70504057ba613edb6620",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2836097,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 954496,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2264291,
+      "13": 825033,
+      "14": 1895832,
+      "15": 605356,
+      "16": 1109793,
+      "17": 399978,
+      "18": 754454,
+      "19": 302520,
+      "20": 667423,
+      "21": 220189,
+      "22": 352005,
+      "23": 118998,
+      "24": 198105,
+      "25": 68318,
+      "26": 90677,
+      "27": 51564,
+      "28": 123658,
+      "29": 52855,
+      "3": 57320,
+      "30": 114344,
+      "31": 49244,
+      "32": 108393,
+      "33": 38681,
+      "34": 66744,
+      "35": 27788,
+      "36": 62210,
+      "37": 22767,
+      "38": 38562,
+      "39": 16219,
+      "4": 133399,
+      "40": 29395,
+      "41": 10719,
+      "42": 14394,
+      "43": 5851,
+      "44": 7666,
+      "45": 3642,
+      "46": 4178,
+      "47": 2531,
+      "48": 3512,
+      "49": 2118,
+      "5": 940498,
+      "50": 2850,
+      "51": 1810,
+      "52": 2675,
+      "53": 1728,
+      "54": 2362,
+      "55": 1683,
+      "56": 2489,
+      "57": 1754,
+      "58": 2273,
+      "59": 1742,
+      "6": 5170518,
+      "60": 2507,
+      "61": 1627,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1960755,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5758678,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1569014,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 57320,
+      "7": 29964488,
+      "9": 133399
+    },
+    "connectivity_max": 137187697,
+    "connectivity_min": 0,
+    "n_cells": 30155207,
+    "n_connectivity_values": 334674692,
+    "n_fan_triangles": 274364278,
+    "n_points": 137187698
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.725883900362835e-11,
+    "float64_area_closure_relative": 7.895367846938028e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274364278,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946308.617722275,
+    "surface_area_float64_in2": 1946308.6177947922,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946308.6177947768,
+    "zero_area_triangles": 224579,
+    "zero_weight_points": 4964
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC048_AoA_14.json b/surface_dual_areas/cases/geo_LHC048_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0967b6e85267521b2544e0c108ad466900025a4
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC048_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC048_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC048_AoA_14/boundary_dual_area_geo_LHC048_AoA_14.npy",
+    "sha256": "ffc4650ecc36fbca7cc295744102dd7a3cae3029a0c7c15ee745265333a804e2",
+    "shape": [
+      140861476
+    ],
+    "size_bytes": 563446032
+  },
+  "runtime": {
+    "accumulation_seconds": 10.792073321994394,
+    "completed_at_utc": "2026-08-07T07:49:59.186483Z",
+    "elapsed_seconds": 20.928652726113796,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2035783561877906,
+    "geometry_read_seconds": 2.0792468660511076,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:49:38.257740Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC048_AoA_14/boundary_geo_LHC048_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC048_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624397000000000,
+    "extracted_vtu_size_bytes": 21639380480,
+    "geometry_sha256": "f0616e1273806e35daae4025785092312dc23ef868d185be6ae4016139baef77",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4075643,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1199273,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2645682,
+      "13": 775815,
+      "14": 1284937,
+      "15": 457649,
+      "16": 907063,
+      "17": 358775,
+      "18": 753490,
+      "19": 306625,
+      "20": 663488,
+      "21": 224635,
+      "22": 347584,
+      "23": 121177,
+      "24": 200696,
+      "25": 68869,
+      "26": 94425,
+      "27": 51809,
+      "28": 124550,
+      "29": 52966,
+      "3": 52934,
+      "30": 115148,
+      "31": 49237,
+      "32": 108433,
+      "33": 38641,
+      "34": 65682,
+      "35": 27820,
+      "36": 62970,
+      "37": 22891,
+      "38": 39281,
+      "39": 16300,
+      "4": 118292,
+      "40": 30045,
+      "41": 10886,
+      "42": 14496,
+      "43": 5959,
+      "44": 7884,
+      "45": 3767,
+      "46": 4270,
+      "47": 2495,
+      "48": 3581,
+      "49": 2218,
+      "5": 937019,
+      "50": 2941,
+      "51": 1826,
+      "52": 2733,
+      "53": 1784,
+      "54": 2409,
+      "55": 1734,
+      "56": 2562,
+      "57": 1768,
+      "58": 2280,
+      "59": 1691,
+      "6": 5241512,
+      "60": 2471,
+      "61": 1653,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2016911,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6117624,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1802375,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52934,
+      "7": 31507489,
+      "9": 118292
+    },
+    "connectivity_max": 140861475,
+    "connectivity_min": 0,
+    "n_cells": 31678715,
+    "n_connectivity_values": 345069251,
+    "n_fan_triangles": 281711821,
+    "n_points": 140861476
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.4590854851881868e-11,
+    "float64_area_closure_relative": 6.515630446973462e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281711821,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936791.9940258716,
+    "surface_area_float64_in2": 1936791.994073499,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936791.9940736252,
+    "zero_area_triangles": 238539,
+    "zero_weight_points": 5783
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC048_AoA_6.json b/surface_dual_areas/cases/geo_LHC048_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3dbead98ee024952be397e64271348393e2b081
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC048_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC048_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC048_AoA_6/boundary_dual_area_geo_LHC048_AoA_6.npy",
+    "sha256": "e88e8dc11c2630f63717034e8bcefbe5306c1db5dd69096e0e905cc37eb959a5",
+    "shape": [
+      137826260
+    ],
+    "size_bytes": 551305168
+  },
+  "runtime": {
+    "accumulation_seconds": 10.376986847957596,
+    "completed_at_utc": "2026-08-07T07:31:11.402726Z",
+    "elapsed_seconds": 19.901982471114025,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9106346368789673,
+    "geometry_read_seconds": 1.9784461711533368,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:30:51.500649Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC048_AoA_6/boundary_geo_LHC048_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC048_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624526000000000,
+    "extracted_vtu_size_bytes": 21166897537,
+    "geometry_sha256": "cee04ddbf6e43b90ae0c07a132b97c245d60ce48d7ac06c9f28bd905053e52b9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3490449,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1094164,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2456452,
+      "13": 781260,
+      "14": 1488411,
+      "15": 499893,
+      "16": 985622,
+      "17": 371883,
+      "18": 752797,
+      "19": 304285,
+      "20": 657694,
+      "21": 221567,
+      "22": 339772,
+      "23": 119290,
+      "24": 195409,
+      "25": 68038,
+      "26": 93384,
+      "27": 51746,
+      "28": 124468,
+      "29": 52945,
+      "3": 51144,
+      "30": 115143,
+      "31": 49239,
+      "32": 108435,
+      "33": 38637,
+      "34": 65683,
+      "35": 27820,
+      "36": 62973,
+      "37": 22890,
+      "38": 39284,
+      "39": 16297,
+      "4": 114156,
+      "40": 30044,
+      "41": 10886,
+      "42": 14496,
+      "43": 5958,
+      "44": 7884,
+      "45": 3768,
+      "46": 4271,
+      "47": 2495,
+      "48": 3579,
+      "49": 2219,
+      "5": 937449,
+      "50": 2941,
+      "51": 1826,
+      "52": 2733,
+      "53": 1784,
+      "54": 2409,
+      "55": 1734,
+      "56": 2562,
+      "57": 1768,
+      "58": 2280,
+      "59": 1691,
+      "6": 5276217,
+      "60": 2471,
+      "61": 1653,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1981542,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5881158,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1679787,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51144,
+      "7": 30582576,
+      "9": 114156
+    },
+    "connectivity_max": 137826259,
+    "connectivity_min": 0,
+    "n_cells": 30747876,
+    "n_connectivity_values": 337137141,
+    "n_fan_triangles": 275641389,
+    "n_points": 137826260
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.4996095988641944e-11,
+    "float64_area_closure_relative": 3.305900762700987e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275641389,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936792.166468457,
+    "surface_area_float64_in2": 1936792.1665168693,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936792.1665169334,
+    "zero_area_triangles": 232995,
+    "zero_weight_points": 5374
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC049_AoA_18.json b/surface_dual_areas/cases/geo_LHC049_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..ebf45fb052d67b1bb1b1029a9c080ec4e108f721
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC049_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC049_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC049_AoA_18/boundary_dual_area_geo_LHC049_AoA_18.npy",
+    "sha256": "e49bad53834f571a781d851ad79327ad54ee385f07479ad4634710655f64af28",
+    "shape": [
+      139465451
+    ],
+    "size_bytes": 557861932
+  },
+  "runtime": {
+    "accumulation_seconds": 10.676710307132453,
+    "completed_at_utc": "2026-08-07T07:50:52.187972Z",
+    "elapsed_seconds": 50.40820732503198,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.207863418152556,
+    "geometry_read_seconds": 31.272341166157275,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T07:50:01.779662Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC049_AoA_18/boundary_geo_LHC049_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC049_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624614000000000,
+    "extracted_vtu_size_bytes": 21420894896,
+    "geometry_sha256": "481706ead45eea8bb3f4ae7a4eda1f92172c42d380b66c74144835567dead99f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3803356,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1156982,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2539378,
+      "13": 769789,
+      "14": 1375486,
+      "15": 475913,
+      "16": 934617,
+      "17": 364631,
+      "18": 761961,
+      "19": 308087,
+      "20": 681117,
+      "21": 226751,
+      "22": 360249,
+      "23": 120971,
+      "24": 193867,
+      "25": 66699,
+      "26": 91900,
+      "27": 51359,
+      "28": 124037,
+      "29": 53439,
+      "3": 50086,
+      "30": 116512,
+      "31": 49987,
+      "32": 109325,
+      "33": 39004,
+      "34": 66334,
+      "35": 28012,
+      "36": 61389,
+      "37": 22686,
+      "38": 37609,
+      "39": 15948,
+      "4": 116664,
+      "40": 28714,
+      "41": 10518,
+      "42": 14138,
+      "43": 5780,
+      "44": 7686,
+      "45": 3625,
+      "46": 4143,
+      "47": 2480,
+      "48": 3457,
+      "49": 2058,
+      "5": 938229,
+      "50": 2761,
+      "51": 1727,
+      "52": 2479,
+      "53": 1632,
+      "54": 2256,
+      "55": 1623,
+      "56": 2414,
+      "57": 1715,
+      "58": 2263,
+      "59": 1738,
+      "6": 5186700,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2012242,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5997393,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1768770,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 50086,
+      "7": 31036993,
+      "9": 116664
+    },
+    "connectivity_max": 139465450,
+    "connectivity_min": 0,
+    "n_cells": 31203743,
+    "n_connectivity_values": 341327309,
+    "n_fan_triangles": 278919823,
+    "n_points": 139465451
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6515802262812955e-11,
+    "float64_area_closure_relative": 4.113087935118215e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278919823,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935968.3377259749,
+    "surface_area_float64_in2": 1935968.3377966683,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935968.3377965887,
+    "zero_area_triangles": 238506,
+    "zero_weight_points": 5419
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC049_AoA_22.json b/surface_dual_areas/cases/geo_LHC049_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..19a9c0b6d771acf1e8b6f9c7a99fd8f84afa4759
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC049_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC049_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC049_AoA_22/boundary_dual_area_geo_LHC049_AoA_22.npy",
+    "sha256": "2c6104b901843612f86562dfedd436fcfcd08d46434f0ea543fd5bae896f43d8",
+    "shape": [
+      139376438
+    ],
+    "size_bytes": 557505880
+  },
+  "runtime": {
+    "accumulation_seconds": 11.056652510073036,
+    "completed_at_utc": "2026-08-07T07:50:16.574691Z",
+    "elapsed_seconds": 20.993009394034743,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.121183509938419,
+    "geometry_read_seconds": 1.9830080100800842,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:49:55.581583Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC049_AoA_22/boundary_geo_LHC049_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC049_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624595000000000,
+    "extracted_vtu_size_bytes": 21407684747,
+    "geometry_sha256": "5c579feeae53d37b6fc9c9b402f4958f3aa507b86550cfe093d5a3b2a9a90fd9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3821199,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1159318,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2507228,
+      "13": 760518,
+      "14": 1351875,
+      "15": 468425,
+      "16": 937320,
+      "17": 364036,
+      "18": 765871,
+      "19": 309181,
+      "20": 684694,
+      "21": 227875,
+      "22": 362265,
+      "23": 121676,
+      "24": 194660,
+      "25": 66952,
+      "26": 92107,
+      "27": 51433,
+      "28": 124079,
+      "29": 53451,
+      "3": 49867,
+      "30": 116518,
+      "31": 49990,
+      "32": 109323,
+      "33": 39012,
+      "34": 66334,
+      "35": 28021,
+      "36": 61382,
+      "37": 22682,
+      "38": 37604,
+      "39": 15947,
+      "4": 116942,
+      "40": 28709,
+      "41": 10521,
+      "42": 14136,
+      "43": 5785,
+      "44": 7684,
+      "45": 3624,
+      "46": 4143,
+      "47": 2480,
+      "48": 3455,
+      "49": 2056,
+      "5": 941429,
+      "50": 2758,
+      "51": 1726,
+      "52": 2480,
+      "53": 1632,
+      "54": 2254,
+      "55": 1623,
+      "56": 2414,
+      "57": 1715,
+      "58": 2263,
+      "59": 1738,
+      "6": 5197638,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2019198,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6002373,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1777618,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 49867,
+      "7": 31035485,
+      "9": 116942
+    },
+    "connectivity_max": 139376437,
+    "connectivity_min": 0,
+    "n_cells": 31202294,
+    "n_connectivity_values": 341146385,
+    "n_fan_triangles": 278741797,
+    "n_points": 139376438
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.688513700021202e-11,
+    "float64_area_closure_relative": 3.824450048767162e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278741797,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935968.406831903,
+    "surface_area_float64_in2": 1935968.4069033114,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935968.4069032373,
+    "zero_area_triangles": 238001,
+    "zero_weight_points": 5360
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC050_AoA_14.json b/surface_dual_areas/cases/geo_LHC050_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..26f0b79a23e50cab86c6987f8f46868c0cce5721
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC050_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC050_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC050_AoA_14/boundary_dual_area_geo_LHC050_AoA_14.npy",
+    "sha256": "826b6235b3729714343632fee78c3ba16632f5c4fb466446d90b6d638e81eed7",
+    "shape": [
+      139610919
+    ],
+    "size_bytes": 558443804
+  },
+  "runtime": {
+    "accumulation_seconds": 10.614969273097813,
+    "completed_at_utc": "2026-08-07T07:31:54.683469Z",
+    "elapsed_seconds": 20.611997820902616,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9834251750726253,
+    "geometry_read_seconds": 2.13027865299955,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:31:34.071371Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC050_AoA_14/boundary_geo_LHC050_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC050_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624609000000000,
+    "extracted_vtu_size_bytes": 21442923174,
+    "geometry_sha256": "4d4ca67ce96e29ec5646e3d70b69a0c8822c95ad200fe0ff1f4bf9521da9501a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3808917,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1143858,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2644953,
+      "13": 769483,
+      "14": 1362750,
+      "15": 461480,
+      "16": 930080,
+      "17": 354351,
+      "18": 756130,
+      "19": 305261,
+      "20": 672635,
+      "21": 227915,
+      "22": 360631,
+      "23": 124897,
+      "24": 199011,
+      "25": 69073,
+      "26": 92687,
+      "27": 52053,
+      "28": 124927,
+      "29": 53438,
+      "3": 53782,
+      "30": 115154,
+      "31": 49642,
+      "32": 108514,
+      "33": 39064,
+      "34": 66257,
+      "35": 28167,
+      "36": 61708,
+      "37": 22855,
+      "38": 38106,
+      "39": 16223,
+      "4": 122001,
+      "40": 29001,
+      "41": 10571,
+      "42": 14282,
+      "43": 5852,
+      "44": 7636,
+      "45": 3639,
+      "46": 4139,
+      "47": 2509,
+      "48": 3527,
+      "49": 2137,
+      "5": 936623,
+      "50": 2910,
+      "51": 1824,
+      "52": 2748,
+      "53": 1750,
+      "54": 2463,
+      "55": 1682,
+      "56": 2494,
+      "57": 1746,
+      "58": 2280,
+      "59": 1742,
+      "6": 5172019,
+      "60": 2509,
+      "61": 1629,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2000894,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6012573,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1737602,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53782,
+      "7": 31047926,
+      "9": 122001
+    },
+    "connectivity_max": 139610918,
+    "connectivity_min": 0,
+    "n_cells": 31223709,
+    "n_connectivity_values": 341658160,
+    "n_fan_triangles": 279210742,
+    "n_points": 139610919
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.440429379242174e-11,
+    "float64_area_closure_relative": 2.764082441344633e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279210742,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937389.6826498725,
+    "surface_area_float64_in2": 1937389.682716527,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937389.6827165324,
+    "zero_area_triangles": 237929,
+    "zero_weight_points": 5731
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC050_AoA_4.json b/surface_dual_areas/cases/geo_LHC050_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..b419cc55bed87583dda6c3dc49b3096a358bf230
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC050_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC050_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC050_AoA_4/boundary_dual_area_geo_LHC050_AoA_4.npy",
+    "sha256": "656f227e2b3160ce95eaa5d1b45287813e11a42c9c8e18ffac716a1158fcb023",
+    "shape": [
+      132487355
+    ],
+    "size_bytes": 529949548
+  },
+  "runtime": {
+    "accumulation_seconds": 10.722217498114333,
+    "completed_at_utc": "2026-08-07T07:51:33.110768Z",
+    "elapsed_seconds": 20.735919157974422,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0024381140246987,
+    "geometry_read_seconds": 2.466971290996298,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:51:12.374766Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC050_AoA_4/boundary_geo_LHC050_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC050_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624623000000000,
+    "extracted_vtu_size_bytes": 20335248951,
+    "geometry_sha256": "5b0a13a76ba85ae397e55e4d382329e927bc5cb3ab2104404e2ec1cb94bedf90",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2785553,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 893672,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2191346,
+      "13": 745440,
+      "14": 1646325,
+      "15": 540891,
+      "16": 1025925,
+      "17": 380184,
+      "18": 762508,
+      "19": 306551,
+      "20": 674727,
+      "21": 227681,
+      "22": 362626,
+      "23": 124643,
+      "24": 198924,
+      "25": 69108,
+      "26": 92772,
+      "27": 52081,
+      "28": 125022,
+      "29": 53466,
+      "3": 47464,
+      "30": 115153,
+      "31": 49642,
+      "32": 108518,
+      "33": 39067,
+      "34": 66255,
+      "35": 28170,
+      "36": 61707,
+      "37": 22855,
+      "38": 38106,
+      "39": 16224,
+      "4": 111110,
+      "40": 29002,
+      "41": 10572,
+      "42": 14281,
+      "43": 5852,
+      "44": 7637,
+      "45": 3638,
+      "46": 4137,
+      "47": 2508,
+      "48": 3528,
+      "49": 2138,
+      "5": 931268,
+      "50": 2909,
+      "51": 1824,
+      "52": 2747,
+      "53": 1750,
+      "54": 2465,
+      "55": 1682,
+      "56": 2494,
+      "57": 1746,
+      "58": 2280,
+      "59": 1742,
+      "6": 5172435,
+      "60": 2509,
+      "61": 1629,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1923626,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5486303,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1482896,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 47464,
+      "7": 28929665,
+      "9": 111110
+    },
+    "connectivity_max": 132487354,
+    "connectivity_min": 0,
+    "n_cells": 29088239,
+    "n_connectivity_values": 323140092,
+    "n_fan_triangles": 264963614,
+    "n_points": 132487355
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4640903009938e-11,
+    "float64_area_closure_relative": 1.562306552445096e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 264963614,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937390.8165835622,
+    "surface_area_float64_in2": 1937390.8166506751,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937390.8166506449,
+    "zero_area_triangles": 224229,
+    "zero_weight_points": 4802
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC051_AoA_6.json b/surface_dual_areas/cases/geo_LHC051_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..a94ac0aaa2a6465046e5107600169352d2261a36
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC051_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC051_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC051_AoA_6/boundary_dual_area_geo_LHC051_AoA_6.npy",
+    "sha256": "c7225c510ef34ff6d6c831cf3733a7f9dcd74235a65030e4c93f6259b9df6cf3",
+    "shape": [
+      135406449
+    ],
+    "size_bytes": 541625924
+  },
+  "runtime": {
+    "accumulation_seconds": 10.465616438072175,
+    "completed_at_utc": "2026-08-07T07:51:05.948651Z",
+    "elapsed_seconds": 48.34083424299024,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.004833097103983,
+    "geometry_read_seconds": 29.45982354786247,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:50:17.607720Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC051_AoA_6/boundary_geo_LHC051_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC051_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624413000000000,
+    "extracted_vtu_size_bytes": 20790941605,
+    "geometry_sha256": "e1fa13c76545c702bb56d068080b5d68a66dddac8d0b0ca6d19f7da04f5d3c62",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3211591,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1058434,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2324752,
+      "13": 733464,
+      "14": 1501880,
+      "15": 469465,
+      "16": 978314,
+      "17": 359944,
+      "18": 754331,
+      "19": 305678,
+      "20": 672297,
+      "21": 227986,
+      "22": 360655,
+      "23": 126031,
+      "24": 210620,
+      "25": 70309,
+      "26": 94988,
+      "27": 51854,
+      "28": 124144,
+      "29": 53044,
+      "3": 49287,
+      "30": 114919,
+      "31": 49653,
+      "32": 108994,
+      "33": 38974,
+      "34": 66881,
+      "35": 28209,
+      "36": 62997,
+      "37": 23069,
+      "38": 39002,
+      "39": 16183,
+      "4": 109710,
+      "40": 29127,
+      "41": 10619,
+      "42": 14053,
+      "43": 5713,
+      "44": 7591,
+      "45": 3643,
+      "46": 4217,
+      "47": 2526,
+      "48": 3524,
+      "49": 2124,
+      "5": 935926,
+      "50": 2974,
+      "51": 1830,
+      "52": 2740,
+      "53": 1744,
+      "54": 2398,
+      "55": 1687,
+      "56": 2506,
+      "57": 1726,
+      "58": 2270,
+      "59": 1719,
+      "6": 5180545,
+      "60": 2504,
+      "61": 1656,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1989742,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5730173,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1673032,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49287,
+      "7": 29875920,
+      "9": 109710
+    },
+    "connectivity_max": 135406448,
+    "connectivity_min": 0,
+    "n_cells": 30034917,
+    "n_connectivity_values": 330871610,
+    "n_fan_triangles": 270801776,
+    "n_points": 135406449
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1661342766333294e-11,
+    "float64_area_closure_relative": 2.1757316246151462e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 270801776,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936927.607395993,
+    "surface_area_float64_in2": 1936927.6074573188,
+    "weight_max_in2": 1.1016537846015613,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936927.6074572767,
+    "zero_area_triangles": 230558,
+    "zero_weight_points": 5050
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC052_AoA_10.json b/surface_dual_areas/cases/geo_LHC052_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..c02aa43890ae23290ad8e36478f7e844f2a0d09d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC052_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC052_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC052_AoA_10/boundary_dual_area_geo_LHC052_AoA_10.npy",
+    "sha256": "277472f8261568d64a26e4668c94c2e7438bda4d6fe236dde6b71b64d806755a",
+    "shape": [
+      137059746
+    ],
+    "size_bytes": 548239112
+  },
+  "runtime": {
+    "accumulation_seconds": 10.596239320002496,
+    "completed_at_utc": "2026-08-07T07:51:27.735423Z",
+    "elapsed_seconds": 20.63407665793784,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0850436999462545,
+    "geometry_read_seconds": 2.0222944000270218,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:51:07.101255Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC052_AoA_10/boundary_geo_LHC052_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC052_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624549000000000,
+    "extracted_vtu_size_bytes": 21045557429,
+    "geometry_sha256": "e71ecf128b079e7111d0b5525299278c3d92533111e2140c861f10b04a42b54f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3373739,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1080610,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2466316,
+      "13": 766117,
+      "14": 1461934,
+      "15": 489103,
+      "16": 984295,
+      "17": 367050,
+      "18": 757002,
+      "19": 304455,
+      "20": 667346,
+      "21": 225593,
+      "22": 361362,
+      "23": 123877,
+      "24": 204021,
+      "25": 69223,
+      "26": 94026,
+      "27": 51554,
+      "28": 124834,
+      "29": 53038,
+      "3": 51904,
+      "30": 115793,
+      "31": 49477,
+      "32": 109033,
+      "33": 38887,
+      "34": 65869,
+      "35": 28034,
+      "36": 62638,
+      "37": 22843,
+      "38": 38866,
+      "39": 16156,
+      "4": 114685,
+      "40": 29337,
+      "41": 10696,
+      "42": 14230,
+      "43": 5715,
+      "44": 7565,
+      "45": 3656,
+      "46": 4198,
+      "47": 2502,
+      "48": 3548,
+      "49": 2136,
+      "5": 927100,
+      "50": 2941,
+      "51": 1855,
+      "52": 2771,
+      "53": 1766,
+      "54": 2417,
+      "55": 1724,
+      "56": 2533,
+      "57": 1749,
+      "58": 2273,
+      "59": 1729,
+      "6": 5165861,
+      "60": 2509,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1980028,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5807279,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1683633,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51904,
+      "7": 30265443,
+      "9": 114685
+    },
+    "connectivity_max": 137059745,
+    "connectivity_min": 0,
+    "n_cells": 30432032,
+    "n_connectivity_values": 334972433,
+    "n_fan_triangles": 274108369,
+    "n_points": 137059746
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.96150533191445e-11,
+    "float64_area_closure_relative": 5.151780688579581e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274108369,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938831.4868677284,
+    "surface_area_float64_in2": 1938831.486925147,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938831.486925247,
+    "zero_area_triangles": 233422,
+    "zero_weight_points": 5443
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC053_AoA_14.json b/surface_dual_areas/cases/geo_LHC053_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..0648fc51c6a39d903687b3de47ef54aa15b367de
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC053_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC053_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC053_AoA_14/boundary_dual_area_geo_LHC053_AoA_14.npy",
+    "sha256": "de01aef2323ff390f7d2015d2d4806cf723c3c289038e31ff9f2902c789a9d8e",
+    "shape": [
+      139920176
+    ],
+    "size_bytes": 559680832
+  },
+  "runtime": {
+    "accumulation_seconds": 10.837794348830357,
+    "completed_at_utc": "2026-08-07T07:51:53.649124Z",
+    "elapsed_seconds": 24.992820061044767,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.154581533977762,
+    "geometry_read_seconds": 4.077569405082613,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:51:28.656210Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC053_AoA_14/boundary_geo_LHC053_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC053_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624612000000000,
+    "extracted_vtu_size_bytes": 21491905169,
+    "geometry_sha256": "adb03d1fcff88fe31d3af491e38cb98a3e5e9b1336fb60cbd663265e2ebcc305",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3882480,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1164650,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2570442,
+      "13": 782974,
+      "14": 1337050,
+      "15": 478734,
+      "16": 931650,
+      "17": 363759,
+      "18": 756678,
+      "19": 303493,
+      "20": 675494,
+      "21": 222418,
+      "22": 356683,
+      "23": 119030,
+      "24": 199437,
+      "25": 66951,
+      "26": 92457,
+      "27": 51280,
+      "28": 124385,
+      "29": 52688,
+      "3": 54155,
+      "30": 115418,
+      "31": 49635,
+      "32": 109406,
+      "33": 38982,
+      "34": 66687,
+      "35": 28092,
+      "36": 62421,
+      "37": 22923,
+      "38": 38551,
+      "39": 16303,
+      "4": 121885,
+      "40": 29366,
+      "41": 10789,
+      "42": 14336,
+      "43": 5839,
+      "44": 7665,
+      "45": 3636,
+      "46": 4119,
+      "47": 2488,
+      "48": 3496,
+      "49": 2110,
+      "5": 936678,
+      "50": 2865,
+      "51": 1860,
+      "52": 2687,
+      "53": 1771,
+      "54": 2530,
+      "55": 1707,
+      "56": 2543,
+      "57": 1745,
+      "58": 2299,
+      "59": 1748,
+      "6": 5195186,
+      "60": 2510,
+      "61": 1628,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2018515,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6033960,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1782002,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 54155,
+      "7": 31176156,
+      "9": 121885
+    },
+    "connectivity_max": 139920175,
+    "connectivity_min": 0,
+    "n_cells": 31352196,
+    "n_connectivity_values": 342533621,
+    "n_fan_triangles": 279829229,
+    "n_points": 139920176
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.510100506749555e-11,
+    "float64_area_closure_relative": 1.5261306551085024e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279829229,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937546.54256003,
+    "surface_area_float64_in2": 1937546.5426280398,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937546.5426280694,
+    "zero_area_triangles": 238658,
+    "zero_weight_points": 5486
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC053_AoA_16.json b/surface_dual_areas/cases/geo_LHC053_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..b53cbe88ddea8ee31249d31c35fbdcb454faab10
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC053_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC053_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC053_AoA_16/boundary_dual_area_geo_LHC053_AoA_16.npy",
+    "sha256": "216fafb391be1810c3a2027fbbe9b834de4104951985964595e7e0733eab38a3",
+    "shape": [
+      139794146
+    ],
+    "size_bytes": 559176712
+  },
+  "runtime": {
+    "accumulation_seconds": 11.20878716907464,
+    "completed_at_utc": "2026-08-07T07:54:18.644126Z",
+    "elapsed_seconds": 90.02053811401129,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 4.13897862797603,
+    "geometry_read_seconds": 69.77391958911903,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T07:52:48.623506Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC053_AoA_16/boundary_geo_LHC053_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC053_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624557000000000,
+    "extracted_vtu_size_bytes": 21471718179,
+    "geometry_sha256": "43c97d066ca1057a56cfdffa0cf06d1638be23b178eab681e58281be5ce99c03",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3818604,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1179049,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2570929,
+      "13": 791948,
+      "14": 1364945,
+      "15": 482834,
+      "16": 942231,
+      "17": 363618,
+      "18": 752310,
+      "19": 301187,
+      "20": 672730,
+      "21": 221120,
+      "22": 354739,
+      "23": 118087,
+      "24": 197962,
+      "25": 66660,
+      "26": 92503,
+      "27": 51351,
+      "28": 124489,
+      "29": 52706,
+      "3": 52422,
+      "30": 115444,
+      "31": 49633,
+      "32": 109414,
+      "33": 38983,
+      "34": 66685,
+      "35": 28090,
+      "36": 62420,
+      "37": 22926,
+      "38": 38549,
+      "39": 16304,
+      "4": 118884,
+      "40": 29365,
+      "41": 10789,
+      "42": 14337,
+      "43": 5839,
+      "44": 7666,
+      "45": 3638,
+      "46": 4120,
+      "47": 2487,
+      "48": 3496,
+      "49": 2109,
+      "5": 932643,
+      "50": 2865,
+      "51": 1860,
+      "52": 2688,
+      "53": 1771,
+      "54": 2528,
+      "55": 1707,
+      "56": 2543,
+      "57": 1745,
+      "58": 2299,
+      "59": 1748,
+      "6": 5185142,
+      "60": 2510,
+      "61": 1628,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2018193,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5999405,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1787010,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52422,
+      "7": 31119508,
+      "9": 118884
+    },
+    "connectivity_max": 139794145,
+    "connectivity_min": 0,
+    "n_cells": 31290814,
+    "n_connectivity_values": 342158797,
+    "n_fan_triangles": 279577169,
+    "n_points": 139794146
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.487352743146703e-11,
+    "float64_area_closure_relative": 2.0188185014443004e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279577169,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937546.5453928628,
+    "surface_area_float64_in2": 1937546.5454604318,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937546.545460471,
+    "zero_area_triangles": 237356,
+    "zero_weight_points": 5474
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC053_AoA_6.json b/surface_dual_areas/cases/geo_LHC053_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..04d0883661fb1d4fe3bb2f79a1e7dd40a484362e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC053_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC053_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC053_AoA_6/boundary_dual_area_geo_LHC053_AoA_6.npy",
+    "sha256": "900860d167d552c018c87925edf6b3b09037aee5c4d3a559d39486a61fe63549",
+    "shape": [
+      136041456
+    ],
+    "size_bytes": 544165952
+  },
+  "runtime": {
+    "accumulation_seconds": 10.427119439002126,
+    "completed_at_utc": "2026-08-07T07:52:46.588345Z",
+    "elapsed_seconds": 20.28316288581118,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0332311170641333,
+    "geometry_read_seconds": 2.2484780959784985,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:52:26.305106Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC053_AoA_6/boundary_geo_LHC053_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC053_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624461000000000,
+    "extracted_vtu_size_bytes": 20886946934,
+    "geometry_sha256": "0ad0ae39ca4c5428429cf0d9c375805afcf311d1209625538dbffae6c67ee879",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3199525,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1014833,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2327054,
+      "13": 781641,
+      "14": 1619701,
+      "15": 537731,
+      "16": 1038288,
+      "17": 383645,
+      "18": 760364,
+      "19": 304086,
+      "20": 668098,
+      "21": 219814,
+      "22": 337309,
+      "23": 115932,
+      "24": 187049,
+      "25": 65227,
+      "26": 90916,
+      "27": 51047,
+      "28": 124306,
+      "29": 52692,
+      "3": 51178,
+      "30": 115421,
+      "31": 49635,
+      "32": 109407,
+      "33": 38985,
+      "34": 66685,
+      "35": 28092,
+      "36": 62424,
+      "37": 22921,
+      "38": 38548,
+      "39": 16306,
+      "4": 116334,
+      "40": 29365,
+      "41": 10789,
+      "42": 14336,
+      "43": 5839,
+      "44": 7666,
+      "45": 3637,
+      "46": 4120,
+      "47": 2488,
+      "48": 3496,
+      "49": 2109,
+      "5": 930464,
+      "50": 2865,
+      "51": 1860,
+      "52": 2688,
+      "53": 1771,
+      "54": 2528,
+      "55": 1707,
+      "56": 2543,
+      "57": 1745,
+      "58": 2299,
+      "59": 1748,
+      "6": 5182464,
+      "60": 2510,
+      "61": 1628,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1961109,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5701584,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1616410,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51178,
+      "7": 29948377,
+      "9": 116334
+    },
+    "connectivity_max": 136041455,
+    "connectivity_min": 0,
+    "n_cells": 30115889,
+    "n_connectivity_values": 332303567,
+    "n_fan_triangles": 272071789,
+    "n_points": 136041456
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.464976452147305e-11,
+    "float64_area_closure_relative": 5.82813497474013e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272071789,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937547.1339911637,
+    "surface_area_float64_in2": 1937547.1340582992,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937547.1340584122,
+    "zero_area_triangles": 231024,
+    "zero_weight_points": 5012
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC053_AoA_8.json b/surface_dual_areas/cases/geo_LHC053_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..db81b66fe9d026bac9367a1486098a6e1ebf919a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC053_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC053_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC053_AoA_8/boundary_dual_area_geo_LHC053_AoA_8.npy",
+    "sha256": "5cc91d362a98adb27e207b0bad8f93a3434f514c7d4b451c6319e7fddc6429ff",
+    "shape": [
+      137751946
+    ],
+    "size_bytes": 551007912
+  },
+  "runtime": {
+    "accumulation_seconds": 10.942469796864316,
+    "completed_at_utc": "2026-08-07T07:50:45.969917Z",
+    "elapsed_seconds": 20.984419201966375,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.349462670041248,
+    "geometry_read_seconds": 2.002119763987139,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:50:24.985381Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC053_AoA_8/boundary_geo_LHC053_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC053_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624637000000000,
+    "extracted_vtu_size_bytes": 21152696496,
+    "geometry_sha256": "a91386cc1b6db6a4ee6fd59785732b690eba819d3386e54d7156bebf1b650878",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3436878,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1066230,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2447401,
+      "13": 791025,
+      "14": 1561577,
+      "15": 524177,
+      "16": 1015466,
+      "17": 378344,
+      "18": 756863,
+      "19": 302916,
+      "20": 666576,
+      "21": 219177,
+      "22": 336723,
+      "23": 115540,
+      "24": 186521,
+      "25": 65068,
+      "26": 90788,
+      "27": 51000,
+      "28": 124285,
+      "29": 52664,
+      "3": 51548,
+      "30": 115415,
+      "31": 49635,
+      "32": 109412,
+      "33": 38980,
+      "34": 66685,
+      "35": 28091,
+      "36": 62421,
+      "37": 22924,
+      "38": 38549,
+      "39": 16303,
+      "4": 117279,
+      "40": 29367,
+      "41": 10789,
+      "42": 14336,
+      "43": 5840,
+      "44": 7665,
+      "45": 3636,
+      "46": 4119,
+      "47": 2487,
+      "48": 3496,
+      "49": 2110,
+      "5": 931508,
+      "50": 2865,
+      "51": 1860,
+      "52": 2687,
+      "53": 1771,
+      "54": 2530,
+      "55": 1707,
+      "56": 2543,
+      "57": 1745,
+      "58": 2299,
+      "59": 1748,
+      "6": 5185816,
+      "60": 2510,
+      "61": 1628,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1980148,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5817818,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1669355,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51548,
+      "7": 30450944,
+      "9": 117279
+    },
+    "connectivity_max": 137751945,
+    "connectivity_min": 0,
+    "n_cells": 30619771,
+    "n_connectivity_values": 336732310,
+    "n_fan_triangles": 275492768,
+    "n_points": 137751946
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4740737438017926e-11,
+    "float64_area_closure_relative": 9.252916903817269e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275492768,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937546.8024930595,
+    "surface_area_float64_in2": 1937546.8025603713,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937546.8025605506,
+    "zero_area_triangles": 233789,
+    "zero_weight_points": 5225
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC054_AoA_12.json b/surface_dual_areas/cases/geo_LHC054_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..00111dc194f8817199db9737171450f4664fd6e0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC054_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC054_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC054_AoA_12/boundary_dual_area_geo_LHC054_AoA_12.npy",
+    "sha256": "dd679eaf800a8d754ad55a9d01018fed151999368f02a6a414eef043d349cf44",
+    "shape": [
+      141670202
+    ],
+    "size_bytes": 566680936
+  },
+  "runtime": {
+    "accumulation_seconds": 10.974685578141361,
+    "completed_at_utc": "2026-08-07T07:51:39.029537Z",
+    "elapsed_seconds": 51.9384433159139,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1278986339457333,
+    "geometry_read_seconds": 32.95419486495666,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:50:47.090998Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC054_AoA_12/boundary_geo_LHC054_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC054_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624478000000000,
+    "extracted_vtu_size_bytes": 21763968356,
+    "geometry_sha256": "ac892acfc76d37b4e8c65891944e1ab4309d6b2bc4ecbd13708dcef24e977681",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3902616,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1207423,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2709581,
+      "13": 803745,
+      "14": 1362714,
+      "15": 479354,
+      "16": 936521,
+      "17": 363393,
+      "18": 743719,
+      "19": 301645,
+      "20": 659219,
+      "21": 221481,
+      "22": 343337,
+      "23": 119825,
+      "24": 199124,
+      "25": 69442,
+      "26": 93800,
+      "27": 52089,
+      "28": 124035,
+      "29": 53050,
+      "3": 53414,
+      "30": 115268,
+      "31": 49653,
+      "32": 108858,
+      "33": 38909,
+      "34": 66873,
+      "35": 27987,
+      "36": 62136,
+      "37": 22805,
+      "38": 38723,
+      "39": 16422,
+      "4": 119461,
+      "40": 29924,
+      "41": 10943,
+      "42": 14650,
+      "43": 5949,
+      "44": 7673,
+      "45": 3642,
+      "46": 4167,
+      "47": 2509,
+      "48": 3532,
+      "49": 2118,
+      "5": 943672,
+      "50": 2951,
+      "51": 1844,
+      "52": 2735,
+      "53": 1765,
+      "54": 2474,
+      "55": 1743,
+      "56": 2539,
+      "57": 1754,
+      "58": 2289,
+      "59": 1749,
+      "6": 5305550,
+      "60": 2506,
+      "61": 1627,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2037696,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6191197,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1799821,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53414,
+      "7": 31701692,
+      "9": 119461
+    },
+    "connectivity_max": 141670201,
+    "connectivity_min": 0,
+    "n_cells": 31874567,
+    "n_connectivity_values": 347078423,
+    "n_fan_triangles": 283329289,
+    "n_points": 141670202
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.820015887484544e-11,
+    "float64_area_closure_relative": 6.182576420181331e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283329289,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939446.8151781543,
+    "surface_area_float64_in2": 1939446.8152522414,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939446.8152523614,
+    "zero_area_triangles": 239193,
+    "zero_weight_points": 5751
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC054_AoA_22.json b/surface_dual_areas/cases/geo_LHC054_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..48e569b2fc3c83f4b42361e7087b9552f310b97a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC054_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC054_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC054_AoA_22/boundary_dual_area_geo_LHC054_AoA_22.npy",
+    "sha256": "ddd1810a84b4f77dcce0d94656ef24f226d48768fefe975b9b7f61924aaf0b46",
+    "shape": [
+      142303028
+    ],
+    "size_bytes": 569212240
+  },
+  "runtime": {
+    "accumulation_seconds": 10.939905320992693,
+    "completed_at_utc": "2026-08-07T07:52:27.232208Z",
+    "elapsed_seconds": 23.279931311961263,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2786423889920115,
+    "geometry_read_seconds": 4.15792496711947,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:52:03.952176Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC054_AoA_22/boundary_geo_LHC054_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC054_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624616000000000,
+    "extracted_vtu_size_bytes": 21863382654,
+    "geometry_sha256": "8d5002d146ce4c595bf3a4d4b73868a07c8d27b7bb5841cbc72e32b2ee882edd",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4083036,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1286571,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2676222,
+      "13": 794369,
+      "14": 1259979,
+      "15": 446533,
+      "16": 909470,
+      "17": 352770,
+      "18": 739320,
+      "19": 299697,
+      "20": 658978,
+      "21": 223644,
+      "22": 356577,
+      "23": 123838,
+      "24": 209569,
+      "25": 71972,
+      "26": 95714,
+      "27": 52627,
+      "28": 124207,
+      "29": 53116,
+      "3": 52484,
+      "30": 115262,
+      "31": 49651,
+      "32": 108862,
+      "33": 38914,
+      "34": 66876,
+      "35": 27993,
+      "36": 62137,
+      "37": 22804,
+      "38": 38727,
+      "39": 16418,
+      "4": 121323,
+      "40": 29918,
+      "41": 10946,
+      "42": 14646,
+      "43": 5946,
+      "44": 7669,
+      "45": 3640,
+      "46": 4166,
+      "47": 2509,
+      "48": 3532,
+      "49": 2119,
+      "5": 941810,
+      "50": 2950,
+      "51": 1843,
+      "52": 2736,
+      "53": 1766,
+      "54": 2473,
+      "55": 1743,
+      "56": 2539,
+      "57": 1754,
+      "58": 2289,
+      "59": 1749,
+      "6": 5261442,
+      "60": 2506,
+      "61": 1627,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2071270,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6258521,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1902114,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52484,
+      "7": 31931002,
+      "9": 121323
+    },
+    "connectivity_max": 142303027,
+    "connectivity_min": 0,
+    "n_cells": 32104809,
+    "n_connectivity_values": 348804559,
+    "n_fan_triangles": 284594941,
+    "n_points": 142303028
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.787300900100132e-11,
+    "float64_area_closure_relative": 7.503124039351784e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284594941,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939447.5089969202,
+    "surface_area_float64_in2": 1939447.509070373,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939447.5090705184,
+    "zero_area_triangles": 238486,
+    "zero_weight_points": 5723
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC055_AoA_12.json b/surface_dual_areas/cases/geo_LHC055_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..85ce7adeccc6d34c7840aee649a6286aa68fb24e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC055_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC055_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC055_AoA_12/boundary_dual_area_geo_LHC055_AoA_12.npy",
+    "sha256": "a04bdbec2559525b8723c78794b8d6449c0da8729cd56e87d52869706adaea15",
+    "shape": [
+      136299066
+    ],
+    "size_bytes": 545196392
+  },
+  "runtime": {
+    "accumulation_seconds": 10.318672458874062,
+    "completed_at_utc": "2026-08-07T07:33:44.052124Z",
+    "elapsed_seconds": 21.16567624709569,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9117212910205126,
+    "geometry_read_seconds": 2.270206883084029,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:33:22.886357Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC055_AoA_12/boundary_geo_LHC055_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC055_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624553000000000,
+    "extracted_vtu_size_bytes": 20922937823,
+    "geometry_sha256": "d1bf3f10acbbb16083c234116c3fe857d4e837dae3d8c47be4485753e4c7eaaa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2834660,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1016851,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2153339,
+      "13": 840743,
+      "14": 1779741,
+      "15": 588653,
+      "16": 1021134,
+      "17": 379791,
+      "18": 751001,
+      "19": 299678,
+      "20": 679207,
+      "21": 226418,
+      "22": 381835,
+      "23": 125408,
+      "24": 207444,
+      "25": 69693,
+      "26": 92006,
+      "27": 51505,
+      "28": 124396,
+      "29": 52741,
+      "3": 57327,
+      "30": 114367,
+      "31": 49166,
+      "32": 109332,
+      "33": 38900,
+      "34": 68800,
+      "35": 28218,
+      "36": 63412,
+      "37": 23030,
+      "38": 37984,
+      "39": 16084,
+      "4": 133103,
+      "40": 28904,
+      "41": 10457,
+      "42": 14063,
+      "43": 5755,
+      "44": 7761,
+      "45": 3678,
+      "46": 4137,
+      "47": 2544,
+      "48": 3522,
+      "49": 2079,
+      "5": 947298,
+      "50": 2842,
+      "51": 1740,
+      "52": 2518,
+      "53": 1630,
+      "54": 2208,
+      "55": 1602,
+      "56": 2412,
+      "57": 1707,
+      "58": 2258,
+      "59": 1733,
+      "6": 5205160,
+      "60": 2504,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 1979282,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5743963,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1612198,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 57327,
+      "7": 29840044,
+      "9": 133103
+    },
+    "connectivity_max": 136299065,
+    "connectivity_min": 0,
+    "n_cells": 30030474,
+    "n_connectivity_values": 332647955,
+    "n_fan_triangles": 272587007,
+    "n_points": 136299066
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.1114442705098505e-11,
+    "float64_area_closure_relative": 6.818137007819221e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272587007,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946476.9734760376,
+    "surface_area_float64_in2": 1946476.973556066,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946476.9735560527,
+    "zero_area_triangles": 224413,
+    "zero_weight_points": 4839
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC055_AoA_20.json b/surface_dual_areas/cases/geo_LHC055_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7bd253edf9074d1796da72d80eba1987cf0046b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC055_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC055_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC055_AoA_20/boundary_dual_area_geo_LHC055_AoA_20.npy",
+    "sha256": "578c96f5e354e707363f540358670b71e7178fcba2371c669617b3ae623172b4",
+    "shape": [
+      147043208
+    ],
+    "size_bytes": 588172960
+  },
+  "runtime": {
+    "accumulation_seconds": 11.293623671866953,
+    "completed_at_utc": "2026-08-07T07:55:03.111489Z",
+    "elapsed_seconds": 72.15104539110325,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.323525863001123,
+    "geometry_read_seconds": 52.52236534212716,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T07:53:50.960336Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC055_AoA_20/boundary_geo_LHC055_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC055_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624519000000000,
+    "extracted_vtu_size_bytes": 22592952864,
+    "geometry_sha256": "d14481923a972515dc4b283c6ae4879b49ffc08216c1cbbe51481d9582492dec",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4284032,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1424355,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2804225,
+      "13": 884176,
+      "14": 1373251,
+      "15": 477598,
+      "16": 902540,
+      "17": 347790,
+      "18": 739755,
+      "19": 295966,
+      "20": 673265,
+      "21": 224464,
+      "22": 375654,
+      "23": 124158,
+      "24": 204670,
+      "25": 69294,
+      "26": 91705,
+      "27": 51446,
+      "28": 124374,
+      "29": 52730,
+      "3": 60928,
+      "30": 114372,
+      "31": 49162,
+      "32": 109340,
+      "33": 38904,
+      "34": 68810,
+      "35": 28221,
+      "36": 63414,
+      "37": 23027,
+      "38": 37993,
+      "39": 16087,
+      "4": 136915,
+      "40": 28896,
+      "41": 10459,
+      "42": 14062,
+      "43": 5757,
+      "44": 7761,
+      "45": 3678,
+      "46": 4137,
+      "47": 2542,
+      "48": 3521,
+      "49": 2078,
+      "5": 947588,
+      "50": 2846,
+      "51": 1735,
+      "52": 2519,
+      "53": 1628,
+      "54": 2206,
+      "55": 1602,
+      "56": 2413,
+      "57": 1705,
+      "58": 2258,
+      "59": 1733,
+      "6": 5205650,
+      "60": 2504,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 2136723,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6490896,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2045685,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60928,
+      "7": 33027912,
+      "9": 136915
+    },
+    "connectivity_max": 147043207,
+    "connectivity_min": 0,
+    "n_cells": 33225755,
+    "n_connectivity_values": 360526801,
+    "n_fan_triangles": 294075291,
+    "n_points": 147043208
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.0854337877567644e-11,
+    "float64_area_closure_relative": 5.119591212727775e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294075291,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946474.0706649031,
+    "surface_area_float64_in2": 1946474.070744425,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946474.0707445247,
+    "zero_area_triangles": 240355,
+    "zero_weight_points": 5897
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC056_AoA_8.json b/surface_dual_areas/cases/geo_LHC056_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..af569e6c7981ba7d8f3c8107087893938ee2b87d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC056_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC056_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC056_AoA_8/boundary_dual_area_geo_LHC056_AoA_8.npy",
+    "sha256": "1d828a83e7b4aca11561e0d7abb9d6040bcac78bfe9633def5f05af30e22905f",
+    "shape": [
+      142984017
+    ],
+    "size_bytes": 571936196
+  },
+  "runtime": {
+    "accumulation_seconds": 10.84046808606945,
+    "completed_at_utc": "2026-08-07T07:33:16.683656Z",
+    "elapsed_seconds": 21.38078637700528,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0389537550508976,
+    "geometry_read_seconds": 2.3155323108658195,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:32:55.302776Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC056_AoA_8/boundary_geo_LHC056_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC056_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624449000000000,
+    "extracted_vtu_size_bytes": 21969366529,
+    "geometry_sha256": "c590f4d1a5d77167dbf4c5a40153e55834bf0eaf01549e93c9a83775b314e99d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3902312,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1223354,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2697263,
+      "13": 799780,
+      "14": 1434568,
+      "15": 473016,
+      "16": 968597,
+      "17": 360357,
+      "18": 733695,
+      "19": 295811,
+      "20": 651461,
+      "21": 219794,
+      "22": 346362,
+      "23": 120296,
+      "24": 198230,
+      "25": 68889,
+      "26": 92563,
+      "27": 52085,
+      "28": 124981,
+      "29": 53151,
+      "3": 53513,
+      "30": 114712,
+      "31": 49194,
+      "32": 107955,
+      "33": 38436,
+      "34": 65696,
+      "35": 27645,
+      "36": 62233,
+      "37": 22894,
+      "38": 39156,
+      "39": 16617,
+      "4": 120122,
+      "40": 30022,
+      "41": 11060,
+      "42": 14536,
+      "43": 5928,
+      "44": 7757,
+      "45": 3661,
+      "46": 4147,
+      "47": 2464,
+      "48": 3553,
+      "49": 2129,
+      "5": 953451,
+      "50": 2933,
+      "51": 1835,
+      "52": 2773,
+      "53": 1790,
+      "54": 2512,
+      "55": 1711,
+      "56": 2586,
+      "57": 1755,
+      "58": 2289,
+      "59": 1741,
+      "6": 5430120,
+      "60": 2509,
+      "61": 1625,
+      "62": 2260,
+      "63": 1602,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 2071034,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6355800,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1837324,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53513,
+      "7": 32139077,
+      "9": 120122
+    },
+    "connectivity_max": 142984016,
+    "connectivity_min": 0,
+    "n_cells": 32312712,
+    "n_connectivity_values": 350582334,
+    "n_fan_triangles": 285956910,
+    "n_points": 142984017
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.117636834435857e-11,
+    "float64_area_closure_relative": 9.479403362895013e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285956910,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940377.4840825952,
+    "surface_area_float64_in2": 1940377.484162493,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940377.4841625113,
+    "zero_area_triangles": 237909,
+    "zero_weight_points": 5586
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC058_AoA_10.json b/surface_dual_areas/cases/geo_LHC058_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..3227a9cfba17a971ae753c9b68d6f80c09b9287d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC058_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC058_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC058_AoA_10/boundary_dual_area_geo_LHC058_AoA_10.npy",
+    "sha256": "3829d7798a17aa7b2be1073dcebada98ee2edfa6f115f633bfebc27da5867679",
+    "shape": [
+      138305801
+    ],
+    "size_bytes": 553223332
+  },
+  "runtime": {
+    "accumulation_seconds": 12.850018152967095,
+    "completed_at_utc": "2026-08-07T07:56:20.073525Z",
+    "elapsed_seconds": 36.95004883897491,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.437621970893815,
+    "geometry_read_seconds": 15.997277317102998,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T07:55:43.123383Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC058_AoA_10/boundary_geo_LHC058_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC058_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624695000000000,
+    "extracted_vtu_size_bytes": 21239482622,
+    "geometry_sha256": "b2ca5f6ad90d46c26a82a476ca63cdc1ae742033bc110798727befbc236e90c6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3545757,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1106271,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2574101,
+      "13": 767027,
+      "14": 1457681,
+      "15": 478714,
+      "16": 960236,
+      "17": 360201,
+      "18": 749326,
+      "19": 302614,
+      "20": 668274,
+      "21": 225433,
+      "22": 355519,
+      "23": 122997,
+      "24": 200401,
+      "25": 68748,
+      "26": 93778,
+      "27": 51675,
+      "28": 124122,
+      "29": 52899,
+      "3": 51469,
+      "30": 114981,
+      "31": 49597,
+      "32": 109218,
+      "33": 39230,
+      "34": 67230,
+      "35": 28184,
+      "36": 62749,
+      "37": 22912,
+      "38": 38178,
+      "39": 16238,
+      "4": 115338,
+      "40": 29150,
+      "41": 10532,
+      "42": 14189,
+      "43": 5821,
+      "44": 7666,
+      "45": 3615,
+      "46": 4272,
+      "47": 2565,
+      "48": 3557,
+      "49": 2161,
+      "5": 928391,
+      "50": 2912,
+      "51": 1874,
+      "52": 2774,
+      "53": 1773,
+      "54": 2401,
+      "55": 1713,
+      "56": 2555,
+      "57": 1724,
+      "58": 2309,
+      "59": 1695,
+      "6": 5189830,
+      "60": 2447,
+      "61": 1665,
+      "62": 2199,
+      "63": 1587,
+      "64": 2148,
+      "65": 1370,
+      "66": 1769,
+      "67": 1096,
+      "68": 1505,
+      "69": 880,
+      "7": 1984665,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5895480,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1704799,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51469,
+      "7": 30645590,
+      "9": 115338
+    },
+    "connectivity_max": 138305800,
+    "connectivity_min": 0,
+    "n_cells": 30812397,
+    "n_connectivity_values": 338225264,
+    "n_fan_triangles": 276600470,
+    "n_points": 138305801
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.902247762557217e-11,
+    "float64_area_closure_relative": 1.2224743452250062e-13,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276600470,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938867.6429780996,
+    "surface_area_float64_in2": 1938867.6430343704,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938867.6430346074,
+    "zero_area_triangles": 239184,
+    "zero_weight_points": 5423
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC058_AoA_20.json b/surface_dual_areas/cases/geo_LHC058_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..3fc3f8fdd308ac9a3e208ce5e764b8a94b445285
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC058_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC058_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC058_AoA_20/boundary_dual_area_geo_LHC058_AoA_20.npy",
+    "sha256": "b129435211e2362e30187d88441d3bd9dc10c3a50dac320e2d556a30ff062a8d",
+    "shape": [
+      140300722
+    ],
+    "size_bytes": 561203016
+  },
+  "runtime": {
+    "accumulation_seconds": 10.487761439057067,
+    "completed_at_utc": "2026-08-07T07:33:40.434210Z",
+    "elapsed_seconds": 20.19184146495536,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.005701876943931,
+    "geometry_read_seconds": 2.0102978688664734,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:33:20.242274Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC058_AoA_20/boundary_geo_LHC058_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC058_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624641000000000,
+    "extracted_vtu_size_bytes": 21551805580,
+    "geometry_sha256": "a64ad5f34175c3f214bade24d178c290bac6b9d3d448d70f2dcd041db9a14923",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3970047,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1194750,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2682948,
+      "13": 745311,
+      "14": 1233971,
+      "15": 430434,
+      "16": 884527,
+      "17": 348147,
+      "18": 752104,
+      "19": 305480,
+      "20": 676111,
+      "21": 231298,
+      "22": 372477,
+      "23": 128540,
+      "24": 211736,
+      "25": 71565,
+      "26": 95485,
+      "27": 52223,
+      "28": 124246,
+      "29": 52932,
+      "3": 52987,
+      "30": 114993,
+      "31": 49608,
+      "32": 109217,
+      "33": 39230,
+      "34": 67235,
+      "35": 28184,
+      "36": 62748,
+      "37": 22904,
+      "38": 38184,
+      "39": 16234,
+      "4": 118792,
+      "40": 29154,
+      "41": 10528,
+      "42": 14190,
+      "43": 5820,
+      "44": 7665,
+      "45": 3615,
+      "46": 4273,
+      "47": 2566,
+      "48": 3557,
+      "49": 2161,
+      "5": 933785,
+      "50": 2910,
+      "51": 1874,
+      "52": 2774,
+      "53": 1773,
+      "54": 2401,
+      "55": 1713,
+      "56": 2555,
+      "57": 1724,
+      "58": 2309,
+      "59": 1695,
+      "6": 5198442,
+      "60": 2447,
+      "61": 1665,
+      "62": 2199,
+      "63": 1587,
+      "64": 2148,
+      "65": 1370,
+      "66": 1769,
+      "67": 1096,
+      "68": 1505,
+      "69": 880,
+      "7": 2028198,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6097637,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1824540,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52987,
+      "7": 31323604,
+      "9": 118792
+    },
+    "connectivity_max": 140300721,
+    "connectivity_min": 0,
+    "n_cells": 31495383,
+    "n_connectivity_values": 343581078,
+    "n_fan_triangles": 280590312,
+    "n_points": 140300722
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.915144529836489e-11,
+    "float64_area_closure_relative": 6.124379354561634e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280590312,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938867.9470282632,
+    "surface_area_float64_in2": 1938867.947084784,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938867.9470849028,
+    "zero_area_triangles": 242586,
+    "zero_weight_points": 5667
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC059_AoA_22.json b/surface_dual_areas/cases/geo_LHC059_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..f1acac2df4b9528a6b851583f8436c4622f585f9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC059_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC059_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC059_AoA_22/boundary_dual_area_geo_LHC059_AoA_22.npy",
+    "sha256": "72819377ec27372f37c390485886cf8ce8b597a700d4771e52770dfe30f8aaaa",
+    "shape": [
+      140540842
+    ],
+    "size_bytes": 562163496
+  },
+  "runtime": {
+    "accumulation_seconds": 10.612562625203282,
+    "completed_at_utc": "2026-08-07T07:34:28.912601Z",
+    "elapsed_seconds": 22.474863326875493,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.019570820964873,
+    "geometry_read_seconds": 2.448374619940296,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:34:06.437648Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC059_AoA_22/boundary_geo_LHC059_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC059_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624375000000000,
+    "extracted_vtu_size_bytes": 21589494437,
+    "geometry_sha256": "bad59062bc75d33525dd3023f591e0b56d2e87ef08319eebf99655bc3050d5eb",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3968132,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1229165,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2633241,
+      "13": 765862,
+      "14": 1240732,
+      "15": 435734,
+      "16": 889281,
+      "17": 346070,
+      "18": 747549,
+      "19": 303615,
+      "20": 673911,
+      "21": 229290,
+      "22": 371648,
+      "23": 127129,
+      "24": 211305,
+      "25": 71851,
+      "26": 94831,
+      "27": 52236,
+      "28": 124365,
+      "29": 52962,
+      "3": 52402,
+      "30": 115096,
+      "31": 49471,
+      "32": 109569,
+      "33": 38984,
+      "34": 67576,
+      "35": 28268,
+      "36": 62316,
+      "37": 22950,
+      "38": 38464,
+      "39": 16243,
+      "4": 118647,
+      "40": 29366,
+      "41": 10688,
+      "42": 14326,
+      "43": 5808,
+      "44": 7683,
+      "45": 3629,
+      "46": 4169,
+      "47": 2495,
+      "48": 3501,
+      "49": 2099,
+      "5": 940415,
+      "50": 2931,
+      "51": 1856,
+      "52": 2744,
+      "53": 1751,
+      "54": 2456,
+      "55": 1716,
+      "56": 2514,
+      "57": 1763,
+      "58": 2279,
+      "59": 1740,
+      "6": 5196860,
+      "60": 2511,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2050318,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6119044,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1857316,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52402,
+      "7": 31410375,
+      "9": 118647
+    },
+    "connectivity_max": 140540841,
+    "connectivity_min": 0,
+    "n_cells": 31581424,
+    "n_connectivity_values": 344233409,
+    "n_fan_triangles": 281070561,
+    "n_points": 140540842
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5705225771063286e-11,
+    "float64_area_closure_relative": 4.8157962033427774e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281070561,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938725.896188481,
+    "surface_area_float64_in2": 1938725.8962577037,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938725.896257797,
+    "zero_area_triangles": 238423,
+    "zero_weight_points": 5610
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC060_AoA_10.json b/surface_dual_areas/cases/geo_LHC060_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..65556b618b50e3c19a1eeb453c9cb309a9326d07
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC060_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC060_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC060_AoA_10/boundary_dual_area_geo_LHC060_AoA_10.npy",
+    "sha256": "b3988ea531375f6b5d01d959811e63a0dc8ad47ccfb637ece19e6d1431ff3cbc",
+    "shape": [
+      140366728
+    ],
+    "size_bytes": 561467040
+  },
+  "runtime": {
+    "accumulation_seconds": 10.773647458991036,
+    "completed_at_utc": "2026-08-07T07:55:35.010701Z",
+    "elapsed_seconds": 20.900474068010226,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.357554428977892,
+    "geometry_read_seconds": 2.1214564740657806,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:55:14.110127Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC060_AoA_10/boundary_geo_LHC060_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC060_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624388000000000,
+    "extracted_vtu_size_bytes": 21560601923,
+    "geometry_sha256": "b32c1125002ada018b4814dd969c2342d9bf8f7c9bc899d97caea36e09b86b3a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3860051,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1210552,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2642673,
+      "13": 795932,
+      "14": 1404326,
+      "15": 480670,
+      "16": 960194,
+      "17": 369117,
+      "18": 756110,
+      "19": 303890,
+      "20": 658081,
+      "21": 218509,
+      "22": 328160,
+      "23": 115319,
+      "24": 185335,
+      "25": 65949,
+      "26": 91637,
+      "27": 50939,
+      "28": 123890,
+      "29": 52812,
+      "3": 50145,
+      "30": 115759,
+      "31": 49276,
+      "32": 107972,
+      "33": 38702,
+      "34": 66646,
+      "35": 27724,
+      "36": 63070,
+      "37": 22848,
+      "38": 39355,
+      "39": 16301,
+      "4": 116289,
+      "40": 29793,
+      "41": 10843,
+      "42": 14411,
+      "43": 5861,
+      "44": 7719,
+      "45": 3651,
+      "46": 4286,
+      "47": 2527,
+      "48": 3544,
+      "49": 2160,
+      "5": 925327,
+      "50": 2935,
+      "51": 1821,
+      "52": 2711,
+      "53": 1784,
+      "54": 2344,
+      "55": 1697,
+      "56": 2512,
+      "57": 1742,
+      "58": 2284,
+      "59": 1731,
+      "6": 5193087,
+      "60": 2502,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2008680,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6018525,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1793150,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50145,
+      "7": 31290028,
+      "9": 116289
+    },
+    "connectivity_max": 140366727,
+    "connectivity_min": 0,
+    "n_cells": 31456462,
+    "n_connectivity_values": 343635308,
+    "n_fan_triangles": 280722384,
+    "n_points": 140366728
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.5472887590008172e-11,
+    "float64_area_closure_relative": 3.609386968289763e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280722384,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935209.3224705772,
+    "surface_area_float64_in2": 1935209.3225198726,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935209.3225198027,
+    "zero_area_triangles": 237398,
+    "zero_weight_points": 5400
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC060_AoA_22.json b/surface_dual_areas/cases/geo_LHC060_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..289a8ac0b5f555c862e2f37419ca9aa477fe44fb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC060_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC060_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC060_AoA_22/boundary_dual_area_geo_LHC060_AoA_22.npy",
+    "sha256": "e74334a05d6a5b687aa57ea1f7e61624d95b417f7a05b3f42e99e12fc83cc200",
+    "shape": [
+      136566666
+    ],
+    "size_bytes": 546266792
+  },
+  "runtime": {
+    "accumulation_seconds": 11.05522732110694,
+    "completed_at_utc": "2026-08-07T07:55:33.545071Z",
+    "elapsed_seconds": 21.27565580396913,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.225288084940985,
+    "geometry_read_seconds": 2.344487908994779,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:55:12.269333Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC060_AoA_22/boundary_geo_LHC060_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC060_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624467000000000,
+    "extracted_vtu_size_bytes": 20973358397,
+    "geometry_sha256": "79664a25ab810afda516089b53c2bf75667f781849202acfc909b8e77832f1b3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3636043,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1136096,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2394028,
+      "13": 746319,
+      "14": 1255802,
+      "15": 461811,
+      "16": 914123,
+      "17": 362905,
+      "18": 760565,
+      "19": 306814,
+      "20": 677613,
+      "21": 226379,
+      "22": 366799,
+      "23": 122753,
+      "24": 212684,
+      "25": 69567,
+      "26": 96171,
+      "27": 51810,
+      "28": 124320,
+      "29": 52915,
+      "3": 47777,
+      "30": 115783,
+      "31": 49274,
+      "32": 107964,
+      "33": 38703,
+      "34": 66650,
+      "35": 27730,
+      "36": 63064,
+      "37": 22843,
+      "38": 39354,
+      "39": 16308,
+      "4": 115012,
+      "40": 29795,
+      "41": 10840,
+      "42": 14415,
+      "43": 5860,
+      "44": 7711,
+      "45": 3656,
+      "46": 4283,
+      "47": 2524,
+      "48": 3543,
+      "49": 2161,
+      "5": 922065,
+      "50": 2936,
+      "51": 1821,
+      "52": 2710,
+      "53": 1785,
+      "54": 2344,
+      "55": 1697,
+      "56": 2512,
+      "57": 1742,
+      "58": 2284,
+      "59": 1730,
+      "6": 5167531,
+      "60": 2502,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1376,
+      "66": 1817,
+      "67": 1100,
+      "68": 1464,
+      "69": 904,
+      "7": 1977433,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5848898,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 1731728,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 47777,
+      "7": 30300299,
+      "9": 115012
+    },
+    "connectivity_max": 136566665,
+    "connectivity_min": 0,
+    "n_cells": 30463088,
+    "n_connectivity_values": 334048436,
+    "n_fan_triangles": 273122260,
+    "n_points": 136566666
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.454621617633283e-11,
+    "float64_area_closure_relative": 4.331260574198519e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273122260,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935211.014840546,
+    "surface_area_float64_in2": 1935211.0148880482,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935211.0148880398,
+    "zero_area_triangles": 230865,
+    "zero_weight_points": 5028
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC062_AoA_14.json b/surface_dual_areas/cases/geo_LHC062_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..4bb4b28dec9032b64467f1d6f6bac3540893870a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC062_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC062_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC062_AoA_14/boundary_dual_area_geo_LHC062_AoA_14.npy",
+    "sha256": "4f56d09001d5662de4e811c15b3aea858c28866fe86bda573d187542afbdd990",
+    "shape": [
+      139386198
+    ],
+    "size_bytes": 557544920
+  },
+  "runtime": {
+    "accumulation_seconds": 10.5187917270232,
+    "completed_at_utc": "2026-08-07T07:36:31.803126Z",
+    "elapsed_seconds": 20.112371713854373,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.944376666098833,
+    "geometry_read_seconds": 2.0750254448503256,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:36:11.690664Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC062_AoA_14/boundary_geo_LHC062_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC062_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624543000000000,
+    "extracted_vtu_size_bytes": 21407420599,
+    "geometry_sha256": "eb8403acf50897b2071903b22cfb42fdf5bd8d4646372fcc44d7c41231b2eab4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3752675,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1158982,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2603493,
+      "13": 792990,
+      "14": 1367169,
+      "15": 476785,
+      "16": 933894,
+      "17": 357227,
+      "18": 747061,
+      "19": 301538,
+      "20": 668534,
+      "21": 225607,
+      "22": 365097,
+      "23": 124343,
+      "24": 202479,
+      "25": 68658,
+      "26": 92751,
+      "27": 51410,
+      "28": 124140,
+      "29": 53092,
+      "3": 54060,
+      "30": 114844,
+      "31": 49571,
+      "32": 109086,
+      "33": 39089,
+      "34": 67079,
+      "35": 28190,
+      "36": 63375,
+      "37": 22960,
+      "38": 38519,
+      "39": 16199,
+      "4": 120413,
+      "40": 29100,
+      "41": 10637,
+      "42": 14112,
+      "43": 5719,
+      "44": 7534,
+      "45": 3664,
+      "46": 4240,
+      "47": 2511,
+      "48": 3525,
+      "49": 2125,
+      "5": 933891,
+      "50": 2926,
+      "51": 1825,
+      "52": 2702,
+      "53": 1721,
+      "54": 2324,
+      "55": 1675,
+      "56": 2519,
+      "57": 1726,
+      "58": 2274,
+      "59": 1716,
+      "6": 5142425,
+      "60": 2503,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1376,
+      "66": 1817,
+      "67": 1100,
+      "68": 1464,
+      "69": 904,
+      "7": 2002747,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5988529,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 1747380,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54060,
+      "7": 30959489,
+      "9": 120413
+    },
+    "connectivity_max": 139386197,
+    "connectivity_min": 0,
+    "n_cells": 31133962,
+    "n_connectivity_values": 341029200,
+    "n_fan_triangles": 278761276,
+    "n_points": 139386198
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.390117217299243e-11,
+    "float64_area_closure_relative": 2.7165460244919245e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278761276,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937008.4287024783,
+    "surface_area_float64_in2": 1937008.4287681452,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937008.4287680925,
+    "zero_area_triangles": 239198,
+    "zero_weight_points": 5629
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC063_AoA_12.json b/surface_dual_areas/cases/geo_LHC063_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..03a18ec7163505c57fc94eb0b7d90ad53ae54d69
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC063_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC063_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC063_AoA_12/boundary_dual_area_geo_LHC063_AoA_12.npy",
+    "sha256": "468135913a0d5fad6b55945de905d052495b1f94e83a804ac89f70d0961a2e7c",
+    "shape": [
+      146971737
+    ],
+    "size_bytes": 587887076
+  },
+  "runtime": {
+    "accumulation_seconds": 11.211046132957563,
+    "completed_at_utc": "2026-08-07T07:35:28.814258Z",
+    "elapsed_seconds": 21.959763335995376,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.151302413083613,
+    "geometry_read_seconds": 2.7145332179497927,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:35:06.854402Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC063_AoA_12/boundary_geo_LHC063_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC063_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624713000000000,
+    "extracted_vtu_size_bytes": 22582247195,
+    "geometry_sha256": "a2e1988a5a3fd67245deab050b41fd8efe064ee0223933ece184db67a9057d08",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4223773,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1301954,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2931159,
+      "13": 831529,
+      "14": 1417766,
+      "15": 471244,
+      "16": 964036,
+      "17": 365668,
+      "18": 757405,
+      "19": 305346,
+      "20": 667881,
+      "21": 221127,
+      "22": 342962,
+      "23": 118096,
+      "24": 195626,
+      "25": 69136,
+      "26": 89326,
+      "27": 51660,
+      "28": 123575,
+      "29": 52932,
+      "3": 58020,
+      "30": 113872,
+      "31": 48905,
+      "32": 107619,
+      "33": 38469,
+      "34": 66829,
+      "35": 27912,
+      "36": 63148,
+      "37": 23085,
+      "38": 39296,
+      "39": 16261,
+      "4": 130069,
+      "40": 29986,
+      "41": 10895,
+      "42": 14309,
+      "43": 5904,
+      "44": 7873,
+      "45": 3756,
+      "46": 4269,
+      "47": 2512,
+      "48": 3602,
+      "49": 2212,
+      "5": 952142,
+      "50": 2953,
+      "51": 1857,
+      "52": 2763,
+      "53": 1755,
+      "54": 2381,
+      "55": 1724,
+      "56": 2509,
+      "57": 1759,
+      "58": 2271,
+      "59": 1686,
+      "6": 5286682,
+      "60": 2466,
+      "61": 1654,
+      "62": 2223,
+      "63": 1600,
+      "64": 2207,
+      "65": 1377,
+      "66": 1811,
+      "67": 1113,
+      "68": 1527,
+      "69": 920,
+      "7": 2126963,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6533172,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1955854,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58020,
+      "7": 33032545,
+      "9": 130069
+    },
+    "connectivity_max": 146971736,
+    "connectivity_min": 0,
+    "n_cells": 33220634,
+    "n_connectivity_values": 360373625,
+    "n_fan_triangles": 293932357,
+    "n_points": 146971737
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.989763779585887e-11,
+    "float64_area_closure_relative": 2.3096404776793944e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293932357,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945597.7957661618,
+    "surface_area_float64_in2": 1945597.7958243305,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945597.7958243755,
+    "zero_area_triangles": 241710,
+    "zero_weight_points": 6047
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC064_AoA_4.json b/surface_dual_areas/cases/geo_LHC064_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..43ac31075df7373a6ca527f410d90cda47a83c38
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC064_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC064_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC064_AoA_4/boundary_dual_area_geo_LHC064_AoA_4.npy",
+    "sha256": "81b28c2efea3cc7f18861b89c16c3a07adda5b07ae59b1fcfb19c4703cb90c4b",
+    "shape": [
+      137025894
+    ],
+    "size_bytes": 548103704
+  },
+  "runtime": {
+    "accumulation_seconds": 13.14900136506185,
+    "completed_at_utc": "2026-08-07T07:56:47.819908Z",
+    "elapsed_seconds": 24.622877351008356,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1960455388762057,
+    "geometry_read_seconds": 3.173155281925574,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:56:23.196920Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC064_AoA_4/boundary_geo_LHC064_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC064_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624393000000000,
+    "extracted_vtu_size_bytes": 21034827132,
+    "geometry_sha256": "677772bac643ed4c6fc5397097ce31fa82f6143c9a9be7d21cc9c269d241e4b3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2868740,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 945983,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2213400,
+      "13": 792908,
+      "14": 1813891,
+      "15": 583524,
+      "16": 1104129,
+      "17": 395700,
+      "18": 762299,
+      "19": 304102,
+      "20": 679874,
+      "21": 224381,
+      "22": 361024,
+      "23": 121377,
+      "24": 198831,
+      "25": 68957,
+      "26": 91234,
+      "27": 51109,
+      "28": 123789,
+      "29": 52533,
+      "3": 57992,
+      "30": 114511,
+      "31": 48800,
+      "32": 108367,
+      "33": 38513,
+      "34": 67507,
+      "35": 28141,
+      "36": 64045,
+      "37": 23061,
+      "38": 39126,
+      "39": 16227,
+      "4": 131074,
+      "40": 29463,
+      "41": 10709,
+      "42": 14213,
+      "43": 5870,
+      "44": 7821,
+      "45": 3736,
+      "46": 4244,
+      "47": 2516,
+      "48": 3558,
+      "49": 2144,
+      "5": 957871,
+      "50": 2839,
+      "51": 1834,
+      "52": 2610,
+      "53": 1699,
+      "54": 2297,
+      "55": 1670,
+      "56": 2497,
+      "57": 1742,
+      "58": 2261,
+      "59": 1681,
+      "6": 5210554,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1378,
+      "66": 1810,
+      "67": 1115,
+      "68": 1527,
+      "69": 920,
+      "7": 2022389,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5772766,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1615934,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57992,
+      "7": 30014157,
+      "9": 131074
+    },
+    "connectivity_max": 137025893,
+    "connectivity_min": 0,
+    "n_cells": 30203223,
+    "n_connectivity_values": 334447114,
+    "n_fan_triangles": 274040668,
+    "n_points": 137025894
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.397170058118888e-11,
+    "float64_area_closure_relative": 1.0409473174761331e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274040668,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945945.3573994648,
+    "surface_area_float64_in2": 1945945.3574461124,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945945.3574461327,
+    "zero_area_triangles": 225994,
+    "zero_weight_points": 5024
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC065_AoA_20.json b/surface_dual_areas/cases/geo_LHC065_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..8737c012712f2c54e926189e418781ec268a0f6c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC065_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC065_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC065_AoA_20/boundary_dual_area_geo_LHC065_AoA_20.npy",
+    "sha256": "3de5493e90a0ae7e02125570a6e32a5737e2bc9934a6a624382d385696705b99",
+    "shape": [
+      146924137
+    ],
+    "size_bytes": 587696676
+  },
+  "runtime": {
+    "accumulation_seconds": 11.176579752005637,
+    "completed_at_utc": "2026-08-07T07:36:46.872952Z",
+    "elapsed_seconds": 53.235647245077416,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1607776468154043,
+    "geometry_read_seconds": 34.09345720312558,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:35:53.637215Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC065_AoA_20/boundary_geo_LHC065_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC065_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624720000000000,
+    "extracted_vtu_size_bytes": 22574594271,
+    "geometry_sha256": "8a6882a8e34a2cab2868d98492b5822d6ab451a35925f1d4bb9ac08dda26887c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4357196,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1289437,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3053093,
+      "13": 821446,
+      "14": 1292442,
+      "15": 455356,
+      "16": 907521,
+      "17": 354442,
+      "18": 754314,
+      "19": 305502,
+      "20": 684229,
+      "21": 225088,
+      "22": 359407,
+      "23": 121758,
+      "24": 206162,
+      "25": 70816,
+      "26": 91005,
+      "27": 51508,
+      "28": 122682,
+      "29": 52532,
+      "3": 58153,
+      "30": 114203,
+      "31": 49450,
+      "32": 109348,
+      "33": 38761,
+      "34": 67329,
+      "35": 28224,
+      "36": 62416,
+      "37": 22981,
+      "38": 38617,
+      "39": 16373,
+      "4": 131003,
+      "40": 29316,
+      "41": 10727,
+      "42": 14327,
+      "43": 5790,
+      "44": 7687,
+      "45": 3626,
+      "46": 4177,
+      "47": 2490,
+      "48": 3516,
+      "49": 2112,
+      "5": 947486,
+      "50": 2857,
+      "51": 1874,
+      "52": 2752,
+      "53": 1771,
+      "54": 2476,
+      "55": 1719,
+      "56": 2549,
+      "57": 1774,
+      "58": 2289,
+      "59": 1751,
+      "6": 5241478,
+      "60": 2511,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2089887,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6556150,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1919872,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 58153,
+      "7": 33007154,
+      "9": 131003
+    },
+    "connectivity_max": 146924136,
+    "connectivity_min": 0,
+    "n_cells": 33196310,
+    "n_connectivity_values": 360229774,
+    "n_fan_triangles": 293837154,
+    "n_points": 146924137
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.2033358862602544e-11,
+    "float64_area_closure_relative": 1.771715802539032e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293837154,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944947.107766463,
+    "surface_area_float64_in2": 1944947.1078482156,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944947.10784825,
+    "zero_area_triangles": 244416,
+    "zero_weight_points": 6168
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC065_AoA_8.json b/surface_dual_areas/cases/geo_LHC065_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..fb4f70628affe8f47873367b616a63646d06c62c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC065_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC065_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC065_AoA_8/boundary_dual_area_geo_LHC065_AoA_8.npy",
+    "sha256": "4b61c7ef335e8b497d533ac7ca87e420cb0061073ccf4346f4d1c523aa47febc",
+    "shape": [
+      142504533
+    ],
+    "size_bytes": 570018260
+  },
+  "runtime": {
+    "accumulation_seconds": 11.006501194089651,
+    "completed_at_utc": "2026-08-07T07:57:10.871811Z",
+    "elapsed_seconds": 21.93470404809341,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1997373818885535,
+    "geometry_read_seconds": 2.0957299519795924,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:56:48.937001Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC065_AoA_8/boundary_geo_LHC065_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC065_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624373000000000,
+    "extracted_vtu_size_bytes": 21885156754,
+    "geometry_sha256": "b649d6ab836bd98ed0ce8cb9c662e6646d58691c89aaec7cc40934bdd2d4a9d6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3559391,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1091013,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2711271,
+      "13": 825488,
+      "14": 1682298,
+      "15": 538926,
+      "16": 1053865,
+      "17": 381169,
+      "18": 760064,
+      "19": 305237,
+      "20": 670546,
+      "21": 219114,
+      "22": 331800,
+      "23": 115016,
+      "24": 189293,
+      "25": 67394,
+      "26": 89120,
+      "27": 51068,
+      "28": 122622,
+      "29": 52500,
+      "3": 55277,
+      "30": 114208,
+      "31": 49451,
+      "32": 109353,
+      "33": 38764,
+      "34": 67327,
+      "35": 28224,
+      "36": 62416,
+      "37": 22980,
+      "38": 38617,
+      "39": 16373,
+      "4": 125643,
+      "40": 29317,
+      "41": 10727,
+      "42": 14327,
+      "43": 5790,
+      "44": 7687,
+      "45": 3626,
+      "46": 4177,
+      "47": 2490,
+      "48": 3516,
+      "49": 2112,
+      "5": 943914,
+      "50": 2857,
+      "51": 1874,
+      "52": 2752,
+      "53": 1771,
+      "54": 2476,
+      "55": 1719,
+      "56": 2549,
+      "57": 1774,
+      "58": 2289,
+      "59": 1751,
+      "6": 5246420,
+      "60": 2511,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2020735,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6192393,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1704931,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 55277,
+      "7": 31601945,
+      "9": 125643
+    },
+    "connectivity_max": 142504532,
+    "connectivity_min": 0,
+    "n_cells": 31782865,
+    "n_connectivity_values": 348563676,
+    "n_fan_triangles": 284997946,
+    "n_points": 142504533
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.2453887355819716e-11,
+    "float64_area_closure_relative": 3.1124726375947092e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284997946,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944947.776126243,
+    "surface_area_float64_in2": 1944947.7762088135,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944947.7762088196,
+    "zero_area_triangles": 237226,
+    "zero_weight_points": 5713
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC066_AoA_10.json b/surface_dual_areas/cases/geo_LHC066_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..e83a72ef346e4295791943308058848a5c3f0ca0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC066_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC066_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC066_AoA_10/boundary_dual_area_geo_LHC066_AoA_10.npy",
+    "sha256": "ef6da8599c0545f01a6ddce7ea7a22243749bc9b9068c85aa2f5ad5ba8f78edd",
+    "shape": [
+      136691446
+    ],
+    "size_bytes": 546765912
+  },
+  "runtime": {
+    "accumulation_seconds": 10.587354101939127,
+    "completed_at_utc": "2026-08-07T07:57:37.506287Z",
+    "elapsed_seconds": 21.476439242018387,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.441995013039559,
+    "geometry_read_seconds": 2.56935126404278,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T07:57:16.029767Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC066_AoA_10/boundary_geo_LHC066_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC066_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624458000000000,
+    "extracted_vtu_size_bytes": 20988179554,
+    "geometry_sha256": "bd9c6fac92fc0227adadb75c36978dc2a18dc5bcabe366acc147a4385b55f60b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3329544,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1094043,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2414426,
+      "13": 776883,
+      "14": 1496347,
+      "15": 498262,
+      "16": 964892,
+      "17": 369512,
+      "18": 760841,
+      "19": 307790,
+      "20": 678274,
+      "21": 227579,
+      "22": 364172,
+      "23": 121797,
+      "24": 197202,
+      "25": 67085,
+      "26": 92711,
+      "27": 51492,
+      "28": 124993,
+      "29": 53209,
+      "3": 51512,
+      "30": 114309,
+      "31": 49297,
+      "32": 108180,
+      "33": 38925,
+      "34": 66852,
+      "35": 28070,
+      "36": 63285,
+      "37": 22958,
+      "38": 38710,
+      "39": 16023,
+      "4": 115578,
+      "40": 29234,
+      "41": 10649,
+      "42": 14147,
+      "43": 5735,
+      "44": 7603,
+      "45": 3659,
+      "46": 4207,
+      "47": 2521,
+      "48": 3502,
+      "49": 2051,
+      "5": 931215,
+      "50": 2811,
+      "51": 1715,
+      "52": 2513,
+      "53": 1615,
+      "54": 2199,
+      "55": 1621,
+      "56": 2426,
+      "57": 1700,
+      "58": 2262,
+      "59": 1718,
+      "6": 5149893,
+      "60": 2505,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1970554,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5757720,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1676124,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51512,
+      "7": 30150163,
+      "9": 115578
+    },
+    "connectivity_max": 136691445,
+    "connectivity_min": 0,
+    "n_cells": 30317253,
+    "n_connectivity_values": 334006275,
+    "n_fan_triangles": 273371769,
+    "n_points": 136691446
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.831082523957697e-11,
+    "float64_area_closure_relative": 2.1877612716351674e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273371769,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936919.6124268607,
+    "surface_area_float64_in2": 1936919.6125010657,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936919.612501108,
+    "zero_area_triangles": 236080,
+    "zero_weight_points": 5202
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC066_AoA_22.json b/surface_dual_areas/cases/geo_LHC066_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..adc605e504088909b38fcc4892da9c90483f507e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC066_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC066_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC066_AoA_22/boundary_dual_area_geo_LHC066_AoA_22.npy",
+    "sha256": "8dd6220542316aa728f2554d2f5ccc71ffed8263899ffc613c763a7bca63eebb",
+    "shape": [
+      140186773
+    ],
+    "size_bytes": 560747220
+  },
+  "runtime": {
+    "accumulation_seconds": 11.008134090108797,
+    "completed_at_utc": "2026-08-07T07:58:24.512295Z",
+    "elapsed_seconds": 64.04765033512376,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2189550758339465,
+    "geometry_read_seconds": 43.84968664706685,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T07:57:20.464545Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC066_AoA_22/boundary_geo_LHC066_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC066_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624376000000000,
+    "extracted_vtu_size_bytes": 21532117750,
+    "geometry_sha256": "30e84f04c48e7e288189e2d0c441fae881039f78a73232d51fd01c04d99d1cc8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3837950,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1186319,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2622120,
+      "13": 786999,
+      "14": 1389133,
+      "15": 477059,
+      "16": 922666,
+      "17": 359437,
+      "18": 745497,
+      "19": 301880,
+      "20": 664775,
+      "21": 224718,
+      "22": 360189,
+      "23": 122478,
+      "24": 201053,
+      "25": 68795,
+      "26": 94812,
+      "27": 52205,
+      "28": 125358,
+      "29": 53325,
+      "3": 51556,
+      "30": 114381,
+      "31": 49324,
+      "32": 108204,
+      "33": 38932,
+      "34": 66861,
+      "35": 28064,
+      "36": 63264,
+      "37": 22969,
+      "38": 38703,
+      "39": 15995,
+      "4": 117562,
+      "40": 29208,
+      "41": 10639,
+      "42": 14119,
+      "43": 5727,
+      "44": 7594,
+      "45": 3650,
+      "46": 4212,
+      "47": 2519,
+      "48": 3505,
+      "49": 2049,
+      "5": 941314,
+      "50": 2806,
+      "51": 1710,
+      "52": 2511,
+      "53": 1617,
+      "54": 2201,
+      "55": 1620,
+      "56": 2426,
+      "57": 1700,
+      "58": 2262,
+      "59": 1718,
+      "6": 5182272,
+      "60": 2505,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2020579,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6011755,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1787043,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51556,
+      "7": 31213327,
+      "9": 117562
+    },
+    "connectivity_max": 140186772,
+    "connectivity_min": 0,
+    "n_cells": 31382445,
+    "n_connectivity_values": 343127313,
+    "n_fan_triangles": 280362423,
+    "n_points": 140186773
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.8099747188826443e-11,
+    "float64_area_closure_relative": 2.4522162430022826e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280362423,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936919.3658642424,
+    "surface_area_float64_in2": 1936919.3659380386,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936919.365938086,
+    "zero_area_triangles": 241171,
+    "zero_weight_points": 5490
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC066_AoA_6.json b/surface_dual_areas/cases/geo_LHC066_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..5272aa30912013051b7dc002764cb846edbc69cc
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC066_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC066_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC066_AoA_6/boundary_dual_area_geo_LHC066_AoA_6.npy",
+    "sha256": "9d9d020894377f7b2b160592a3953ba711c5836fbba202ad29022ab51c58e895",
+    "shape": [
+      131914035
+    ],
+    "size_bytes": 527656268
+  },
+  "runtime": {
+    "accumulation_seconds": 9.968022709945217,
+    "completed_at_utc": "2026-08-07T07:37:37.685819Z",
+    "elapsed_seconds": 19.06214091205038,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.7881857310421765,
+    "geometry_read_seconds": 1.951248510973528,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:37:18.623577Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC066_AoA_6/boundary_geo_LHC066_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC066_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624605000000000,
+    "extracted_vtu_size_bytes": 20246141300,
+    "geometry_sha256": "1c8698ec0494389fecf22e563c5f5c530627b67fa6fc01b3f257027f715c961d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2710431,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 927013,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2084935,
+      "13": 747515,
+      "14": 1652239,
+      "15": 536673,
+      "16": 1020737,
+      "17": 381760,
+      "18": 764955,
+      "19": 309580,
+      "20": 681305,
+      "21": 229547,
+      "22": 370316,
+      "23": 123848,
+      "24": 201245,
+      "25": 67950,
+      "26": 93803,
+      "27": 51662,
+      "28": 125151,
+      "29": 53234,
+      "3": 49399,
+      "30": 114318,
+      "31": 49305,
+      "32": 108193,
+      "33": 38931,
+      "34": 66849,
+      "35": 28067,
+      "36": 63279,
+      "37": 22968,
+      "38": 38714,
+      "39": 16020,
+      "4": 112003,
+      "40": 29235,
+      "41": 10648,
+      "42": 14140,
+      "43": 5744,
+      "44": 7593,
+      "45": 3659,
+      "46": 4213,
+      "47": 2523,
+      "48": 3502,
+      "49": 2050,
+      "5": 927807,
+      "50": 2813,
+      "51": 1715,
+      "52": 2512,
+      "53": 1616,
+      "54": 2199,
+      "55": 1621,
+      "56": 2426,
+      "57": 1700,
+      "58": 2262,
+      "59": 1718,
+      "6": 5143678,
+      "60": 2505,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1912517,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5457298,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1507756,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49399,
+      "7": 28756594,
+      "9": 112003
+    },
+    "connectivity_max": 131914034,
+    "connectivity_min": 0,
+    "n_cells": 28917996,
+    "n_connectivity_values": 321652939,
+    "n_fan_triangles": 263816947,
+    "n_points": 131914035
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.764221330417555e-11,
+    "float64_area_closure_relative": 3.4859911537145323e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 263816947,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936920.7688646314,
+    "surface_area_float64_in2": 1936920.7689375414,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936920.768937609,
+    "zero_area_triangles": 225624,
+    "zero_weight_points": 4657
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC067_AoA_12.json b/surface_dual_areas/cases/geo_LHC067_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d259af35bb665c04466ef0c29ae289fd9951a4f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC067_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC067_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC067_AoA_12/boundary_dual_area_geo_LHC067_AoA_12.npy",
+    "sha256": "e4f6e503e5e65b5021607f5df03dc794b2451b2ad96a1c2645e7ce661a8e36af",
+    "shape": [
+      142344533
+    ],
+    "size_bytes": 569378260
+  },
+  "runtime": {
+    "accumulation_seconds": 11.096380047034472,
+    "completed_at_utc": "2026-08-07T07:37:25.758645Z",
+    "elapsed_seconds": 21.736473829019815,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.205617854837328,
+    "geometry_read_seconds": 2.3197394360322505,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:37:04.022076Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC067_AoA_12/boundary_geo_LHC067_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC067_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624376000000000,
+    "extracted_vtu_size_bytes": 21866585714,
+    "geometry_sha256": "f41097efe05cb0ab8f9ae11c9fcc551efe57f4972aefb92f77fd02a9010df880",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3974656,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1219740,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2797743,
+      "13": 804314,
+      "14": 1407695,
+      "15": 472989,
+      "16": 934980,
+      "17": 354964,
+      "18": 732187,
+      "19": 295419,
+      "20": 653814,
+      "21": 219569,
+      "22": 347134,
+      "23": 121247,
+      "24": 199446,
+      "25": 69907,
+      "26": 93192,
+      "27": 52265,
+      "28": 124111,
+      "29": 53136,
+      "3": 54220,
+      "30": 114467,
+      "31": 49092,
+      "32": 108043,
+      "33": 38679,
+      "34": 66502,
+      "35": 27834,
+      "36": 62993,
+      "37": 22985,
+      "38": 39348,
+      "39": 16512,
+      "4": 118902,
+      "40": 29959,
+      "41": 10851,
+      "42": 14445,
+      "43": 5830,
+      "44": 7642,
+      "45": 3694,
+      "46": 4272,
+      "47": 2476,
+      "48": 3518,
+      "49": 2134,
+      "5": 936628,
+      "50": 2961,
+      "51": 1880,
+      "52": 2798,
+      "53": 1779,
+      "54": 2436,
+      "55": 1751,
+      "56": 2568,
+      "57": 1748,
+      "58": 2289,
+      "59": 1726,
+      "6": 5218375,
+      "60": 2503,
+      "61": 1656,
+      "62": 2231,
+      "63": 1636,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2039575,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6195812,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1818884,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54220,
+      "7": 31814103,
+      "9": 118902
+    },
+    "connectivity_max": 142344532,
+    "connectivity_min": 0,
+    "n_cells": 31987225,
+    "n_connectivity_values": 348652391,
+    "n_fan_triangles": 284677941,
+    "n_points": 142344533
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.774312003512361e-11,
+    "float64_area_closure_relative": 3.3354909718426706e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284677941,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940551.4654286348,
+    "surface_area_float64_in2": 1940551.4655018772,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940551.465501942,
+    "zero_area_triangles": 237822,
+    "zero_weight_points": 5701
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC067_AoA_4.json b/surface_dual_areas/cases/geo_LHC067_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..24af5f138b3b2bede93a7c03230c89fd1e2618b4
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC067_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC067_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC067_AoA_4/boundary_dual_area_geo_LHC067_AoA_4.npy",
+    "sha256": "041b91c8bea7637ade4dd03d60fab17e01267384fd85abc6a78de0e9e7f6fcb5",
+    "shape": [
+      130836275
+    ],
+    "size_bytes": 523345228
+  },
+  "runtime": {
+    "accumulation_seconds": 10.146699869073927,
+    "completed_at_utc": "2026-08-07T07:37:07.607607Z",
+    "elapsed_seconds": 19.675524833146483,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.814603586914018,
+    "geometry_read_seconds": 1.7230613590218127,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:36:47.931990Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC067_AoA_4/boundary_geo_LHC067_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC067_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624468000000000,
+    "extracted_vtu_size_bytes": 20077926279,
+    "geometry_sha256": "ce5935ddc60e65c8073f2781eab791e23705a6f905cfb3a164e5b09dcec92cc9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2474386,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 835663,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1941648,
+      "13": 743973,
+      "14": 1847952,
+      "15": 575873,
+      "16": 1098828,
+      "17": 385909,
+      "18": 749339,
+      "19": 299264,
+      "20": 659519,
+      "21": 221756,
+      "22": 352456,
+      "23": 123038,
+      "24": 203028,
+      "25": 70907,
+      "26": 94014,
+      "27": 52553,
+      "28": 124326,
+      "29": 53195,
+      "3": 48604,
+      "30": 114483,
+      "31": 49100,
+      "32": 108046,
+      "33": 38679,
+      "34": 66501,
+      "35": 27834,
+      "36": 62990,
+      "37": 22984,
+      "38": 39348,
+      "39": 16513,
+      "4": 112314,
+      "40": 29961,
+      "41": 10851,
+      "42": 14445,
+      "43": 5829,
+      "44": 7640,
+      "45": 3694,
+      "46": 4272,
+      "47": 2475,
+      "48": 3518,
+      "49": 2135,
+      "5": 925824,
+      "50": 2961,
+      "51": 1880,
+      "52": 2797,
+      "53": 1779,
+      "54": 2438,
+      "55": 1751,
+      "56": 2568,
+      "57": 1748,
+      "58": 2289,
+      "59": 1726,
+      "6": 5188013,
+      "60": 2503,
+      "61": 1656,
+      "62": 2231,
+      "63": 1636,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 1887383,
+      "70": 1023,
+      "71": 571,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5400944,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1422682,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 48604,
+      "7": 28408817,
+      "9": 112314
+    },
+    "connectivity_max": 130836274,
+    "connectivity_min": 0,
+    "n_cells": 28569735,
+    "n_connectivity_values": 318800895,
+    "n_fan_triangles": 261661425,
+    "n_points": 130836275
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.888971601897439e-11,
+    "float64_area_closure_relative": 4.1273627979203443e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 261661425,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940554.9096428643,
+    "surface_area_float64_in2": 1940554.9097183319,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940554.9097182518,
+    "zero_area_triangles": 215625,
+    "zero_weight_points": 4307
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC068_AoA_12.json b/surface_dual_areas/cases/geo_LHC068_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..213dee28ff7c5ae8cd1f8011afa0c0437262d81d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC068_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC068_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC068_AoA_12/boundary_dual_area_geo_LHC068_AoA_12.npy",
+    "sha256": "b46f1b67e74bc752bcd866b5c012c878a560d4d4579628e20410e0f5bafb1930",
+    "shape": [
+      145373505
+    ],
+    "size_bytes": 581494148
+  },
+  "runtime": {
+    "accumulation_seconds": 10.960725869983435,
+    "completed_at_utc": "2026-08-07T07:36:34.621370Z",
+    "elapsed_seconds": 20.92871740506962,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.081340064993128,
+    "geometry_read_seconds": 2.1756779151037335,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:36:13.692559Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC068_AoA_12/boundary_geo_LHC068_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC068_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624543000000000,
+    "extracted_vtu_size_bytes": 22335787784,
+    "geometry_sha256": "3b3cdd89f255ad44a4f80c4f683fcf03b4a14827ca9338c58d065ae04c4827a6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4143446,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1320365,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2787999,
+      "13": 822317,
+      "14": 1377814,
+      "15": 457530,
+      "16": 906002,
+      "17": 347420,
+      "18": 736938,
+      "19": 299286,
+      "20": 676782,
+      "21": 225411,
+      "22": 371441,
+      "23": 126032,
+      "24": 214283,
+      "25": 72142,
+      "26": 93497,
+      "27": 51893,
+      "28": 123712,
+      "29": 52815,
+      "3": 57399,
+      "30": 114803,
+      "31": 49387,
+      "32": 109126,
+      "33": 38822,
+      "34": 66866,
+      "35": 28052,
+      "36": 62680,
+      "37": 22959,
+      "38": 38946,
+      "39": 16266,
+      "4": 128406,
+      "40": 29485,
+      "41": 10675,
+      "42": 14096,
+      "43": 5717,
+      "44": 7562,
+      "45": 3644,
+      "46": 4251,
+      "47": 2531,
+      "48": 3552,
+      "49": 2145,
+      "5": 932086,
+      "50": 2969,
+      "51": 1821,
+      "52": 2703,
+      "53": 1721,
+      "54": 2311,
+      "55": 1656,
+      "56": 2469,
+      "57": 1708,
+      "58": 2264,
+      "59": 1718,
+      "6": 5312429,
+      "60": 2505,
+      "61": 1655,
+      "62": 2230,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 2067846,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6508255,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1934233,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57399,
+      "7": 32637986,
+      "9": 128406
+    },
+    "connectivity_max": 145373504,
+    "connectivity_min": 0,
+    "n_cells": 32823791,
+    "n_connectivity_values": 356383475,
+    "n_fan_triangles": 290735893,
+    "n_points": 145373505
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.811624351456428e-11,
+    "float64_area_closure_relative": 5.0262231405741166e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290735893,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945573.5966335954,
+    "surface_area_float64_in2": 1945573.5967077534,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945573.5967078512,
+    "zero_area_triangles": 236471,
+    "zero_weight_points": 5583
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC069_AoA_18.json b/surface_dual_areas/cases/geo_LHC069_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..e965cb909a9e2ac24e30e210f6fb4e003661a58f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC069_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC069_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC069_AoA_18/boundary_dual_area_geo_LHC069_AoA_18.npy",
+    "sha256": "f4dae656a441f4207a30fb6b00a2353ff3b0f93b71ba11d3a56144fa33297a74",
+    "shape": [
+      141450698
+    ],
+    "size_bytes": 565802920
+  },
+  "runtime": {
+    "accumulation_seconds": 10.675324767129496,
+    "completed_at_utc": "2026-08-07T07:38:43.570620Z",
+    "elapsed_seconds": 21.205816275207326,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9872276759706438,
+    "geometry_read_seconds": 2.257373330183327,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:38:22.364716Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC069_AoA_18/boundary_geo_LHC069_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC069_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624503000000000,
+    "extracted_vtu_size_bytes": 21729569791,
+    "geometry_sha256": "4d35ef80f08059a4983d79b1f9e7a50cdcb0f99d48075aa9d3e766b073d950e5",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3954364,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1271434,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2700516,
+      "13": 795502,
+      "14": 1301726,
+      "15": 442395,
+      "16": 907646,
+      "17": 348936,
+      "18": 744227,
+      "19": 299846,
+      "20": 664919,
+      "21": 224064,
+      "22": 360860,
+      "23": 123377,
+      "24": 207817,
+      "25": 69920,
+      "26": 94884,
+      "27": 52011,
+      "28": 124572,
+      "29": 52952,
+      "3": 53228,
+      "30": 114911,
+      "31": 49495,
+      "32": 108962,
+      "33": 38789,
+      "34": 66155,
+      "35": 27878,
+      "36": 62503,
+      "37": 23122,
+      "38": 38946,
+      "39": 16498,
+      "4": 121131,
+      "40": 29668,
+      "41": 10717,
+      "42": 14307,
+      "43": 5896,
+      "44": 7707,
+      "45": 3595,
+      "46": 4290,
+      "47": 2528,
+      "48": 3536,
+      "49": 2135,
+      "5": 940048,
+      "50": 2932,
+      "51": 1867,
+      "52": 2747,
+      "53": 1770,
+      "54": 2456,
+      "55": 1750,
+      "56": 2592,
+      "57": 1717,
+      "58": 2312,
+      "59": 1709,
+      "6": 5205047,
+      "60": 2449,
+      "61": 1667,
+      "62": 2198,
+      "63": 1588,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2055049,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6128046,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1877204,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53228,
+      "7": 31623731,
+      "9": 121131
+    },
+    "connectivity_max": 141450697,
+    "connectivity_min": 0,
+    "n_cells": 31798090,
+    "n_connectivity_values": 346486455,
+    "n_fan_triangles": 282890275,
+    "n_points": 141450698
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6909416424776816e-11,
+    "float64_area_closure_relative": 1.6810902174412547e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282890275,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938997.0729799757,
+    "surface_area_float64_in2": 1938997.073051543,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938997.0730515462,
+    "zero_area_triangles": 238411,
+    "zero_weight_points": 5708
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC070_AoA_14.json b/surface_dual_areas/cases/geo_LHC070_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..63d01daa070580eeeeacb8a89941aa352960a45f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC070_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC070_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC070_AoA_14/boundary_dual_area_geo_LHC070_AoA_14.npy",
+    "sha256": "45bea1890c8cef6232f4c95d8a1351d0804a9891e3f27cc37c7eaaf8bd6343c4",
+    "shape": [
+      143392084
+    ],
+    "size_bytes": 573568464
+  },
+  "runtime": {
+    "accumulation_seconds": 11.037718361010775,
+    "completed_at_utc": "2026-08-07T08:00:59.330128Z",
+    "elapsed_seconds": 55.41437086998485,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2336637231055647,
+    "geometry_read_seconds": 36.31936407182366,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:00:03.915667Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC070_AoA_14/boundary_geo_LHC070_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC070_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624529000000000,
+    "extracted_vtu_size_bytes": 22033884068,
+    "geometry_sha256": "a317a12c3fe743f13c375f791e3d9081d6e8c288248e46a32cc2ee87306af119",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4251522,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1322610,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2792113,
+      "13": 786523,
+      "14": 1242237,
+      "15": 422386,
+      "16": 876660,
+      "17": 347004,
+      "18": 738631,
+      "19": 302465,
+      "20": 655644,
+      "21": 224613,
+      "22": 350391,
+      "23": 122999,
+      "24": 202961,
+      "25": 69148,
+      "26": 96249,
+      "27": 51923,
+      "28": 124262,
+      "29": 52840,
+      "3": 52965,
+      "30": 113930,
+      "31": 48805,
+      "32": 107936,
+      "33": 38406,
+      "34": 66138,
+      "35": 27647,
+      "36": 63503,
+      "37": 23048,
+      "38": 39849,
+      "39": 16617,
+      "4": 120229,
+      "40": 30840,
+      "41": 11301,
+      "42": 14642,
+      "43": 6078,
+      "44": 7991,
+      "45": 3727,
+      "46": 4261,
+      "47": 2515,
+      "48": 3569,
+      "49": 2192,
+      "5": 948125,
+      "50": 2943,
+      "51": 1832,
+      "52": 2730,
+      "53": 1774,
+      "54": 2474,
+      "55": 1724,
+      "56": 2576,
+      "57": 1766,
+      "58": 2275,
+      "59": 1692,
+      "6": 5321306,
+      "60": 2465,
+      "61": 1651,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 921,
+      "7": 2085429,
+      "70": 991,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6304215,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1934267,
+      "90": 58,
+      "91": 57,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52965,
+      "7": 32304461,
+      "9": 120229
+    },
+    "connectivity_max": 143392083,
+    "connectivity_min": 0,
+    "n_cells": 32477655,
+    "n_connectivity_values": 351728360,
+    "n_fan_triangles": 286773050,
+    "n_points": 143392084
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.191404079865749e-11,
+    "float64_area_closure_relative": 3.566659937536227e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 286773050,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938808.3634000788,
+    "surface_area_float64_in2": 1938808.363461954,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938808.363461885,
+    "zero_area_triangles": 241528,
+    "zero_weight_points": 5731
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC070_AoA_16.json b/surface_dual_areas/cases/geo_LHC070_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..14dd24b5ef307480632371976927e9460c48557a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC070_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC070_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC070_AoA_16/boundary_dual_area_geo_LHC070_AoA_16.npy",
+    "sha256": "282f4cf3ece52b204532450bb0b1204f40b0bca764d0bb761de3d15e7f952f91",
+    "shape": [
+      142198278
+    ],
+    "size_bytes": 568793240
+  },
+  "runtime": {
+    "accumulation_seconds": 10.694388427073136,
+    "completed_at_utc": "2026-08-07T07:38:12.635417Z",
+    "elapsed_seconds": 20.548643158050254,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.047446846961975,
+    "geometry_read_seconds": 1.8629023300018162,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:37:52.086682Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC070_AoA_16/boundary_geo_LHC070_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC070_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624681000000000,
+    "extracted_vtu_size_bytes": 21848923847,
+    "geometry_sha256": "f3dc65677b534cd7a27202945f6fa6d3b3c030bd6b1600eb98282bef5042183c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4183723,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1269195,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2724687,
+      "13": 762409,
+      "14": 1222630,
+      "15": 425212,
+      "16": 878689,
+      "17": 349429,
+      "18": 739370,
+      "19": 303019,
+      "20": 656358,
+      "21": 226143,
+      "22": 356056,
+      "23": 125586,
+      "24": 208412,
+      "25": 71286,
+      "26": 97553,
+      "27": 52531,
+      "28": 124464,
+      "29": 52910,
+      "3": 51935,
+      "30": 113953,
+      "31": 48811,
+      "32": 107955,
+      "33": 38402,
+      "34": 66123,
+      "35": 27636,
+      "36": 63497,
+      "37": 23051,
+      "38": 39854,
+      "39": 16619,
+      "4": 118659,
+      "40": 30841,
+      "41": 11295,
+      "42": 14640,
+      "43": 6082,
+      "44": 7989,
+      "45": 3729,
+      "46": 4260,
+      "47": 2515,
+      "48": 3567,
+      "49": 2194,
+      "5": 943443,
+      "50": 2941,
+      "51": 1832,
+      "52": 2731,
+      "53": 1775,
+      "54": 2474,
+      "55": 1724,
+      "56": 2576,
+      "57": 1766,
+      "58": 2275,
+      "59": 1692,
+      "6": 5310274,
+      "60": 2465,
+      "61": 1651,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 921,
+      "7": 2061679,
+      "70": 991,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6269698,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1883272,
+      "90": 58,
+      "91": 57,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51935,
+      "7": 31975984,
+      "9": 118659
+    },
+    "connectivity_max": 142198277,
+    "connectivity_min": 0,
+    "n_cells": 32146578,
+    "n_connectivity_values": 348678593,
+    "n_fan_triangles": 284385437,
+    "n_points": 142198278
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.223826852093832e-11,
+    "float64_area_closure_relative": 3.6387120832939636e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284385437,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938809.2107849459,
+    "surface_area_float64_in2": 1938809.2108474497,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938809.2108475203,
+    "zero_area_triangles": 239433,
+    "zero_weight_points": 5663
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC071_AoA_10.json b/surface_dual_areas/cases/geo_LHC071_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..1e7f91a251cab99171a688ed0d89354fe3ab012c
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC071_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC071_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC071_AoA_10/boundary_dual_area_geo_LHC071_AoA_10.npy",
+    "sha256": "2202797b210754f4e6ebdfaaf84c10dc089c683325b61c8f4719d8eecd2700bd",
+    "shape": [
+      141043500
+    ],
+    "size_bytes": 564174128
+  },
+  "runtime": {
+    "accumulation_seconds": 10.864589619915932,
+    "completed_at_utc": "2026-08-07T08:01:56.859462Z",
+    "elapsed_seconds": 20.641701587010175,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1240847560111433,
+    "geometry_read_seconds": 1.9360146820545197,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:01:36.217666Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC071_AoA_10/boundary_geo_LHC071_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC071_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624530000000000,
+    "extracted_vtu_size_bytes": 21660742803,
+    "geometry_sha256": "515e3ee1c15a01dc4bd38ccc80b89d3e3b0034fb296e005c7127ab6b6b93a05f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3498841,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1115116,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2567701,
+      "13": 803962,
+      "14": 1581474,
+      "15": 508632,
+      "16": 979537,
+      "17": 362453,
+      "18": 743241,
+      "19": 300078,
+      "20": 672781,
+      "21": 228234,
+      "22": 379804,
+      "23": 127578,
+      "24": 213160,
+      "25": 72586,
+      "26": 92777,
+      "27": 51986,
+      "28": 123363,
+      "29": 53054,
+      "3": 56495,
+      "30": 114913,
+      "31": 49688,
+      "32": 108931,
+      "33": 39045,
+      "34": 67522,
+      "35": 28408,
+      "36": 62851,
+      "37": 23009,
+      "38": 38368,
+      "39": 16229,
+      "4": 133004,
+      "40": 29209,
+      "41": 10680,
+      "42": 14285,
+      "43": 5771,
+      "44": 7598,
+      "45": 3595,
+      "46": 4102,
+      "47": 2491,
+      "48": 3517,
+      "49": 2130,
+      "5": 951835,
+      "50": 2909,
+      "51": 1843,
+      "52": 2716,
+      "53": 1756,
+      "54": 2434,
+      "55": 1702,
+      "56": 2507,
+      "57": 1754,
+      "58": 2282,
+      "59": 1743,
+      "6": 5234679,
+      "60": 2505,
+      "61": 1626,
+      "62": 2257,
+      "63": 1601,
+      "64": 2166,
+      "65": 1404,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 2021510,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 303,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6179044,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 55,
+      "88": 71,
+      "89": 59,
+      "9": 1725652,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 52,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 56495,
+      "7": 31266123,
+      "9": 133004
+    },
+    "connectivity_max": 141043499,
+    "connectivity_min": 0,
+    "n_cells": 31455622,
+    "n_connectivity_values": 344987125,
+    "n_fan_triangles": 282075881,
+    "n_points": 141043500
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.4304843181209806e-11,
+    "float64_area_closure_relative": 2.475364725167797e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282075881,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947023.9170895775,
+    "surface_area_float64_in2": 1947023.9171758401,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947023.9171758883,
+    "zero_area_triangles": 232209,
+    "zero_weight_points": 5438
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC071_AoA_14.json b/surface_dual_areas/cases/geo_LHC071_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..1506af4b6f75dd49f91b11e13edcc18c01d2e0f9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC071_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC071_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC071_AoA_14/boundary_dual_area_geo_LHC071_AoA_14.npy",
+    "sha256": "ce8491f482742e07dbb51603bf13a51fe86b4153a9fddeb7bc71795bbd8d082c",
+    "shape": [
+      145351601
+    ],
+    "size_bytes": 581406532
+  },
+  "runtime": {
+    "accumulation_seconds": 11.07612050510943,
+    "completed_at_utc": "2026-08-07T08:02:24.739642Z",
+    "elapsed_seconds": 21.298470138106495,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.26059140288271,
+    "geometry_read_seconds": 2.0308835960458964,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:02:03.441053Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC071_AoA_14/boundary_geo_LHC071_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC071_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624674000000000,
+    "extracted_vtu_size_bytes": 22330316526,
+    "geometry_sha256": "1d45415666e05b2f8bd291092f14d96b219915bf17bfb1acd519b95b11740e4a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4054780,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1294360,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2830276,
+      "13": 829810,
+      "14": 1435236,
+      "15": 464821,
+      "16": 923245,
+      "17": 347576,
+      "18": 739154,
+      "19": 298188,
+      "20": 670332,
+      "21": 226986,
+      "22": 376995,
+      "23": 126631,
+      "24": 211890,
+      "25": 72200,
+      "26": 92642,
+      "27": 51919,
+      "28": 123317,
+      "29": 53047,
+      "3": 59317,
+      "30": 114910,
+      "31": 49683,
+      "32": 108930,
+      "33": 39053,
+      "34": 67524,
+      "35": 28409,
+      "36": 62852,
+      "37": 23009,
+      "38": 38368,
+      "39": 16230,
+      "4": 135706,
+      "40": 29201,
+      "41": 10681,
+      "42": 14284,
+      "43": 5772,
+      "44": 7596,
+      "45": 3596,
+      "46": 4104,
+      "47": 2492,
+      "48": 3517,
+      "49": 2129,
+      "5": 954655,
+      "50": 2909,
+      "51": 1843,
+      "52": 2717,
+      "53": 1756,
+      "54": 2432,
+      "55": 1702,
+      "56": 2507,
+      "57": 1754,
+      "58": 2282,
+      "59": 1743,
+      "6": 5242287,
+      "60": 2505,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 2085678,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6444174,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1912348,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59317,
+      "7": 32539590,
+      "9": 135706
+    },
+    "connectivity_max": 145351600,
+    "connectivity_min": 0,
+    "n_cells": 32734613,
+    "n_connectivity_values": 356161309,
+    "n_fan_triangles": 290692083,
+    "n_points": 145351601
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.4756762168163415e-11,
+    "float64_area_closure_relative": 2.475365579444425e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290692083,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947023.2451487465,
+    "surface_area_float64_in2": 1947023.245235889,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947023.2452359372,
+    "zero_area_triangles": 238591,
+    "zero_weight_points": 5880
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC072_AoA_12.json b/surface_dual_areas/cases/geo_LHC072_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..b3b7a682fe78535a85591a8ff22ca1c374476a96
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC072_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC072_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC072_AoA_12/boundary_dual_area_geo_LHC072_AoA_12.npy",
+    "sha256": "9aaad55d3de89fc6362e3540852bce375a85d61fd1bca104f50bfc26f00f87ae",
+    "shape": [
+      149100187
+    ],
+    "size_bytes": 596400876
+  },
+  "runtime": {
+    "accumulation_seconds": 11.788622454041615,
+    "completed_at_utc": "2026-08-07T08:00:21.510453Z",
+    "elapsed_seconds": 23.303217673907056,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5492594530805945,
+    "geometry_read_seconds": 2.7276687058620155,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T07:59:58.207150Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC072_AoA_12/boundary_geo_LHC072_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC072_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624635000000000,
+    "extracted_vtu_size_bytes": 22912439310,
+    "geometry_sha256": "d0f7bf2826ced8c6632d0c6990dd71be7cbc037dee7f0357dddf184c3db1a2cc",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4302368,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1346557,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3063020,
+      "13": 857136,
+      "14": 1429976,
+      "15": 481831,
+      "16": 963034,
+      "17": 369120,
+      "18": 747311,
+      "19": 303375,
+      "20": 662013,
+      "21": 220580,
+      "22": 348501,
+      "23": 117970,
+      "24": 189286,
+      "25": 67097,
+      "26": 88536,
+      "27": 50958,
+      "28": 123727,
+      "29": 52590,
+      "3": 59411,
+      "30": 115363,
+      "31": 49244,
+      "32": 109129,
+      "33": 38695,
+      "34": 66739,
+      "35": 27841,
+      "36": 61992,
+      "37": 22826,
+      "38": 38771,
+      "39": 16345,
+      "4": 136346,
+      "40": 29922,
+      "41": 10978,
+      "42": 14564,
+      "43": 5998,
+      "44": 7759,
+      "45": 3653,
+      "46": 4177,
+      "47": 2494,
+      "48": 3479,
+      "49": 2127,
+      "5": 962309,
+      "50": 2891,
+      "51": 1825,
+      "52": 2717,
+      "53": 1760,
+      "54": 2433,
+      "55": 1706,
+      "56": 2539,
+      "57": 1742,
+      "58": 2295,
+      "59": 1751,
+      "6": 5372843,
+      "60": 2510,
+      "61": 1625,
+      "62": 2261,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2164345,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6666052,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2004790,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59411,
+      "7": 33632144,
+      "9": 136346
+    },
+    "connectivity_max": 149100186,
+    "connectivity_min": 0,
+    "n_cells": 33827901,
+    "n_connectivity_values": 365845039,
+    "n_fan_triangles": 298189237,
+    "n_points": 149100187
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.681225582186389e-11,
+    "float64_area_closure_relative": 1.781852536596871e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 298189237,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946949.323262169,
+    "surface_area_float64_in2": 1946949.32335331,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946949.3233532754,
+    "zero_area_triangles": 244680,
+    "zero_weight_points": 6257
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC075_AoA_6.json b/surface_dual_areas/cases/geo_LHC075_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..678022cc3f2cde9da06b85e63ad19106bd470e6f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC075_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC075_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC075_AoA_6/boundary_dual_area_geo_LHC075_AoA_6.npy",
+    "sha256": "ee5816d196892b66537e7604c43f9b23619ae7cc6191952c648dae3b8870ba66",
+    "shape": [
+      138442022
+    ],
+    "size_bytes": 553768216
+  },
+  "runtime": {
+    "accumulation_seconds": 10.942818528972566,
+    "completed_at_utc": "2026-08-07T08:04:48.092888Z",
+    "elapsed_seconds": 53.19004611601122,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2170752461533993,
+    "geometry_read_seconds": 33.87027029087767,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:03:54.902735Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC075_AoA_6/boundary_geo_LHC075_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC075_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624538000000000,
+    "extracted_vtu_size_bytes": 21264771797,
+    "geometry_sha256": "76194f41b5a6073aa8b560670776509095e08abfd9c285ab2c2e7158f461b5c7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3532329,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1146051,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2528172,
+      "13": 774575,
+      "14": 1405866,
+      "15": 468029,
+      "16": 947685,
+      "17": 363740,
+      "18": 748383,
+      "19": 305841,
+      "20": 661962,
+      "21": 225938,
+      "22": 346037,
+      "23": 122767,
+      "24": 200530,
+      "25": 69206,
+      "26": 94574,
+      "27": 52140,
+      "28": 124314,
+      "29": 53036,
+      "3": 51407,
+      "30": 114556,
+      "31": 49252,
+      "32": 108072,
+      "33": 38352,
+      "34": 65795,
+      "35": 27564,
+      "36": 62937,
+      "37": 22922,
+      "38": 39353,
+      "39": 16592,
+      "4": 116555,
+      "40": 30320,
+      "41": 11059,
+      "42": 14622,
+      "43": 5846,
+      "44": 7697,
+      "45": 3728,
+      "46": 4294,
+      "47": 2525,
+      "48": 3546,
+      "49": 2133,
+      "5": 944366,
+      "50": 2978,
+      "51": 1853,
+      "52": 2753,
+      "53": 1781,
+      "54": 2460,
+      "55": 1725,
+      "56": 2547,
+      "57": 1764,
+      "58": 2289,
+      "59": 1724,
+      "6": 5334494,
+      "60": 2504,
+      "61": 1658,
+      "62": 2231,
+      "63": 1638,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2010806,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5975364,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1737216,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51407,
+      "7": 30849574,
+      "9": 116555
+    },
+    "connectivity_max": 138442021,
+    "connectivity_min": 0,
+    "n_cells": 31017536,
+    "n_connectivity_values": 338907983,
+    "n_fan_triangles": 276872911,
+    "n_points": 138442022
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.530564718352451e-11,
+    "float64_area_closure_relative": 2.93153448176846e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276872911,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937916.0437255774,
+    "surface_area_float64_in2": 1937916.0437939968,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937916.04379394,
+    "zero_area_triangles": 232623,
+    "zero_weight_points": 5333
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC076_AoA_12.json b/surface_dual_areas/cases/geo_LHC076_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..9263ffecdd82ea7e1e5fd7a1fa24cab36dbacf02
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC076_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC076_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC076_AoA_12/boundary_dual_area_geo_LHC076_AoA_12.npy",
+    "sha256": "d9e69d26b13e1494f410504d6eb0af724f56713c544118e72a1928a262888e5e",
+    "shape": [
+      145056062
+    ],
+    "size_bytes": 580224376
+  },
+  "runtime": {
+    "accumulation_seconds": 11.24329199292697,
+    "completed_at_utc": "2026-08-07T08:04:56.755845Z",
+    "elapsed_seconds": 23.164542671991512,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.230465996079147,
+    "geometry_read_seconds": 3.070385670987889,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:04:33.591219Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC076_AoA_12/boundary_geo_LHC076_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC076_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624495000000000,
+    "extracted_vtu_size_bytes": 22282176204,
+    "geometry_sha256": "956eec411b8b8f1ddc0030299f93171b654cd86e3e3f7a56d63863cb12217085",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3793534,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1260523,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2788288,
+      "13": 855088,
+      "14": 1591963,
+      "15": 511058,
+      "16": 1004576,
+      "17": 368118,
+      "18": 739330,
+      "19": 295720,
+      "20": 662392,
+      "21": 218175,
+      "22": 351620,
+      "23": 119753,
+      "24": 201878,
+      "25": 69518,
+      "26": 91450,
+      "27": 51473,
+      "28": 123354,
+      "29": 52844,
+      "3": 59695,
+      "30": 115052,
+      "31": 49412,
+      "32": 108938,
+      "33": 38883,
+      "34": 67281,
+      "35": 27977,
+      "36": 62503,
+      "37": 22956,
+      "38": 38807,
+      "39": 16335,
+      "4": 134082,
+      "40": 29554,
+      "41": 10678,
+      "42": 14378,
+      "43": 5911,
+      "44": 7614,
+      "45": 3673,
+      "46": 4164,
+      "47": 2492,
+      "48": 3489,
+      "49": 2091,
+      "5": 954973,
+      "50": 2839,
+      "51": 1799,
+      "52": 2689,
+      "53": 1717,
+      "54": 2390,
+      "55": 1659,
+      "56": 2498,
+      "57": 1734,
+      "58": 2277,
+      "59": 1740,
+      "6": 5239335,
+      "60": 2510,
+      "61": 1625,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2114030,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6322976,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1906255,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59695,
+      "7": 32364814,
+      "9": 134082
+    },
+    "connectivity_max": 145056061,
+    "connectivity_min": 0,
+    "n_cells": 32558591,
+    "n_connectivity_values": 355218187,
+    "n_fan_triangles": 290101005,
+    "n_points": 145056062
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.4734464812648234e-11,
+    "float64_area_closure_relative": 5.4071196748549945e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290101005,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946312.5888676303,
+    "surface_area_float64_in2": 1946312.5889546976,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946312.5889548028,
+    "zero_area_triangles": 238975,
+    "zero_weight_points": 5839
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC077_AoA_22.json b/surface_dual_areas/cases/geo_LHC077_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..f97988084b45ce76dc0852f0782111a3e1c17952
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC077_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC077_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC077_AoA_22/boundary_dual_area_geo_LHC077_AoA_22.npy",
+    "sha256": "eec544745127264faab8406709f80870261c6f158f639856baaf9b05905ef8d6",
+    "shape": [
+      147295957
+    ],
+    "size_bytes": 589183956
+  },
+  "runtime": {
+    "accumulation_seconds": 11.21252498589456,
+    "completed_at_utc": "2026-08-07T07:39:58.074735Z",
+    "elapsed_seconds": 21.05864900886081,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.123952314024791,
+    "geometry_read_seconds": 1.963525319006294,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:39:37.015974Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC077_AoA_22/boundary_geo_LHC077_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC077_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624459000000000,
+    "extracted_vtu_size_bytes": 22637386765,
+    "geometry_sha256": "7f8edc65aebc0a98a0300ca73ca8eaa91e9257a7d41caff6b024ee030246e627",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4371983,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1418077,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2783458,
+      "13": 840554,
+      "14": 1251996,
+      "15": 439499,
+      "16": 885824,
+      "17": 347686,
+      "18": 738214,
+      "19": 301040,
+      "20": 665548,
+      "21": 227137,
+      "22": 372490,
+      "23": 127976,
+      "24": 216529,
+      "25": 74841,
+      "26": 96209,
+      "27": 53049,
+      "28": 124787,
+      "29": 52892,
+      "3": 58434,
+      "30": 114479,
+      "31": 49036,
+      "32": 107468,
+      "33": 38592,
+      "34": 66331,
+      "35": 27679,
+      "36": 63054,
+      "37": 23027,
+      "38": 39649,
+      "39": 16755,
+      "4": 134137,
+      "40": 30438,
+      "41": 11091,
+      "42": 14573,
+      "43": 5995,
+      "44": 7926,
+      "45": 3756,
+      "46": 4247,
+      "47": 2543,
+      "48": 3596,
+      "49": 2195,
+      "5": 954109,
+      "50": 2958,
+      "51": 1851,
+      "52": 2764,
+      "53": 1774,
+      "54": 2404,
+      "55": 1729,
+      "56": 2538,
+      "57": 1762,
+      "58": 2279,
+      "59": 1692,
+      "6": 5410633,
+      "60": 2465,
+      "61": 1653,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2144522,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6690297,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2047577,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58434,
+      "7": 33314265,
+      "9": 134137
+    },
+    "connectivity_max": 147295956,
+    "connectivity_min": 0,
+    "n_cells": 33506836,
+    "n_connectivity_values": 361594464,
+    "n_fan_triangles": 294580792,
+    "n_points": 147295957
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.12664054468428e-11,
+    "float64_area_closure_relative": 2.988327017266952e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294580792,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947834.376048329,
+    "surface_area_float64_in2": 1947834.3761287092,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947834.3761287674,
+    "zero_area_triangles": 236856,
+    "zero_weight_points": 5808
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC077_AoA_6.json b/surface_dual_areas/cases/geo_LHC077_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..08e7c85dc14a403dc5ebcbf5e118c04717b51b59
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC077_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC077_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC077_AoA_6/boundary_dual_area_geo_LHC077_AoA_6.npy",
+    "sha256": "e268dfd0b45a81fdd99117e808059b366fb95700bdc177d1517c1742254ab5b7",
+    "shape": [
+      138631568
+    ],
+    "size_bytes": 554526400
+  },
+  "runtime": {
+    "accumulation_seconds": 10.696293555898592,
+    "completed_at_utc": "2026-08-07T08:05:27.723128Z",
+    "elapsed_seconds": 21.42651847982779,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2224417300894856,
+    "geometry_read_seconds": 2.7180268238298595,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:05:06.296521Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC077_AoA_6/boundary_geo_LHC077_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC077_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624447000000000,
+    "extracted_vtu_size_bytes": 21287233918,
+    "geometry_sha256": "f15b4373357c1aa321f53519f7577bf5589ec48ff6322b87d10d854291e78a25",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3187954,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1087559,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2317636,
+      "13": 832471,
+      "14": 1673199,
+      "15": 558753,
+      "16": 1006975,
+      "17": 380747,
+      "18": 739876,
+      "19": 299890,
+      "20": 659320,
+      "21": 222276,
+      "22": 365637,
+      "23": 123645,
+      "24": 211055,
+      "25": 72174,
+      "26": 95055,
+      "27": 52485,
+      "28": 124682,
+      "29": 52839,
+      "3": 55619,
+      "30": 114477,
+      "31": 49036,
+      "32": 107471,
+      "33": 38597,
+      "34": 66323,
+      "35": 27679,
+      "36": 63055,
+      "37": 23028,
+      "38": 39644,
+      "39": 16750,
+      "4": 126859,
+      "40": 30440,
+      "41": 11090,
+      "42": 14574,
+      "43": 5996,
+      "44": 7926,
+      "45": 3756,
+      "46": 4247,
+      "47": 2543,
+      "48": 3596,
+      "49": 2195,
+      "5": 932749,
+      "50": 2958,
+      "51": 1851,
+      "52": 2764,
+      "53": 1774,
+      "54": 2404,
+      "55": 1729,
+      "56": 2538,
+      "57": 1762,
+      "58": 2279,
+      "59": 1692,
+      "6": 5335703,
+      "60": 2465,
+      "61": 1653,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1977358,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5954709,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1669349,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 55619,
+      "7": 30611427,
+      "9": 126859
+    },
+    "connectivity_max": 138631567,
+    "connectivity_min": 0,
+    "n_cells": 30793905,
+    "n_connectivity_values": 338839824,
+    "n_fan_triangles": 277252014,
+    "n_points": 138631568
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.093933065800967e-11,
+    "float64_area_closure_relative": 1.4702557332201993e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277252014,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947835.9118878823,
+    "surface_area_float64_in2": 1947835.9119676254,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947835.911967654,
+    "zero_area_triangles": 224933,
+    "zero_weight_points": 4989
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC078_AoA_18.json b/surface_dual_areas/cases/geo_LHC078_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..4f1e8f219b5ec01f3145897766fc3151de3cb2ae
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC078_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC078_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC078_AoA_18/boundary_dual_area_geo_LHC078_AoA_18.npy",
+    "sha256": "cbf1b2705ff163597dafab481ff7962823735987ec56367969cfa5d28d92238e",
+    "shape": [
+      148107267
+    ],
+    "size_bytes": 592429196
+  },
+  "runtime": {
+    "accumulation_seconds": 11.378155556041747,
+    "completed_at_utc": "2026-08-07T08:06:34.845498Z",
+    "elapsed_seconds": 23.17896685190499,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6093367589637637,
+    "geometry_read_seconds": 3.1330575360916555,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:06:11.666442Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC078_AoA_18/boundary_geo_LHC078_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC078_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624550000000000,
+    "extracted_vtu_size_bytes": 22758899595,
+    "geometry_sha256": "b260f040c6006f7bdc05a39f2e1f4dfd8314e70c25b5e2554ccc5524e70b8ea1",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4431211,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1406361,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2987054,
+      "13": 852281,
+      "14": 1285548,
+      "15": 446880,
+      "16": 889386,
+      "17": 342825,
+      "18": 736152,
+      "19": 294489,
+      "20": 670107,
+      "21": 224100,
+      "22": 378660,
+      "23": 126156,
+      "24": 213588,
+      "25": 72502,
+      "26": 92969,
+      "27": 52143,
+      "28": 123747,
+      "29": 52848,
+      "3": 60265,
+      "30": 114552,
+      "31": 49133,
+      "32": 108554,
+      "33": 38689,
+      "34": 67201,
+      "35": 28078,
+      "36": 63277,
+      "37": 23029,
+      "38": 39051,
+      "39": 16445,
+      "4": 139105,
+      "40": 29475,
+      "41": 10742,
+      "42": 14182,
+      "43": 5790,
+      "44": 7750,
+      "45": 3706,
+      "46": 4240,
+      "47": 2536,
+      "48": 3565,
+      "49": 2220,
+      "5": 941333,
+      "50": 2913,
+      "51": 1852,
+      "52": 2723,
+      "53": 1754,
+      "54": 2397,
+      "55": 1735,
+      "56": 2536,
+      "57": 1747,
+      "58": 2268,
+      "59": 1691,
+      "6": 5260722,
+      "60": 2462,
+      "61": 1653,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1377,
+      "66": 1811,
+      "67": 1113,
+      "68": 1527,
+      "69": 920,
+      "7": 2109020,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6675826,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2022132,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60265,
+      "7": 33365024,
+      "9": 139105
+    },
+    "connectivity_max": 148107266,
+    "connectivity_min": 0,
+    "n_cells": 33564394,
+    "n_connectivity_values": 363332200,
+    "n_fan_triangles": 296203412,
+    "n_points": 148107267
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.706583446081255e-11,
+    "float64_area_closure_relative": 3.370784028645967e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296203412,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947862.602586623,
+    "surface_area_float64_in2": 1947862.6026588222,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947862.6026588879,
+    "zero_area_triangles": 241376,
+    "zero_weight_points": 6128
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC079_AoA_14.json b/surface_dual_areas/cases/geo_LHC079_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..c9c446a9f1987b9184e4b36c204ac5dc331bfb34
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC079_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC079_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC079_AoA_14/boundary_dual_area_geo_LHC079_AoA_14.npy",
+    "sha256": "5e7b471d21f7275b248ce23ae81bebc7e546e141edc1dd3f1ba3806002be9b2d",
+    "shape": [
+      137563094
+    ],
+    "size_bytes": 550252504
+  },
+  "runtime": {
+    "accumulation_seconds": 12.412338786991313,
+    "completed_at_utc": "2026-08-07T08:07:19.143750Z",
+    "elapsed_seconds": 68.6784602298867,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.41567364288494,
+    "geometry_read_seconds": 1.9882536770310253,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:06:10.465188Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC079_AoA_14/boundary_geo_LHC079_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC079_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624428000000000,
+    "extracted_vtu_size_bytes": 21127065810,
+    "geometry_sha256": "378b25ab54edd4db296ffa33d3abb8519af21aab323ecc22cf143c42979fa141",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3710371,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1134275,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2479454,
+      "13": 739714,
+      "14": 1300651,
+      "15": 445183,
+      "16": 918038,
+      "17": 351700,
+      "18": 762936,
+      "19": 306882,
+      "20": 678382,
+      "21": 229880,
+      "22": 370609,
+      "23": 127615,
+      "24": 208191,
+      "25": 70514,
+      "26": 94665,
+      "27": 52317,
+      "28": 124776,
+      "29": 53275,
+      "3": 51415,
+      "30": 114599,
+      "31": 49214,
+      "32": 108409,
+      "33": 39075,
+      "34": 67053,
+      "35": 28276,
+      "36": 63016,
+      "37": 22926,
+      "38": 38273,
+      "39": 15876,
+      "4": 113539,
+      "40": 29094,
+      "41": 10491,
+      "42": 13938,
+      "43": 5761,
+      "44": 7736,
+      "45": 3627,
+      "46": 4214,
+      "47": 2524,
+      "48": 3565,
+      "49": 2214,
+      "5": 937881,
+      "50": 2918,
+      "51": 1813,
+      "52": 2701,
+      "53": 1700,
+      "54": 2267,
+      "55": 1641,
+      "56": 2477,
+      "57": 1728,
+      "58": 2256,
+      "59": 1681,
+      "6": 5174930,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2003867,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5858043,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1739228,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51415,
+      "7": 30547595,
+      "9": 113539
+    },
+    "connectivity_max": 137563093,
+    "connectivity_min": 0,
+    "n_cells": 30712549,
+    "n_connectivity_values": 336540157,
+    "n_fan_triangles": 275115059,
+    "n_points": 137563094
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.66340164800465e-11,
+    "float64_area_closure_relative": 3.7057409414230516e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275115059,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935155.1923439768,
+    "surface_area_float64_in2": 1935155.1924148693,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935155.192414941,
+    "zero_area_triangles": 235646,
+    "zero_weight_points": 5402
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC080_AoA_16.json b/surface_dual_areas/cases/geo_LHC080_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..33c718fe16fcd1683ea49045198e796bc075c396
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC080_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC080_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC080_AoA_16/boundary_dual_area_geo_LHC080_AoA_16.npy",
+    "sha256": "08f7fc8bbb42260c2fac332cf9a2bb1ce556db79930a433c17571d92073c4458",
+    "shape": [
+      149552144
+    ],
+    "size_bytes": 598208704
+  },
+  "runtime": {
+    "accumulation_seconds": 11.42949237395078,
+    "completed_at_utc": "2026-08-07T07:42:08.965484Z",
+    "elapsed_seconds": 22.567385334987193,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3487075320445,
+    "geometry_read_seconds": 2.369975306093693,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:41:46.398021Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC080_AoA_16/boundary_geo_LHC080_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC080_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624663000000000,
+    "extracted_vtu_size_bytes": 22986082640,
+    "geometry_sha256": "55600315b7434424e38bc833fd87584bd4f2860445471d25ed6de93bdc75719a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4571329,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1447345,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3029708,
+      "13": 852827,
+      "14": 1298401,
+      "15": 442027,
+      "16": 895511,
+      "17": 351611,
+      "18": 739076,
+      "19": 301219,
+      "20": 662886,
+      "21": 220631,
+      "22": 347421,
+      "23": 119559,
+      "24": 204309,
+      "25": 70676,
+      "26": 92585,
+      "27": 51982,
+      "28": 123780,
+      "29": 52859,
+      "3": 59289,
+      "30": 115081,
+      "31": 49502,
+      "32": 109705,
+      "33": 38994,
+      "34": 66609,
+      "35": 27792,
+      "36": 61488,
+      "37": 22865,
+      "38": 38759,
+      "39": 16377,
+      "4": 134020,
+      "40": 29892,
+      "41": 10916,
+      "42": 14647,
+      "43": 5941,
+      "44": 7741,
+      "45": 3642,
+      "46": 4143,
+      "47": 2453,
+      "48": 3509,
+      "49": 2111,
+      "5": 952796,
+      "50": 2897,
+      "51": 1845,
+      "52": 2808,
+      "53": 1780,
+      "54": 2460,
+      "55": 1741,
+      "56": 2547,
+      "57": 1758,
+      "58": 2282,
+      "59": 1750,
+      "6": 5416261,
+      "60": 2514,
+      "61": 1627,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2126151,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6800237,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2056445,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59289,
+      "7": 33904734,
+      "9": 134020
+    },
+    "connectivity_max": 149552143,
+    "connectivity_min": 0,
+    "n_cells": 34098043,
+    "n_connectivity_values": 367289255,
+    "n_fan_triangles": 299093169,
+    "n_points": 149552144
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.775163262860163e-11,
+    "float64_area_closure_relative": 1.3519173013947158e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 299093169,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946114.803379708,
+    "surface_area_float64_in2": 1946114.803453177,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946114.8034532033,
+    "zero_area_triangles": 244397,
+    "zero_weight_points": 6153
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC081_AoA_10.json b/surface_dual_areas/cases/geo_LHC081_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7c7811021714c48a24f7428db3e26f3758afb44
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC081_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC081_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC081_AoA_10/boundary_dual_area_geo_LHC081_AoA_10.npy",
+    "sha256": "f258f74ada5bb57b58fc34f2130e525bed377249b6bd5a5e94d50cb3d764788c",
+    "shape": [
+      148228314
+    ],
+    "size_bytes": 592913384
+  },
+  "runtime": {
+    "accumulation_seconds": 11.417984755942598,
+    "completed_at_utc": "2026-08-07T08:05:29.781056Z",
+    "elapsed_seconds": 23.4849987749476,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4727506309282035,
+    "geometry_read_seconds": 3.31363452388905,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:05:06.295981Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC081_AoA_10/boundary_geo_LHC081_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC081_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624448000000000,
+    "extracted_vtu_size_bytes": 22780757146,
+    "geometry_sha256": "2b3f91c377456d7e4e0fd63e870eedae087d3c6be0b7dce959b4742ce0e18d73",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4348357,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1384061,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2961207,
+      "13": 843468,
+      "14": 1347217,
+      "15": 453602,
+      "16": 907323,
+      "17": 351996,
+      "18": 730105,
+      "19": 298443,
+      "20": 659390,
+      "21": 221783,
+      "22": 357502,
+      "23": 122592,
+      "24": 204995,
+      "25": 71566,
+      "26": 93857,
+      "27": 52384,
+      "28": 123346,
+      "29": 52767,
+      "3": 58256,
+      "30": 114331,
+      "31": 48884,
+      "32": 107824,
+      "33": 38422,
+      "34": 66381,
+      "35": 27758,
+      "36": 63763,
+      "37": 23157,
+      "38": 39799,
+      "39": 16618,
+      "4": 133237,
+      "40": 30558,
+      "41": 11177,
+      "42": 14622,
+      "43": 5995,
+      "44": 7863,
+      "45": 3753,
+      "46": 4253,
+      "47": 2509,
+      "48": 3588,
+      "49": 2201,
+      "5": 947964,
+      "50": 2878,
+      "51": 1893,
+      "52": 2780,
+      "53": 1759,
+      "54": 2435,
+      "55": 1756,
+      "56": 2528,
+      "57": 1772,
+      "58": 2274,
+      "59": 1690,
+      "6": 5435281,
+      "60": 2464,
+      "61": 1653,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2107623,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6782371,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1993031,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58256,
+      "7": 33530608,
+      "9": 133237
+    },
+    "connectivity_max": 148228313,
+    "connectivity_min": 0,
+    "n_cells": 33722101,
+    "n_connectivity_values": 363889698,
+    "n_fan_triangles": 296445496,
+    "n_points": 148228314
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.737575574184792e-11,
+    "float64_area_closure_relative": 1.7335804664376168e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296445496,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947440.2245616298,
+    "surface_area_float64_in2": 1947440.2246344169,
+    "weight_max_in2": 1.101064467658409,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947440.224634383,
+    "zero_area_triangles": 239171,
+    "zero_weight_points": 5944
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC081_AoA_18.json b/surface_dual_areas/cases/geo_LHC081_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..cd7471ce094ac2724a57f505f090d4c7c179bac6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC081_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC081_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC081_AoA_18/boundary_dual_area_geo_LHC081_AoA_18.npy",
+    "sha256": "9738167193e7dd7ba6ca63731e6a45c40e4681a5c8ecf3713ac53c6fdfe013f2",
+    "shape": [
+      149435195
+    ],
+    "size_bytes": 597740908
+  },
+  "runtime": {
+    "accumulation_seconds": 11.360997342970222,
+    "completed_at_utc": "2026-08-07T07:42:31.800876Z",
+    "elapsed_seconds": 21.844752168050036,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.322512656915933,
+    "geometry_read_seconds": 2.0715298070572317,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:42:09.956035Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC081_AoA_18/boundary_geo_LHC081_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC081_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624580000000000,
+    "extracted_vtu_size_bytes": 22968344051,
+    "geometry_sha256": "5f0b37f6acb6746af10e8a5b27092a51d1d902676b421dd07a3c501f5e1e1461",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4696795,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1466608,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3008278,
+      "13": 838738,
+      "14": 1201281,
+      "15": 420682,
+      "16": 854504,
+      "17": 342798,
+      "18": 742390,
+      "19": 302745,
+      "20": 671685,
+      "21": 225373,
+      "22": 363276,
+      "23": 124408,
+      "24": 207021,
+      "25": 72451,
+      "26": 94246,
+      "27": 52597,
+      "28": 123335,
+      "29": 52804,
+      "3": 60164,
+      "30": 114326,
+      "31": 48888,
+      "32": 107805,
+      "33": 38432,
+      "34": 66383,
+      "35": 27769,
+      "36": 63766,
+      "37": 23160,
+      "38": 39808,
+      "39": 16621,
+      "4": 137244,
+      "40": 30559,
+      "41": 11179,
+      "42": 14622,
+      "43": 5995,
+      "44": 7863,
+      "45": 3753,
+      "46": 4253,
+      "47": 2509,
+      "48": 3588,
+      "49": 2201,
+      "5": 942114,
+      "50": 2878,
+      "51": 1893,
+      "52": 2780,
+      "53": 1759,
+      "54": 2435,
+      "55": 1756,
+      "56": 2528,
+      "57": 1772,
+      "58": 2274,
+      "59": 1690,
+      "6": 5353160,
+      "60": 2464,
+      "61": 1653,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2119539,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6848210,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2079995,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60164,
+      "7": 33883434,
+      "9": 137244
+    },
+    "connectivity_max": 149435194,
+    "connectivity_min": 0,
+    "n_cells": 34080842,
+    "n_connectivity_values": 367020941,
+    "n_fan_triangles": 298859257,
+    "n_points": 149435195
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.778569518485846e-11,
+    "float64_area_closure_relative": 1.1597048644446145e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 298859257,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947441.3815094056,
+    "surface_area_float64_in2": 1947441.381582991,
+    "weight_max_in2": 1.101064467658409,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947441.3815830136,
+    "zero_area_triangles": 241356,
+    "zero_weight_points": 6121
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC082_AoA_12.json b/surface_dual_areas/cases/geo_LHC082_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..566103090a42e73d42477740dadf1bfe5472f244
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC082_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC082_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC082_AoA_12/boundary_dual_area_geo_LHC082_AoA_12.npy",
+    "sha256": "951c2d5e31817c9eb5d8ec4440b7a9d53e65c6bd1d960b0ebdfe91c5db6a72dc",
+    "shape": [
+      148230472
+    ],
+    "size_bytes": 592922016
+  },
+  "runtime": {
+    "accumulation_seconds": 11.42674365406856,
+    "completed_at_utc": "2026-08-07T08:09:26.226512Z",
+    "elapsed_seconds": 53.7585080571007,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.467686998192221,
+    "geometry_read_seconds": 33.85455113113858,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:08:32.467912Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC082_AoA_12/boundary_geo_LHC082_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC082_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624530000000000,
+    "extracted_vtu_size_bytes": 22777128260,
+    "geometry_sha256": "3fada56c6b5b4f2bef747e64df014b966609d4123069142c47d9343d54533984",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4344189,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1335613,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3023934,
+      "13": 830696,
+      "14": 1427245,
+      "15": 461660,
+      "16": 959556,
+      "17": 357899,
+      "18": 747420,
+      "19": 301289,
+      "20": 664297,
+      "21": 221672,
+      "22": 346771,
+      "23": 118995,
+      "24": 195418,
+      "25": 68966,
+      "26": 90101,
+      "27": 51805,
+      "28": 122855,
+      "29": 52798,
+      "3": 58024,
+      "30": 114391,
+      "31": 49293,
+      "32": 108794,
+      "33": 38759,
+      "34": 66703,
+      "35": 28087,
+      "36": 63111,
+      "37": 23149,
+      "38": 39033,
+      "39": 16348,
+      "4": 130241,
+      "40": 29363,
+      "41": 10700,
+      "42": 14063,
+      "43": 5714,
+      "44": 7540,
+      "45": 3639,
+      "46": 4220,
+      "47": 2534,
+      "48": 3524,
+      "49": 2114,
+      "5": 954746,
+      "50": 2975,
+      "51": 1864,
+      "52": 2792,
+      "53": 1761,
+      "54": 2379,
+      "55": 1707,
+      "56": 2528,
+      "57": 1726,
+      "58": 2289,
+      "59": 1722,
+      "6": 5293895,
+      "60": 2506,
+      "61": 1656,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2154529,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6570676,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2002946,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58024,
+      "7": 33375902,
+      "9": 130241
+    },
+    "connectivity_max": 148230471,
+    "connectivity_min": 0,
+    "n_cells": 33564167,
+    "n_connectivity_values": 363578156,
+    "n_fan_triangles": 296449822,
+    "n_points": 148230472
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.8441994951743323e-11,
+    "float64_area_closure_relative": 1.2925581189429362e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296449822,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945421.9616999212,
+    "surface_area_float64_in2": 1945421.961774707,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945421.961774682,
+    "zero_area_triangles": 245173,
+    "zero_weight_points": 6115
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC082_AoA_6.json b/surface_dual_areas/cases/geo_LHC082_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d60aa10178ca0497031da1d5dd9e7a8f55c44ee
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC082_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC082_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC082_AoA_6/boundary_dual_area_geo_LHC082_AoA_6.npy",
+    "sha256": "47b8f8d6821ec993324a4922e20bf19424eed5fd49f9bb88bd3f966cbe0725d1",
+    "shape": [
+      138751740
+    ],
+    "size_bytes": 555007088
+  },
+  "runtime": {
+    "accumulation_seconds": 10.803722118027508,
+    "completed_at_utc": "2026-08-07T08:08:54.165657Z",
+    "elapsed_seconds": 21.49193930486217,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2579439119435847,
+    "geometry_read_seconds": 2.6981513230130076,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:08:32.673608Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC082_AoA_6/boundary_geo_LHC082_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC082_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624425000000000,
+    "extracted_vtu_size_bytes": 21304289974,
+    "geometry_sha256": "92bf5930415b6109af48c1c148bb8bae4040a9b0f55a9f36995728de2dfb49aa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3055604,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 947039,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2360652,
+      "13": 776477,
+      "14": 1811429,
+      "15": 571728,
+      "16": 1097847,
+      "17": 391932,
+      "18": 758318,
+      "19": 304476,
+      "20": 666967,
+      "21": 222554,
+      "22": 349078,
+      "23": 119874,
+      "24": 196502,
+      "25": 69348,
+      "26": 90286,
+      "27": 51883,
+      "28": 122908,
+      "29": 52811,
+      "3": 54554,
+      "30": 114397,
+      "31": 49288,
+      "32": 108792,
+      "33": 38771,
+      "34": 66717,
+      "35": 28075,
+      "36": 63119,
+      "37": 23154,
+      "38": 39033,
+      "39": 16348,
+      "4": 127444,
+      "40": 29360,
+      "41": 10701,
+      "42": 14062,
+      "43": 5713,
+      "44": 7541,
+      "45": 3640,
+      "46": 4220,
+      "47": 2533,
+      "48": 3523,
+      "49": 2114,
+      "5": 953162,
+      "50": 2978,
+      "51": 1864,
+      "52": 2791,
+      "53": 1761,
+      "54": 2379,
+      "55": 1707,
+      "56": 2528,
+      "57": 1726,
+      "58": 2289,
+      "59": 1722,
+      "6": 5306146,
+      "60": 2506,
+      "61": 1656,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2020916,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5993851,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1614988,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54554,
+      "7": 30582731,
+      "9": 127444
+    },
+    "connectivity_max": 138751739,
+    "connectivity_min": 0,
+    "n_cells": 30764729,
+    "n_connectivity_values": 339021816,
+    "n_fan_triangles": 277492358,
+    "n_points": 138751740
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.042889452411113e-11,
+    "float64_area_closure_relative": 1.9268666888831995e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277492358,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945424.343210999,
+    "surface_area_float64_in2": 1945424.3432896503,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945424.3432896878,
+    "zero_area_triangles": 228225,
+    "zero_weight_points": 5084
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC083_AoA_10.json b/surface_dual_areas/cases/geo_LHC083_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..1c00b5fdb588131222f656359d65c521649eae44
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC083_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC083_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC083_AoA_10/boundary_dual_area_geo_LHC083_AoA_10.npy",
+    "sha256": "e1212e317b861191942e657651c79ec990e9a31fb0c7030bf34c57facd3a92c7",
+    "shape": [
+      148397306
+    ],
+    "size_bytes": 593589352
+  },
+  "runtime": {
+    "accumulation_seconds": 11.425530730048195,
+    "completed_at_utc": "2026-08-07T08:09:51.073475Z",
+    "elapsed_seconds": 55.88097510393709,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.364423234015703,
+    "geometry_read_seconds": 36.14559497800656,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:08:55.192409Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC083_AoA_10/boundary_geo_LHC083_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC083_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624544000000000,
+    "extracted_vtu_size_bytes": 22806534687,
+    "geometry_sha256": "5396862eff32012c7120805abf30bdbc9f3ecfe3cd5374d60432bb4906155de4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4366444,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1388871,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2981849,
+      "13": 846984,
+      "14": 1356393,
+      "15": 455512,
+      "16": 918806,
+      "17": 353819,
+      "18": 728449,
+      "19": 296043,
+      "20": 654833,
+      "21": 219471,
+      "22": 354434,
+      "23": 121454,
+      "24": 206865,
+      "25": 72037,
+      "26": 93192,
+      "27": 52529,
+      "28": 124528,
+      "29": 53070,
+      "3": 58309,
+      "30": 114058,
+      "31": 48840,
+      "32": 106755,
+      "33": 38045,
+      "34": 65347,
+      "35": 27510,
+      "36": 62634,
+      "37": 22922,
+      "38": 39744,
+      "39": 16584,
+      "4": 133443,
+      "40": 30857,
+      "41": 11198,
+      "42": 14728,
+      "43": 6037,
+      "44": 7971,
+      "45": 3783,
+      "46": 4292,
+      "47": 2497,
+      "48": 3581,
+      "49": 2199,
+      "5": 962690,
+      "50": 2968,
+      "51": 1842,
+      "52": 2748,
+      "53": 1767,
+      "54": 2442,
+      "55": 1724,
+      "56": 2549,
+      "57": 1789,
+      "58": 2273,
+      "59": 1695,
+      "6": 5383195,
+      "60": 2467,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2133534,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6751491,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2009990,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58309,
+      "7": 33561018,
+      "9": 133443
+    },
+    "connectivity_max": 148397305,
+    "connectivity_min": 0,
+    "n_cells": 33752770,
+    "n_connectivity_values": 364289020,
+    "n_fan_triangles": 296783480,
+    "n_points": 148397306
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.501793971297485e-11,
+    "float64_area_closure_relative": 4.660407001040868e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296783480,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948412.4670130524,
+    "surface_area_float64_in2": 1948412.4670812818,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948412.467081291,
+    "zero_area_triangles": 239873,
+    "zero_weight_points": 5888
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC084_AoA_22.json b/surface_dual_areas/cases/geo_LHC084_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..279692e09720a634994755d8ea834858c304a776
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC084_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC084_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC084_AoA_22/boundary_dual_area_geo_LHC084_AoA_22.npy",
+    "sha256": "6f11effec5bf5e6b2c2791ec4e654d0a8fd81e8e7e6c90cec0c905b3a497f28d",
+    "shape": [
+      137644786
+    ],
+    "size_bytes": 550579272
+  },
+  "runtime": {
+    "accumulation_seconds": 10.902575897984207,
+    "completed_at_utc": "2026-08-07T08:08:55.597371Z",
+    "elapsed_seconds": 22.710399201139808,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3122541150078177,
+    "geometry_read_seconds": 3.778316328069195,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:08:32.886855Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC084_AoA_22/boundary_geo_LHC084_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC084_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624514000000000,
+    "extracted_vtu_size_bytes": 21140827601,
+    "geometry_sha256": "514b53315da47b125c8899a0e64a980886e0f1dfd954af1bacb40eb7f3740cec",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3650273,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1176846,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2455819,
+      "13": 750073,
+      "14": 1248039,
+      "15": 440815,
+      "16": 907018,
+      "17": 353664,
+      "18": 752051,
+      "19": 304028,
+      "20": 671811,
+      "21": 227780,
+      "22": 375315,
+      "23": 127068,
+      "24": 222257,
+      "25": 72625,
+      "26": 98762,
+      "27": 52683,
+      "28": 125444,
+      "29": 53247,
+      "3": 49694,
+      "30": 115091,
+      "31": 49273,
+      "32": 108074,
+      "33": 38669,
+      "34": 66032,
+      "35": 27879,
+      "36": 62973,
+      "37": 23104,
+      "38": 39115,
+      "39": 16357,
+      "4": 114394,
+      "40": 29545,
+      "41": 10823,
+      "42": 14310,
+      "43": 5784,
+      "44": 7632,
+      "45": 3688,
+      "46": 4312,
+      "47": 2514,
+      "48": 3515,
+      "49": 2139,
+      "5": 941335,
+      "50": 2951,
+      "51": 1837,
+      "52": 2766,
+      "53": 1789,
+      "54": 2453,
+      "55": 1742,
+      "56": 2558,
+      "57": 1756,
+      "58": 2285,
+      "59": 1723,
+      "6": 5193865,
+      "60": 2504,
+      "61": 1657,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2035614,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5904962,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1798124,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49694,
+      "7": 30615316,
+      "9": 114394
+    },
+    "connectivity_max": 137644785,
+    "connectivity_min": 0,
+    "n_cells": 30779404,
+    "n_connectivity_values": 336837251,
+    "n_fan_triangles": 275278443,
+    "n_points": 137644786
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.593969800079922e-11,
+    "float64_area_closure_relative": 4.651555670630611e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275278443,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937103.744876681,
+    "surface_area_float64_in2": 1937103.7449462998,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937103.74494639,
+    "zero_area_triangles": 233997,
+    "zero_weight_points": 5390
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC084_AoA_6.json b/surface_dual_areas/cases/geo_LHC084_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..c571fefc83809902833f82896134e1a7e7e749d6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC084_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC084_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC084_AoA_6/boundary_dual_area_geo_LHC084_AoA_6.npy",
+    "sha256": "6194ff779eb436ad6bd71515a081c8ee9fc183017416f43a681c09c3271853a8",
+    "shape": [
+      135559569
+    ],
+    "size_bytes": 542238404
+  },
+  "runtime": {
+    "accumulation_seconds": 10.376076829852536,
+    "completed_at_utc": "2026-08-07T07:43:15.851283Z",
+    "elapsed_seconds": 19.752207905985415,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.040653496980667,
+    "geometry_read_seconds": 1.7796647129580379,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:42:56.098987Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC084_AoA_6/boundary_geo_LHC084_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC084_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624480000000000,
+    "extracted_vtu_size_bytes": 20812990734,
+    "geometry_sha256": "20f5b78692e5a1e2565c9ee9401970c7d423d876f38f1741c50132d121727e25",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3114770,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1059849,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2326619,
+      "13": 782003,
+      "14": 1611327,
+      "15": 511593,
+      "16": 1017032,
+      "17": 372743,
+      "18": 748666,
+      "19": 301026,
+      "20": 657259,
+      "21": 221608,
+      "22": 341963,
+      "23": 119622,
+      "24": 199455,
+      "25": 68029,
+      "26": 94708,
+      "27": 51574,
+      "28": 125031,
+      "29": 53105,
+      "3": 49098,
+      "30": 115039,
+      "31": 49263,
+      "32": 108066,
+      "33": 38669,
+      "34": 66037,
+      "35": 27880,
+      "36": 62973,
+      "37": 23099,
+      "38": 39115,
+      "39": 16359,
+      "4": 111303,
+      "40": 29545,
+      "41": 10822,
+      "42": 14311,
+      "43": 5785,
+      "44": 7631,
+      "45": 3688,
+      "46": 4312,
+      "47": 2514,
+      "48": 3515,
+      "49": 2139,
+      "5": 937204,
+      "50": 2951,
+      "51": 1837,
+      "52": 2766,
+      "53": 1789,
+      "54": 2453,
+      "55": 1742,
+      "56": 2558,
+      "57": 1756,
+      "58": 2285,
+      "59": 1723,
+      "6": 5187997,
+      "60": 2504,
+      "61": 1657,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1983801,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5634713,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1652585,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49098,
+      "7": 29850013,
+      "9": 111303
+    },
+    "connectivity_max": 135559568,
+    "connectivity_min": 0,
+    "n_cells": 30010414,
+    "n_connectivity_values": 331128837,
+    "n_fan_triangles": 271108009,
+    "n_points": 135559569
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5441979231435643e-11,
+    "float64_area_closure_relative": 2.8005497883557177e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 271108009,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937103.214339937,
+    "surface_area_float64_in2": 1937103.2144085919,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937103.2144085376,
+    "zero_area_triangles": 228455,
+    "zero_weight_points": 5027
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC085_AoA_12.json b/surface_dual_areas/cases/geo_LHC085_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..f3f849c3f059e1a85d697d052944d981a3801ee1
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC085_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC085_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC085_AoA_12/boundary_dual_area_geo_LHC085_AoA_12.npy",
+    "sha256": "a4eaf88d888fbdc46ca7dbf9de08970d01b0c8bbe29ffa190d52ed40f41953fb",
+    "shape": [
+      145694147
+    ],
+    "size_bytes": 582776716
+  },
+  "runtime": {
+    "accumulation_seconds": 11.203566187992692,
+    "completed_at_utc": "2026-08-07T07:43:40.952590Z",
+    "elapsed_seconds": 22.021732036024332,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.172758727101609,
+    "geometry_read_seconds": 2.776406293036416,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:43:18.930747Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC085_AoA_12/boundary_geo_LHC085_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC085_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624677000000000,
+    "extracted_vtu_size_bytes": 22381716327,
+    "geometry_sha256": "1f5430e19bd1b2894df212f3b94057dad2c07663d379b74931af5bbbc3293084",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3940808,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1306910,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2754069,
+      "13": 898248,
+      "14": 1569609,
+      "15": 526704,
+      "16": 975662,
+      "17": 362406,
+      "18": 729130,
+      "19": 291498,
+      "20": 654468,
+      "21": 217325,
+      "22": 357434,
+      "23": 119499,
+      "24": 201597,
+      "25": 69606,
+      "26": 91623,
+      "27": 51869,
+      "28": 123975,
+      "29": 53119,
+      "3": 58402,
+      "30": 114546,
+      "31": 49363,
+      "32": 107973,
+      "33": 38657,
+      "34": 66035,
+      "35": 27839,
+      "36": 62449,
+      "37": 22822,
+      "38": 38740,
+      "39": 16503,
+      "4": 132539,
+      "40": 29638,
+      "41": 10815,
+      "42": 14471,
+      "43": 5878,
+      "44": 7773,
+      "45": 3633,
+      "46": 4325,
+      "47": 2518,
+      "48": 3522,
+      "49": 2141,
+      "5": 946142,
+      "50": 2919,
+      "51": 1860,
+      "52": 2754,
+      "53": 1788,
+      "54": 2444,
+      "55": 1712,
+      "56": 2550,
+      "57": 1732,
+      "58": 2313,
+      "59": 1695,
+      "6": 5253290,
+      "60": 2441,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2086327,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6404335,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1911865,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58402,
+      "7": 32571793,
+      "9": 132539
+    },
+    "connectivity_max": 145694146,
+    "connectivity_min": 0,
+    "n_cells": 32762734,
+    "n_connectivity_values": 356902639,
+    "n_fan_triangles": 291377171,
+    "n_points": 145694147
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.583653949526385e-11,
+    "float64_area_closure_relative": 3.130945518005065e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 291377171,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948345.26133805,
+    "surface_area_float64_in2": 1948345.261407872,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948345.261407933,
+    "zero_area_triangles": 232996,
+    "zero_weight_points": 5561
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC085_AoA_18.json b/surface_dual_areas/cases/geo_LHC085_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..803ff31f2c40816938f30c6f639556eed7cf6f0f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC085_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC085_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC085_AoA_18/boundary_dual_area_geo_LHC085_AoA_18.npy",
+    "sha256": "76a7ab06c920b2301bd5e021d1d29ea9aee9e70bf57e2b00c65af3facbf79e10",
+    "shape": [
+      148167142
+    ],
+    "size_bytes": 592668696
+  },
+  "runtime": {
+    "accumulation_seconds": 11.414175851037726,
+    "completed_at_utc": "2026-08-07T08:11:12.869696Z",
+    "elapsed_seconds": 56.81610040483065,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3142690709792078,
+    "geometry_read_seconds": 37.15765167796053,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:10:16.053517Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC085_AoA_18/boundary_geo_LHC085_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC085_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624496000000000,
+    "extracted_vtu_size_bytes": 22767826237,
+    "geometry_sha256": "6f73dbef31791b5caa45e569483a2194d2b4c1129be9ba9bac7f1d55aeea9cb9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4386794,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1434316,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2831017,
+      "13": 886511,
+      "14": 1351599,
+      "15": 474395,
+      "16": 917246,
+      "17": 352115,
+      "18": 746953,
+      "19": 296077,
+      "20": 671078,
+      "21": 220565,
+      "22": 368141,
+      "23": 121208,
+      "24": 206405,
+      "25": 70188,
+      "26": 92027,
+      "27": 51944,
+      "28": 123975,
+      "29": 53115,
+      "3": 60214,
+      "30": 114548,
+      "31": 49363,
+      "32": 107979,
+      "33": 38652,
+      "34": 66039,
+      "35": 27840,
+      "36": 62448,
+      "37": 22822,
+      "38": 38738,
+      "39": 16503,
+      "4": 135444,
+      "40": 29638,
+      "41": 10816,
+      "42": 14471,
+      "43": 5878,
+      "44": 7773,
+      "45": 3633,
+      "46": 4325,
+      "47": 2518,
+      "48": 3522,
+      "49": 2141,
+      "5": 945931,
+      "50": 2919,
+      "51": 1860,
+      "52": 2754,
+      "53": 1788,
+      "54": 2444,
+      "55": 1712,
+      "56": 2550,
+      "57": 1732,
+      "58": 2313,
+      "59": 1695,
+      "6": 5248035,
+      "60": 2441,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2143359,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6635512,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2068555,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60214,
+      "7": 33371342,
+      "9": 135444
+    },
+    "connectivity_max": 148167141,
+    "connectivity_min": 0,
+    "n_cells": 33567000,
+    "n_connectivity_values": 363457161,
+    "n_fan_triangles": 296323161,
+    "n_points": 148167142
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.549106228537299e-11,
+    "float64_area_closure_relative": 2.617088218031693e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296323161,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948345.1343775175,
+    "surface_area_float64_in2": 1948345.1344466663,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948345.1344467173,
+    "zero_area_triangles": 237261,
+    "zero_weight_points": 5781
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC086_AoA_8.json b/surface_dual_areas/cases/geo_LHC086_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..5dd724429a1fa82a1c053ed4789d3c03ce8aa243
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC086_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC086_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC086_AoA_8/boundary_dual_area_geo_LHC086_AoA_8.npy",
+    "sha256": "e0385ac34bc76af93d7ff626a9fe264e2c54d16ef12c833f24d551a2f10f097e",
+    "shape": [
+      140504655
+    ],
+    "size_bytes": 562018748
+  },
+  "runtime": {
+    "accumulation_seconds": 10.774993837811053,
+    "completed_at_utc": "2026-08-07T07:43:02.402663Z",
+    "elapsed_seconds": 20.717109168181196,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1239656899124384,
+    "geometry_read_seconds": 2.134572630049661,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:42:41.685470Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC086_AoA_8/boundary_geo_LHC086_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC086_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624624000000000,
+    "extracted_vtu_size_bytes": 21575734359,
+    "geometry_sha256": "dcd8f19216477ca6a2b64346bdef4b8841c9b33fab438fc4d06c54917b7620a8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3321196,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1034857,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2539139,
+      "13": 793817,
+      "14": 1643762,
+      "15": 534931,
+      "16": 1064218,
+      "17": 384485,
+      "18": 767116,
+      "19": 308691,
+      "20": 678868,
+      "21": 227463,
+      "22": 366137,
+      "23": 122499,
+      "24": 195305,
+      "25": 68677,
+      "26": 88014,
+      "27": 51214,
+      "28": 124266,
+      "29": 53228,
+      "3": 55007,
+      "30": 115617,
+      "31": 49650,
+      "32": 108491,
+      "33": 38919,
+      "34": 66235,
+      "35": 28076,
+      "36": 62152,
+      "37": 22864,
+      "38": 38015,
+      "39": 15960,
+      "4": 129314,
+      "40": 28998,
+      "41": 10562,
+      "42": 14014,
+      "43": 5800,
+      "44": 7714,
+      "45": 3665,
+      "46": 4223,
+      "47": 2526,
+      "48": 3629,
+      "49": 2192,
+      "5": 956826,
+      "50": 2907,
+      "51": 1826,
+      "52": 2699,
+      "53": 1728,
+      "54": 2374,
+      "55": 1687,
+      "56": 2498,
+      "57": 1745,
+      "58": 2255,
+      "59": 1680,
+      "6": 5252107,
+      "60": 2468,
+      "61": 1651,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1378,
+      "66": 1810,
+      "67": 1115,
+      "68": 1527,
+      "69": 920,
+      "7": 2031072,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6114061,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1665115,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 55007,
+      "7": 31060925,
+      "9": 129314
+    },
+    "connectivity_max": 140504654,
+    "connectivity_min": 0,
+    "n_cells": 31245246,
+    "n_connectivity_values": 343488685,
+    "n_fan_triangles": 280998193,
+    "n_points": 140504655
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.0228695443977767e-11,
+    "float64_area_closure_relative": 1.866411972318741e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280998193,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946064.4781324195,
+    "surface_area_float64_in2": 1946064.4781912465,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946064.4781912828,
+    "zero_area_triangles": 232406,
+    "zero_weight_points": 5413
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC087_AoA_18.json b/surface_dual_areas/cases/geo_LHC087_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..d998cb6d231e3e0a69de8fde36538a3e03464cda
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC087_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC087_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC087_AoA_18/boundary_dual_area_geo_LHC087_AoA_18.npy",
+    "sha256": "f0c5619a62b727690a02eb67ee635f6c06e355b5f4b680fc2fba596565a7db1d",
+    "shape": [
+      141138693
+    ],
+    "size_bytes": 564554900
+  },
+  "runtime": {
+    "accumulation_seconds": 10.962960984092206,
+    "completed_at_utc": "2026-08-07T07:44:25.549244Z",
+    "elapsed_seconds": 21.224697292083874,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.144483556970954,
+    "geometry_read_seconds": 2.361862702993676,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:44:04.324449Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC087_AoA_18/boundary_geo_LHC087_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC087_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624516000000000,
+    "extracted_vtu_size_bytes": 21679554264,
+    "geometry_sha256": "0006b79486d230421a1659c611562f9182274125c02db61e45443262875639cb",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4050322,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1180924,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2775947,
+      "13": 762282,
+      "14": 1322291,
+      "15": 448191,
+      "16": 893043,
+      "17": 345162,
+      "18": 736355,
+      "19": 299472,
+      "20": 665060,
+      "21": 227008,
+      "22": 368240,
+      "23": 127046,
+      "24": 210125,
+      "25": 71725,
+      "26": 94230,
+      "27": 52497,
+      "28": 125135,
+      "29": 53402,
+      "3": 55310,
+      "30": 114967,
+      "31": 49491,
+      "32": 108039,
+      "33": 38514,
+      "34": 66194,
+      "35": 28010,
+      "36": 62317,
+      "37": 23059,
+      "38": 38651,
+      "39": 16427,
+      "4": 120927,
+      "40": 29335,
+      "41": 10723,
+      "42": 14311,
+      "43": 5825,
+      "44": 7707,
+      "45": 3577,
+      "46": 4145,
+      "47": 2489,
+      "48": 3499,
+      "49": 2103,
+      "5": 920753,
+      "50": 2921,
+      "51": 1846,
+      "52": 2751,
+      "53": 1765,
+      "54": 2481,
+      "55": 1713,
+      "56": 2530,
+      "57": 1750,
+      "58": 2297,
+      "59": 1743,
+      "6": 5169136,
+      "60": 2508,
+      "61": 1625,
+      "62": 2259,
+      "63": 1602,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 1987067,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6135942,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1772701,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 55310,
+      "7": 31468298,
+      "9": 120927
+    },
+    "connectivity_max": 141138692,
+    "connectivity_min": 0,
+    "n_cells": 31644535,
+    "n_connectivity_values": 345555346,
+    "n_fan_triangles": 282266276,
+    "n_points": 141138693
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.468192230753521e-11,
+    "float64_area_closure_relative": 2.280852464601773e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282266276,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939530.196681297,
+    "surface_area_float64_in2": 1939530.1967485636,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939530.1967485591,
+    "zero_area_triangles": 238792,
+    "zero_weight_points": 5562
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC088_AoA_14.json b/surface_dual_areas/cases/geo_LHC088_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..f3ad992e5a4412b8bd5bf25ec34aed429ca00f0e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC088_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC088_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC088_AoA_14/boundary_dual_area_geo_LHC088_AoA_14.npy",
+    "sha256": "7a10c318ef80b0b1ca29a3430ca9645c1fb2e17d190961a1d1fd7956dfb05ad8",
+    "shape": [
+      140158337
+    ],
+    "size_bytes": 560633476
+  },
+  "runtime": {
+    "accumulation_seconds": 13.059374792035669,
+    "completed_at_utc": "2026-08-07T08:10:45.068270Z",
+    "elapsed_seconds": 23.674015447031707,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.634026609128341,
+    "geometry_read_seconds": 2.1047193449921906,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:10:21.394168Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC088_AoA_14/boundary_geo_LHC088_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC088_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624705000000000,
+    "extracted_vtu_size_bytes": 21527773818,
+    "geometry_sha256": "56952b2414833987fc95a3e2e2e433da856347de23cc8a534468ac214a3c40b8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3756946,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1193777,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2665340,
+      "13": 803249,
+      "14": 1376833,
+      "15": 481919,
+      "16": 923952,
+      "17": 362053,
+      "18": 743708,
+      "19": 300470,
+      "20": 661470,
+      "21": 221453,
+      "22": 353816,
+      "23": 120487,
+      "24": 205614,
+      "25": 68545,
+      "26": 94896,
+      "27": 51760,
+      "28": 124478,
+      "29": 53003,
+      "3": 54378,
+      "30": 115340,
+      "31": 49498,
+      "32": 108930,
+      "33": 38743,
+      "34": 66918,
+      "35": 27825,
+      "36": 62720,
+      "37": 22970,
+      "38": 38830,
+      "39": 16390,
+      "4": 120110,
+      "40": 29644,
+      "41": 10793,
+      "42": 14415,
+      "43": 5898,
+      "44": 7766,
+      "45": 3622,
+      "46": 4257,
+      "47": 2557,
+      "48": 3559,
+      "49": 2149,
+      "5": 944331,
+      "50": 2910,
+      "51": 1848,
+      "52": 2742,
+      "53": 1811,
+      "54": 2501,
+      "55": 1698,
+      "56": 2596,
+      "57": 1721,
+      "58": 2313,
+      "59": 1707,
+      "6": 5193883,
+      "60": 2445,
+      "61": 1664,
+      "62": 2198,
+      "63": 1588,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2034563,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5994664,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1793792,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54378,
+      "7": 31202545,
+      "9": 120110
+    },
+    "connectivity_max": 140158336,
+    "connectivity_min": 0,
+    "n_cells": 31377033,
+    "n_connectivity_values": 343059604,
+    "n_fan_triangles": 280305538,
+    "n_points": 140158337
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.2273193106090796e-11,
+    "float64_area_closure_relative": 1.6686904244087834e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280305538,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939452.5787076275,
+    "surface_area_float64_in2": 1939452.5787702198,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939452.5787702522,
+    "zero_area_triangles": 237159,
+    "zero_weight_points": 5621
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC088_AoA_18.json b/surface_dual_areas/cases/geo_LHC088_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..38f05b47f0034efae8820a3a1224bafac78f5d52
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC088_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC088_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC088_AoA_18/boundary_dual_area_geo_LHC088_AoA_18.npy",
+    "sha256": "1606899e3d63fef8ca8b6d15471b89d553f0781cc3eba5a7ca9105ec0b5c8b2f",
+    "shape": [
+      141800488
+    ],
+    "size_bytes": 567202080
+  },
+  "runtime": {
+    "accumulation_seconds": 10.837666721083224,
+    "completed_at_utc": "2026-08-07T07:43:18.848283Z",
+    "elapsed_seconds": 21.52622909285128,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1500978639815003,
+    "geometry_read_seconds": 2.657580368919298,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:42:57.321958Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC088_AoA_18/boundary_geo_LHC088_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC088_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624407000000000,
+    "extracted_vtu_size_bytes": 21784101691,
+    "geometry_sha256": "45cab614dabe5942ffa40e8b1702b79fcb52c01602da176ca38b7a43a8f07efa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4006117,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1285749,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2739995,
+      "13": 810325,
+      "14": 1260706,
+      "15": 451435,
+      "16": 884855,
+      "17": 350439,
+      "18": 737239,
+      "19": 298677,
+      "20": 661142,
+      "21": 222937,
+      "22": 364196,
+      "23": 123001,
+      "24": 212788,
+      "25": 70172,
+      "26": 95869,
+      "27": 52091,
+      "28": 124530,
+      "29": 53012,
+      "3": 54094,
+      "30": 115340,
+      "31": 49497,
+      "32": 108929,
+      "33": 38740,
+      "34": 66919,
+      "35": 27828,
+      "36": 62725,
+      "37": 22968,
+      "38": 38829,
+      "39": 16387,
+      "4": 121845,
+      "40": 29643,
+      "41": 10794,
+      "42": 14414,
+      "43": 5901,
+      "44": 7765,
+      "45": 3622,
+      "46": 4258,
+      "47": 2558,
+      "48": 3559,
+      "49": 2148,
+      "5": 948042,
+      "50": 2910,
+      "51": 1848,
+      "52": 2743,
+      "53": 1811,
+      "54": 2499,
+      "55": 1698,
+      "56": 2596,
+      "57": 1721,
+      "58": 2313,
+      "59": 1707,
+      "6": 5200074,
+      "60": 2445,
+      "61": 1664,
+      "62": 2198,
+      "63": 1588,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2077289,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6126306,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1898147,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54094,
+      "7": 31732675,
+      "9": 121845
+    },
+    "connectivity_max": 141800487,
+    "connectivity_min": 0,
+    "n_cells": 31908614,
+    "n_connectivity_values": 347407068,
+    "n_fan_triangles": 283589840,
+    "n_points": 141800488
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.2056627825948884e-11,
+    "float64_area_closure_relative": 1.6927005870016602e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283589840,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939452.316980323,
+    "surface_area_float64_in2": 1939452.3170424954,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939452.3170424625,
+    "zero_area_triangles": 238390,
+    "zero_weight_points": 5705
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC088_AoA_22.json b/surface_dual_areas/cases/geo_LHC088_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe696a4e9d25cc9191d75cd0251d2c5935b38760
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC088_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC088_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC088_AoA_22/boundary_dual_area_geo_LHC088_AoA_22.npy",
+    "sha256": "549fb2618031f4d58f3dba076c91ca4af028159b4da1306aa8aa1efde43b6185",
+    "shape": [
+      140807274
+    ],
+    "size_bytes": 563229224
+  },
+  "runtime": {
+    "accumulation_seconds": 10.71182478708215,
+    "completed_at_utc": "2026-08-07T07:44:47.605099Z",
+    "elapsed_seconds": 21.007806470850483,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1670509590767324,
+    "geometry_read_seconds": 2.1611699229106307,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:44:26.597202Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC088_AoA_22/boundary_geo_LHC088_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC088_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624723000000000,
+    "extracted_vtu_size_bytes": 21631226269,
+    "geometry_sha256": "4d173f6716ac519a72cdf37b9e1f9bdbd53cd45dd014d8cb94f9a5465c71bbdd",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3974798,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1258476,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2598429,
+      "13": 777390,
+      "14": 1221955,
+      "15": 443065,
+      "16": 894850,
+      "17": 353132,
+      "18": 745717,
+      "19": 301839,
+      "20": 666915,
+      "21": 226346,
+      "22": 371687,
+      "23": 125545,
+      "24": 217807,
+      "25": 71354,
+      "26": 96965,
+      "27": 52384,
+      "28": 124690,
+      "29": 53060,
+      "3": 53522,
+      "30": 115359,
+      "31": 49497,
+      "32": 108927,
+      "33": 38747,
+      "34": 66917,
+      "35": 27825,
+      "36": 62720,
+      "37": 22970,
+      "38": 38829,
+      "39": 16391,
+      "4": 121706,
+      "40": 29644,
+      "41": 10794,
+      "42": 14415,
+      "43": 5897,
+      "44": 7765,
+      "45": 3623,
+      "46": 4257,
+      "47": 2557,
+      "48": 3559,
+      "49": 2149,
+      "5": 949547,
+      "50": 2910,
+      "51": 1848,
+      "52": 2742,
+      "53": 1811,
+      "54": 2501,
+      "55": 1698,
+      "56": 2596,
+      "57": 1721,
+      "58": 2313,
+      "59": 1707,
+      "6": 5205266,
+      "60": 2445,
+      "61": 1664,
+      "62": 2198,
+      "63": 1588,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2078134,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6120321,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1890963,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53522,
+      "7": 31498196,
+      "9": 121706
+    },
+    "connectivity_max": 140807273,
+    "connectivity_min": 0,
+    "n_cells": 31673424,
+    "n_connectivity_values": 344950260,
+    "n_fan_triangles": 281603412,
+    "n_points": 140807274
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1482659779333223e-11,
+    "float64_area_closure_relative": 7.443078114596774e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281603412,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939452.9633883184,
+    "surface_area_float64_in2": 1939452.9634493776,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939452.9634493631,
+    "zero_area_triangles": 237488,
+    "zero_weight_points": 5682
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC089_AoA_14.json b/surface_dual_areas/cases/geo_LHC089_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..effb6037a20f2438c1a6213b6947d34fe1959533
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC089_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC089_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC089_AoA_14/boundary_dual_area_geo_LHC089_AoA_14.npy",
+    "sha256": "1540ee8547846bb8f71bf672f647322530e100f262c39088bd014498b66649f8",
+    "shape": [
+      146594975
+    ],
+    "size_bytes": 586380028
+  },
+  "runtime": {
+    "accumulation_seconds": 11.205581147922203,
+    "completed_at_utc": "2026-08-07T08:13:41.227975Z",
+    "elapsed_seconds": 22.323336557950824,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4279037569649518,
+    "geometry_read_seconds": 2.2606985808815807,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:13:18.904551Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC089_AoA_14/boundary_geo_LHC089_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC089_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624718000000000,
+    "extracted_vtu_size_bytes": 22525429427,
+    "geometry_sha256": "8af8c47a586f74b0d9cdeac1d06a966d2d64b448af2b00661de6a08b942d068b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4232120,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1421692,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2809739,
+      "13": 882348,
+      "14": 1320055,
+      "15": 477785,
+      "16": 906976,
+      "17": 360449,
+      "18": 739557,
+      "19": 300885,
+      "20": 665103,
+      "21": 221432,
+      "22": 355746,
+      "23": 120957,
+      "24": 207661,
+      "25": 71302,
+      "26": 93309,
+      "27": 52619,
+      "28": 123977,
+      "29": 52935,
+      "3": 58476,
+      "30": 114251,
+      "31": 48905,
+      "32": 108136,
+      "33": 38207,
+      "34": 66466,
+      "35": 27552,
+      "36": 62343,
+      "37": 22687,
+      "38": 38998,
+      "39": 16504,
+      "4": 131644,
+      "40": 30299,
+      "41": 10989,
+      "42": 14665,
+      "43": 6015,
+      "44": 7952,
+      "45": 3652,
+      "46": 4322,
+      "47": 2554,
+      "48": 3528,
+      "49": 2114,
+      "5": 941273,
+      "50": 2837,
+      "51": 1794,
+      "52": 2607,
+      "53": 1710,
+      "54": 2346,
+      "55": 1704,
+      "56": 2541,
+      "57": 1715,
+      "58": 2310,
+      "59": 1693,
+      "6": 5259545,
+      "60": 2443,
+      "61": 1667,
+      "62": 2197,
+      "63": 1588,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 881,
+      "7": 2126802,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 446,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6534964,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2034733,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58476,
+      "7": 32988234,
+      "9": 131644
+    },
+    "connectivity_max": 146594974,
+    "connectivity_min": 0,
+    "n_cells": 33178354,
+    "n_connectivity_values": 359535542,
+    "n_fan_triangles": 293178834,
+    "n_points": 146594975
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.0658196987631795e-11,
+    "float64_area_closure_relative": 2.870628894866019e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293178834,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946589.2848481068,
+    "surface_area_float64_in2": 1946589.2849077857,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946589.2849078416,
+    "zero_area_triangles": 237996,
+    "zero_weight_points": 5812
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC089_AoA_18.json b/surface_dual_areas/cases/geo_LHC089_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..ec484a6bc2405d2854f9d1511eadd1ca4e1f70d1
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC089_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC089_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC089_AoA_18/boundary_dual_area_geo_LHC089_AoA_18.npy",
+    "sha256": "9a5d878ca07db1ce0ba4fd94b2db008692dab9a8c681826f9f2e1d66f987b1f5",
+    "shape": [
+      148267991
+    ],
+    "size_bytes": 593072092
+  },
+  "runtime": {
+    "accumulation_seconds": 11.442037689965218,
+    "completed_at_utc": "2026-08-07T08:11:44.262364Z",
+    "elapsed_seconds": 58.04277588916011,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6205482960212976,
+    "geometry_read_seconds": 37.70093298214488,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:10:46.219494Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC089_AoA_18/boundary_geo_LHC089_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC089_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624592000000000,
+    "extracted_vtu_size_bytes": 22786093920,
+    "geometry_sha256": "e1035a1dfbe41b7034c37144c003bd434c5bc7c72cc9b20bb4aa9407a5f6cf94",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4499068,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1499351,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2878612,
+      "13": 868802,
+      "14": 1246883,
+      "15": 440539,
+      "16": 871854,
+      "17": 348910,
+      "18": 740436,
+      "19": 302778,
+      "20": 668046,
+      "21": 224076,
+      "22": 358645,
+      "23": 123153,
+      "24": 209781,
+      "25": 72483,
+      "26": 93816,
+      "27": 52885,
+      "28": 124059,
+      "29": 53000,
+      "3": 59545,
+      "30": 114244,
+      "31": 48902,
+      "32": 108132,
+      "33": 38202,
+      "34": 66468,
+      "35": 27553,
+      "36": 62333,
+      "37": 22687,
+      "38": 38994,
+      "39": 16509,
+      "4": 134633,
+      "40": 30305,
+      "41": 10990,
+      "42": 14666,
+      "43": 6020,
+      "44": 7957,
+      "45": 3650,
+      "46": 4323,
+      "47": 2554,
+      "48": 3528,
+      "49": 2114,
+      "5": 942721,
+      "50": 2837,
+      "51": 1794,
+      "52": 2607,
+      "53": 1710,
+      "54": 2346,
+      "55": 1704,
+      "56": 2541,
+      "57": 1715,
+      "58": 2310,
+      "59": 1693,
+      "6": 5240117,
+      "60": 2443,
+      "61": 1667,
+      "62": 2197,
+      "63": 1588,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2168554,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6666349,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2137321,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59545,
+      "7": 33506501,
+      "9": 134633
+    },
+    "connectivity_max": 148267990,
+    "connectivity_min": 0,
+    "n_cells": 33700679,
+    "n_connectivity_values": 363926224,
+    "n_fan_triangles": 296524866,
+    "n_points": 148267991
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.101655034638814e-11,
+    "float64_area_closure_relative": 3.755739856454843e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296524866,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946589.0849548115,
+    "surface_area_float64_in2": 1946589.085015188,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946589.0850151149,
+    "zero_area_triangles": 240321,
+    "zero_weight_points": 5999
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC090_AoA_16.json b/surface_dual_areas/cases/geo_LHC090_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..9cd6ee97b260ad1ff72de43c564a1bd37518b23e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC090_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC090_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC090_AoA_16/boundary_dual_area_geo_LHC090_AoA_16.npy",
+    "sha256": "11690bb64b60a4141ce6e7ea09b1565eac601d12d331cf53ec1e8348a8dcb8de",
+    "shape": [
+      146100742
+    ],
+    "size_bytes": 584403096
+  },
+  "runtime": {
+    "accumulation_seconds": 11.42187457694672,
+    "completed_at_utc": "2026-08-07T08:13:19.505809Z",
+    "elapsed_seconds": 23.15909700607881,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.488393706968054,
+    "geometry_read_seconds": 2.946088354103267,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:12:56.346575Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC090_AoA_16/boundary_geo_LHC090_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC090_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624485000000000,
+    "extracted_vtu_size_bytes": 22446784370,
+    "geometry_sha256": "57fd25d6ec2e5077ceac5d3fea589312d7d4ac4a0aa59fc2174f01d41d580212",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4009078,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1387977,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2710391,
+      "13": 900686,
+      "14": 1457894,
+      "15": 501012,
+      "16": 957443,
+      "17": 358008,
+      "18": 735607,
+      "19": 292968,
+      "20": 659881,
+      "21": 219439,
+      "22": 363832,
+      "23": 122017,
+      "24": 208844,
+      "25": 71222,
+      "26": 92461,
+      "27": 51832,
+      "28": 123155,
+      "29": 52732,
+      "3": 60269,
+      "30": 114327,
+      "31": 49162,
+      "32": 108598,
+      "33": 38998,
+      "34": 67679,
+      "35": 28095,
+      "36": 63139,
+      "37": 22858,
+      "38": 38750,
+      "39": 16066,
+      "4": 136461,
+      "40": 29283,
+      "41": 10659,
+      "42": 14095,
+      "43": 5758,
+      "44": 7741,
+      "45": 3704,
+      "46": 4239,
+      "47": 2496,
+      "48": 3571,
+      "49": 2180,
+      "5": 955774,
+      "50": 2907,
+      "51": 1784,
+      "52": 2603,
+      "53": 1671,
+      "54": 2280,
+      "55": 1659,
+      "56": 2462,
+      "57": 1735,
+      "58": 2261,
+      "59": 1686,
+      "6": 5247663,
+      "60": 2462,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2140197,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6456518,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2009455,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60269,
+      "7": 32761683,
+      "9": 136461
+    },
+    "connectivity_max": 146100741,
+    "connectivity_min": 0,
+    "n_cells": 32958413,
+    "n_connectivity_values": 358107188,
+    "n_fan_triangles": 292190362,
+    "n_points": 146100742
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.6326431144780375e-11,
+    "float64_area_closure_relative": 2.6191169897501495e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 292190362,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946835.943503205,
+    "surface_area_float64_in2": 1946835.9435544582,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946835.9435545092,
+    "zero_area_triangles": 235628,
+    "zero_weight_points": 5679
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC090_AoA_18.json b/surface_dual_areas/cases/geo_LHC090_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..e6aee2933038c3c9bf736ec58ee4acb5124e1aaa
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC090_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC090_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC090_AoA_18/boundary_dual_area_geo_LHC090_AoA_18.npy",
+    "sha256": "8ca991cd03751cf98d2cb0fcab545a9b665e51859d9976e48cfe3c5d4fb655b1",
+    "shape": [
+      147039563
+    ],
+    "size_bytes": 588158380
+  },
+  "runtime": {
+    "accumulation_seconds": 12.362018825020641,
+    "completed_at_utc": "2026-08-07T08:14:37.006469Z",
+    "elapsed_seconds": 54.84280735300854,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5688092089258134,
+    "geometry_read_seconds": 33.750874381978065,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:13:42.163584Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC090_AoA_18/boundary_geo_LHC090_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC090_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624503000000000,
+    "extracted_vtu_size_bytes": 22593860903,
+    "geometry_sha256": "c99e26d2388e8a7ad88fb0feb5882a2e879f2c2b9627270b13fbafd55701d163",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4203372,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1435907,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2751162,
+      "13": 885728,
+      "14": 1350146,
+      "15": 471573,
+      "16": 922162,
+      "17": 350067,
+      "18": 738434,
+      "19": 295353,
+      "20": 668947,
+      "21": 223036,
+      "22": 373540,
+      "23": 124844,
+      "24": 213192,
+      "25": 72252,
+      "26": 92723,
+      "27": 51917,
+      "28": 123192,
+      "29": 52741,
+      "3": 60854,
+      "30": 114329,
+      "31": 49157,
+      "32": 108596,
+      "33": 38997,
+      "34": 67678,
+      "35": 28097,
+      "36": 63140,
+      "37": 22857,
+      "38": 38753,
+      "39": 16066,
+      "4": 137988,
+      "40": 29283,
+      "41": 10662,
+      "42": 14094,
+      "43": 5758,
+      "44": 7740,
+      "45": 3704,
+      "46": 4239,
+      "47": 2495,
+      "48": 3572,
+      "49": 2180,
+      "5": 957450,
+      "50": 2907,
+      "51": 1784,
+      "52": 2603,
+      "53": 1671,
+      "54": 2280,
+      "55": 1659,
+      "56": 2462,
+      "57": 1735,
+      "58": 2261,
+      "59": 1686,
+      "6": 5244707,
+      "60": 2462,
+      "61": 1650,
+      "62": 2222,
+      "63": 1600,
+      "64": 2206,
+      "65": 1378,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2169107,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 304,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6562006,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 58,
+      "88": 71,
+      "89": 59,
+      "9": 2075659,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60854,
+      "7": 33084812,
+      "9": 137988
+    },
+    "connectivity_max": 147039562,
+    "connectivity_min": 0,
+    "n_cells": 33283654,
+    "n_connectivity_values": 360635312,
+    "n_fan_triangles": 294068004,
+    "n_points": 147039563
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.610542160418598e-11,
+    "float64_area_closure_relative": 4.448911200944272e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294068004,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946835.8779243561,
+    "surface_area_float64_in2": 1946835.877975179,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946835.8779752657,
+    "zero_area_triangles": 237006,
+    "zero_weight_points": 5784
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC090_AoA_4.json b/surface_dual_areas/cases/geo_LHC090_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..5c73fd950229b39ce02092438e126ba9d7ee787d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC090_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC090_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC090_AoA_4/boundary_dual_area_geo_LHC090_AoA_4.npy",
+    "sha256": "5c6999ce90896b12224d697c849e5fe3888c33ced5ed41a3b0f9b8377e197365",
+    "shape": [
+      136804143
+    ],
+    "size_bytes": 547216700
+  },
+  "runtime": {
+    "accumulation_seconds": 10.960070696892217,
+    "completed_at_utc": "2026-08-07T07:43:11.121850Z",
+    "elapsed_seconds": 20.496905954787508,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.965092483907938,
+    "geometry_read_seconds": 1.8572723809629679,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:42:50.624861Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC090_AoA_4/boundary_geo_LHC090_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC090_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624647000000000,
+    "extracted_vtu_size_bytes": 21000391468,
+    "geometry_sha256": "2a54db9f3295ac4445c2ae04bcef872e2ce1910d2e6713cd94bbaa3fa0a1ed69",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3074409,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1063646,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2276474,
+      "13": 835034,
+      "14": 1620616,
+      "15": 562053,
+      "16": 1017209,
+      "17": 384350,
+      "18": 756454,
+      "19": 303092,
+      "20": 677871,
+      "21": 225428,
+      "22": 378438,
+      "23": 124749,
+      "24": 213828,
+      "25": 71877,
+      "26": 93041,
+      "27": 51885,
+      "28": 123257,
+      "29": 52733,
+      "3": 53781,
+      "30": 114327,
+      "31": 49168,
+      "32": 108592,
+      "33": 38996,
+      "34": 67682,
+      "35": 28099,
+      "36": 63146,
+      "37": 22859,
+      "38": 38748,
+      "39": 16062,
+      "4": 121998,
+      "40": 29283,
+      "41": 10656,
+      "42": 14095,
+      "43": 5766,
+      "44": 7740,
+      "45": 3703,
+      "46": 4238,
+      "47": 2497,
+      "48": 3570,
+      "49": 2180,
+      "5": 932487,
+      "50": 2907,
+      "51": 1784,
+      "52": 2603,
+      "53": 1671,
+      "54": 2280,
+      "55": 1659,
+      "56": 2462,
+      "57": 1735,
+      "58": 2261,
+      "59": 1685,
+      "6": 5152587,
+      "60": 2462,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1378,
+      "66": 1810,
+      "67": 1115,
+      "68": 1527,
+      "69": 920,
+      "7": 1977224,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5672587,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1645849,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53781,
+      "7": 29962784,
+      "9": 121998
+    },
+    "connectivity_max": 136804142,
+    "connectivity_min": 0,
+    "n_cells": 30138563,
+    "n_connectivity_values": 333874290,
+    "n_fan_triangles": 273597164,
+    "n_points": 136804143
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.612704513662611e-11,
+    "float64_area_closure_relative": 2.5593176263539932e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273597164,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946837.5955980162,
+    "surface_area_float64_in2": 1946837.5956488813,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946837.595648931,
+    "zero_area_triangles": 226760,
+    "zero_weight_points": 5033
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC090_AoA_8.json b/surface_dual_areas/cases/geo_LHC090_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d591194e2629e1300c3002f4921ca5f33d9d9ab
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC090_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC090_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC090_AoA_8/boundary_dual_area_geo_LHC090_AoA_8.npy",
+    "sha256": "e40b6b5d001ca632bb40a754a92e6c72335ba31c32ae69174194b4e5d2090c4f",
+    "shape": [
+      135593469
+    ],
+    "size_bytes": 542374004
+  },
+  "runtime": {
+    "accumulation_seconds": 10.457238158909604,
+    "completed_at_utc": "2026-08-07T07:45:11.920008Z",
+    "elapsed_seconds": 20.92550077009946,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0553490379825234,
+    "geometry_read_seconds": 2.7621690870728344,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:44:50.994416Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC090_AoA_8/boundary_geo_LHC090_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC090_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624403000000000,
+    "extracted_vtu_size_bytes": 20812120065,
+    "geometry_sha256": "14801102b2898b9f594fdd9ff00e9d8f210b3c4b22885543d55cfb65d133f32e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2703391,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1000862,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2115007,
+      "13": 856367,
+      "14": 1831217,
+      "15": 604672,
+      "16": 1066471,
+      "17": 389214,
+      "18": 749720,
+      "19": 298494,
+      "20": 669017,
+      "21": 221145,
+      "22": 368091,
+      "23": 122095,
+      "24": 209256,
+      "25": 70987,
+      "26": 92516,
+      "27": 51773,
+      "28": 123175,
+      "29": 52729,
+      "3": 56913,
+      "30": 114329,
+      "31": 49152,
+      "32": 108597,
+      "33": 38997,
+      "34": 67683,
+      "35": 28096,
+      "36": 63137,
+      "37": 22859,
+      "38": 38750,
+      "39": 16067,
+      "4": 128787,
+      "40": 29281,
+      "41": 10658,
+      "42": 14095,
+      "43": 5760,
+      "44": 7741,
+      "45": 3702,
+      "46": 4239,
+      "47": 2496,
+      "48": 3572,
+      "49": 2180,
+      "5": 942205,
+      "50": 2907,
+      "51": 1784,
+      "52": 2603,
+      "53": 1671,
+      "54": 2280,
+      "55": 1659,
+      "56": 2462,
+      "57": 1735,
+      "58": 2261,
+      "59": 1686,
+      "6": 5191327,
+      "60": 2462,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1966478,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5635917,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1581481,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56913,
+      "7": 29589197,
+      "9": 128787
+    },
+    "connectivity_max": 135593468,
+    "connectivity_min": 0,
+    "n_cells": 29774897,
+    "n_connectivity_values": 330725610,
+    "n_fan_triangles": 271175816,
+    "n_points": 135593469
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.593699719310254e-11,
+    "float64_area_closure_relative": 1.626481437815306e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 271175816,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946838.5436133496,
+    "surface_area_float64_in2": 1946838.5436638447,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946838.5436638764,
+    "zero_area_triangles": 222340,
+    "zero_weight_points": 4781
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC091_AoA_14.json b/surface_dual_areas/cases/geo_LHC091_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..1843266da2a9ebe4a5eb148bd7728f76394d4e4f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC091_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC091_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC091_AoA_14/boundary_dual_area_geo_LHC091_AoA_14.npy",
+    "sha256": "15be604dee7e8edc81c115187e4bfa67ffd4ea85053b5459be9fbad0b58e0a15",
+    "shape": [
+      138124491
+    ],
+    "size_bytes": 552498092
+  },
+  "runtime": {
+    "accumulation_seconds": 10.690910469042137,
+    "completed_at_utc": "2026-08-07T08:13:31.465151Z",
+    "elapsed_seconds": 20.472558751003817,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.205577014014125,
+    "geometry_read_seconds": 1.968204549048096,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:13:10.992502Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC091_AoA_14/boundary_geo_LHC091_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC091_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624607000000000,
+    "extracted_vtu_size_bytes": 21211835278,
+    "geometry_sha256": "ef8d0e517cd76eb62c48c48c0dde22058edeacc4a00e53a92d5397bcc0ca538d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3498331,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1132415,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2507451,
+      "13": 791482,
+      "14": 1425391,
+      "15": 495435,
+      "16": 938525,
+      "17": 366114,
+      "18": 757129,
+      "19": 306999,
+      "20": 680528,
+      "21": 227272,
+      "22": 357369,
+      "23": 121941,
+      "24": 200884,
+      "25": 68867,
+      "26": 93078,
+      "27": 51791,
+      "28": 124486,
+      "29": 53275,
+      "3": 52862,
+      "30": 114920,
+      "31": 49620,
+      "32": 109325,
+      "33": 39169,
+      "34": 67637,
+      "35": 27989,
+      "36": 62783,
+      "37": 22709,
+      "38": 38149,
+      "39": 15839,
+      "4": 117044,
+      "40": 28719,
+      "41": 10483,
+      "42": 14046,
+      "43": 5716,
+      "44": 7518,
+      "45": 3692,
+      "46": 4179,
+      "47": 2493,
+      "48": 3452,
+      "49": 2063,
+      "5": 945143,
+      "50": 2775,
+      "51": 1700,
+      "52": 2454,
+      "53": 1601,
+      "54": 2156,
+      "55": 1596,
+      "56": 2409,
+      "57": 1686,
+      "58": 2254,
+      "59": 1711,
+      "6": 5167445,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2022474,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5868119,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1734057,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52862,
+      "7": 30609947,
+      "9": 117044
+    },
+    "connectivity_max": 138124490,
+    "connectivity_min": 0,
+    "n_cells": 30779853,
+    "n_connectivity_values": 337797573,
+    "n_fan_triangles": 276237867,
+    "n_points": 138124491
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.871486540548752e-11,
+    "float64_area_closure_relative": 2.331605398110851e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276237867,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937255.1163116891,
+    "surface_area_float64_in2": 1937255.1163866897,
+    "weight_max_in2": 1.1006773151980247,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937255.1163867349,
+    "zero_area_triangles": 238837,
+    "zero_weight_points": 5512
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC091_AoA_22.json b/surface_dual_areas/cases/geo_LHC091_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..443b1e441f01614448971520dd3db3aad5336b69
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC091_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC091_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC091_AoA_22/boundary_dual_area_geo_LHC091_AoA_22.npy",
+    "sha256": "6c5a48923a953da012f9cd451339ffa022330c0a6f09b50ce5105e692db0be44",
+    "shape": [
+      141164733
+    ],
+    "size_bytes": 564659060
+  },
+  "runtime": {
+    "accumulation_seconds": 12.584550955099985,
+    "completed_at_utc": "2026-08-07T08:15:43.152029Z",
+    "elapsed_seconds": 65.19472365593538,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2954696679953486,
+    "geometry_read_seconds": 44.43118307902478,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:14:37.957211Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC091_AoA_22/boundary_geo_LHC091_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC091_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624427000000000,
+    "extracted_vtu_size_bytes": 21684596469,
+    "geometry_sha256": "1d666a84ba2b1840e914b490d3fc0678a7f947564918d3551169661ebb1a5496",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3861637,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1222431,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2641881,
+      "13": 810775,
+      "14": 1400169,
+      "15": 487548,
+      "16": 920302,
+      "17": 359315,
+      "18": 742913,
+      "19": 301551,
+      "20": 664775,
+      "21": 223898,
+      "22": 348511,
+      "23": 121039,
+      "24": 200999,
+      "25": 69449,
+      "26": 93829,
+      "27": 52046,
+      "28": 124529,
+      "29": 53287,
+      "3": 53176,
+      "30": 114871,
+      "31": 49623,
+      "32": 109295,
+      "33": 39169,
+      "34": 67642,
+      "35": 27996,
+      "36": 62776,
+      "37": 22699,
+      "38": 38137,
+      "39": 15832,
+      "4": 118892,
+      "40": 28709,
+      "41": 10472,
+      "42": 14033,
+      "43": 5714,
+      "44": 7508,
+      "45": 3687,
+      "46": 4175,
+      "47": 2489,
+      "48": 3449,
+      "49": 2064,
+      "5": 955905,
+      "50": 2773,
+      "51": 1700,
+      "52": 2452,
+      "53": 1600,
+      "54": 2156,
+      "55": 1596,
+      "56": 2409,
+      "57": 1686,
+      "58": 2254,
+      "59": 1711,
+      "6": 5208173,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2071378,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6068214,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1841666,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53176,
+      "7": 31520000,
+      "9": 118892
+    },
+    "connectivity_max": 141164732,
+    "connectivity_min": 0,
+    "n_cells": 31692068,
+    "n_connectivity_values": 345702487,
+    "n_fan_triangles": 282318351,
+    "n_points": 141164733
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.762550951978818e-11,
+    "float64_area_closure_relative": 7.812081730992464e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282318351,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937254.672706739,
+    "surface_area_float64_in2": 1937254.6727796292,
+    "weight_max_in2": 1.1006773151980247,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937254.6727796444,
+    "zero_area_triangles": 242910,
+    "zero_weight_points": 5735
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC092_AoA_16.json b/surface_dual_areas/cases/geo_LHC092_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..acaa518dc35bfeb31d272ea2cf588b56799c0ade
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC092_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC092_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC092_AoA_16/boundary_dual_area_geo_LHC092_AoA_16.npy",
+    "sha256": "d48cfb471a5072863ce6fa40874019950bba67322debc8d39845e1f4db9b15cc",
+    "shape": [
+      138598888
+    ],
+    "size_bytes": 554395680
+  },
+  "runtime": {
+    "accumulation_seconds": 10.60384249011986,
+    "completed_at_utc": "2026-08-07T07:45:56.331772Z",
+    "elapsed_seconds": 20.656850151950493,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1010964419692755,
+    "geometry_read_seconds": 1.9100262268912047,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:45:35.674834Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC092_AoA_16/boundary_geo_LHC092_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC092_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624489000000000,
+    "extracted_vtu_size_bytes": 21286922916,
+    "geometry_sha256": "e544f19bd5a62302bbbb6afa9bdb9b221e746ab2b301c8eae639c4b714c1a232",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3836275,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1140683,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2547389,
+      "13": 746269,
+      "14": 1286835,
+      "15": 452952,
+      "16": 900709,
+      "17": 354803,
+      "18": 757557,
+      "19": 304642,
+      "20": 675186,
+      "21": 227875,
+      "22": 366053,
+      "23": 125855,
+      "24": 212161,
+      "25": 72569,
+      "26": 95588,
+      "27": 52697,
+      "28": 124486,
+      "29": 53083,
+      "3": 53231,
+      "30": 114846,
+      "31": 49397,
+      "32": 108461,
+      "33": 38730,
+      "34": 66559,
+      "35": 27973,
+      "36": 62852,
+      "37": 23174,
+      "38": 39303,
+      "39": 16461,
+      "4": 116122,
+      "40": 29754,
+      "41": 10841,
+      "42": 14348,
+      "43": 5794,
+      "44": 7619,
+      "45": 3690,
+      "46": 4234,
+      "47": 2532,
+      "48": 3515,
+      "49": 2164,
+      "5": 922694,
+      "50": 2974,
+      "51": 1849,
+      "52": 2758,
+      "53": 1782,
+      "54": 2459,
+      "55": 1755,
+      "56": 2549,
+      "57": 1739,
+      "58": 2293,
+      "59": 1728,
+      "6": 5163029,
+      "60": 2502,
+      "61": 1658,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1990645,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5965457,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1752850,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53231,
+      "7": 30805582,
+      "9": 116122
+    },
+    "connectivity_max": 138598887,
+    "connectivity_min": 0,
+    "n_cells": 30974935,
+    "n_connectivity_values": 339136510,
+    "n_fan_triangles": 277186640,
+    "n_points": 138598888
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.057717392205466e-11,
+    "float64_area_closure_relative": 3.254590067388883e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277186640,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938711.2699846516,
+    "surface_area_float64_in2": 1938711.270043932,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938711.2700438688,
+    "zero_area_triangles": 234420,
+    "zero_weight_points": 5450
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC092_AoA_20.json b/surface_dual_areas/cases/geo_LHC092_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b19caec0d3dddcabade2806e492fda67233dd5b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC092_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC092_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC092_AoA_20/boundary_dual_area_geo_LHC092_AoA_20.npy",
+    "sha256": "7ac03f4c98f446b131f53b405301d4246fdb32d8d84004a31756a8146fd7bf9e",
+    "shape": [
+      138265800
+    ],
+    "size_bytes": 553063328
+  },
+  "runtime": {
+    "accumulation_seconds": 10.677797476062551,
+    "completed_at_utc": "2026-08-07T08:12:13.449716Z",
+    "elapsed_seconds": 52.22263653599657,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2268475990276784,
+    "geometry_read_seconds": 33.41737324302085,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:11:21.226980Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC092_AoA_20/boundary_geo_LHC092_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC092_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624568000000000,
+    "extracted_vtu_size_bytes": 21235776792,
+    "geometry_sha256": "b1c35866404a93eeb270fb96a0b1bcf57ecfbd640b3fc2a9210fd28a38944fb9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3701059,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1180995,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2520628,
+      "13": 759795,
+      "14": 1277248,
+      "15": 436844,
+      "16": 910720,
+      "17": 347503,
+      "18": 755320,
+      "19": 302797,
+      "20": 675571,
+      "21": 228208,
+      "22": 371087,
+      "23": 127383,
+      "24": 215700,
+      "25": 73566,
+      "26": 96268,
+      "27": 52997,
+      "28": 124509,
+      "29": 53133,
+      "3": 51990,
+      "30": 114846,
+      "31": 49402,
+      "32": 108468,
+      "33": 38729,
+      "34": 66556,
+      "35": 27971,
+      "36": 62843,
+      "37": 23173,
+      "38": 39309,
+      "39": 16463,
+      "4": 114920,
+      "40": 29754,
+      "41": 10841,
+      "42": 14348,
+      "43": 5794,
+      "44": 7619,
+      "45": 3690,
+      "46": 4234,
+      "47": 2532,
+      "48": 3515,
+      "49": 2164,
+      "5": 925756,
+      "50": 2974,
+      "51": 1849,
+      "52": 2758,
+      "53": 1782,
+      "54": 2459,
+      "55": 1755,
+      "56": 2549,
+      "57": 1739,
+      "58": 2293,
+      "59": 1728,
+      "6": 5185128,
+      "60": 2502,
+      "61": 1658,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2008879,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5942650,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1783073,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51990,
+      "7": 30734061,
+      "9": 114920
+    },
+    "connectivity_max": 138265799,
+    "connectivity_min": 0,
+    "n_cells": 30900971,
+    "n_connectivity_values": 338322406,
+    "n_fan_triangles": 276520464,
+    "n_points": 138265800
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.986872885760815e-11,
+    "float64_area_closure_relative": 6.004778466637212e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276520464,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938711.3524714657,
+    "surface_area_float64_in2": 1938711.3525293726,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938711.3525293714,
+    "zero_area_triangles": 233901,
+    "zero_weight_points": 5472
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC093_AoA_10.json b/surface_dual_areas/cases/geo_LHC093_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..0fdca4a48178067498b4481ab327c3a7df370674
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC093_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC093_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC093_AoA_10/boundary_dual_area_geo_LHC093_AoA_10.npy",
+    "sha256": "c00a17c3281238e53828d0d8373c8c100692d863476ff01ebb40bce2ffaa9832",
+    "shape": [
+      140468249
+    ],
+    "size_bytes": 561873124
+  },
+  "runtime": {
+    "accumulation_seconds": 10.99825273710303,
+    "completed_at_utc": "2026-08-07T08:14:25.915121Z",
+    "elapsed_seconds": 35.50175557588227,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5424878080375493,
+    "geometry_read_seconds": 15.683033637935296,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:13:50.413259Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC093_AoA_10/boundary_geo_LHC093_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC093_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624398000000000,
+    "extracted_vtu_size_bytes": 21576239735,
+    "geometry_sha256": "24c026168feae371d8b23c2d3d6815579a55a8b1776b47a9e0b47fcfe99e17a0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3788270,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1175675,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2646290,
+      "13": 776764,
+      "14": 1431852,
+      "15": 465556,
+      "16": 957584,
+      "17": 354663,
+      "18": 737148,
+      "19": 296190,
+      "20": 654397,
+      "21": 221211,
+      "22": 349266,
+      "23": 122057,
+      "24": 202037,
+      "25": 70642,
+      "26": 94451,
+      "27": 52441,
+      "28": 124638,
+      "29": 53203,
+      "3": 51061,
+      "30": 115483,
+      "31": 49227,
+      "32": 107641,
+      "33": 38427,
+      "34": 66461,
+      "35": 27856,
+      "36": 63221,
+      "37": 23186,
+      "38": 39644,
+      "39": 16351,
+      "4": 113480,
+      "40": 29821,
+      "41": 10885,
+      "42": 14198,
+      "43": 5856,
+      "44": 7766,
+      "45": 3730,
+      "46": 4245,
+      "47": 2501,
+      "48": 3593,
+      "49": 2216,
+      "5": 922401,
+      "50": 2925,
+      "51": 1836,
+      "52": 2737,
+      "53": 1733,
+      "54": 2464,
+      "55": 1724,
+      "56": 2547,
+      "57": 1768,
+      "58": 2281,
+      "59": 1692,
+      "6": 5241291,
+      "60": 2466,
+      "61": 1651,
+      "62": 2223,
+      "63": 1601,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2016559,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6100919,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1783772,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51061,
+      "7": 31316449,
+      "9": 113480
+    },
+    "connectivity_max": 140468248,
+    "connectivity_min": 0,
+    "n_cells": 31480990,
+    "n_connectivity_values": 343887344,
+    "n_fan_triangles": 280925364,
+    "n_points": 140468249
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.318925019019906e-11,
+    "float64_area_closure_relative": 3.014055245225408e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280925364,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938932.3287014524,
+    "surface_area_float64_in2": 1938932.3287851934,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938932.328785135,
+    "zero_area_triangles": 236089,
+    "zero_weight_points": 5571
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC093_AoA_8.json b/surface_dual_areas/cases/geo_LHC093_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..2a9f034e0b4801c3a07ce6de72786c08919f63a8
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC093_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC093_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC093_AoA_8/boundary_dual_area_geo_LHC093_AoA_8.npy",
+    "sha256": "67a774541e72c244ab7e1977c65f24c7e31530daabff0e0daa37dcdb8b3f8410",
+    "shape": [
+      138703002
+    ],
+    "size_bytes": 554812136
+  },
+  "runtime": {
+    "accumulation_seconds": 11.347666015150025,
+    "completed_at_utc": "2026-08-07T08:14:36.125942Z",
+    "elapsed_seconds": 55.80219479999505,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3065926181152463,
+    "geometry_read_seconds": 36.42407923610881,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:13:40.323618Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC093_AoA_8/boundary_geo_LHC093_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC093_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624623000000000,
+    "extracted_vtu_size_bytes": 21301864904,
+    "geometry_sha256": "1804f5dedd76b7f09fd2c51f53f272cf2391f7a1ffde919c2c44a55818a68ef6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3518234,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1131497,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2501692,
+      "13": 773838,
+      "14": 1505515,
+      "15": 477443,
+      "16": 998012,
+      "17": 358947,
+      "18": 741865,
+      "19": 296615,
+      "20": 654977,
+      "21": 221226,
+      "22": 348974,
+      "23": 121917,
+      "24": 201299,
+      "25": 70586,
+      "26": 94063,
+      "27": 52389,
+      "28": 124606,
+      "29": 53200,
+      "3": 50831,
+      "30": 115488,
+      "31": 49218,
+      "32": 107640,
+      "33": 38433,
+      "34": 66463,
+      "35": 27853,
+      "36": 63218,
+      "37": 23190,
+      "38": 39644,
+      "39": 16352,
+      "4": 113022,
+      "40": 29821,
+      "41": 10885,
+      "42": 14198,
+      "43": 5856,
+      "44": 7766,
+      "45": 3729,
+      "46": 4244,
+      "47": 2500,
+      "48": 3593,
+      "49": 2217,
+      "5": 922131,
+      "50": 2925,
+      "51": 1836,
+      "52": 2736,
+      "53": 1733,
+      "54": 2466,
+      "55": 1724,
+      "56": 2547,
+      "57": 1768,
+      "58": 2281,
+      "59": 1692,
+      "6": 5244652,
+      "60": 2466,
+      "61": 1651,
+      "62": 2223,
+      "63": 1601,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1997932,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5970610,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1733013,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50831,
+      "7": 30792406,
+      "9": 113022
+    },
+    "connectivity_max": 138703001,
+    "connectivity_min": 0,
+    "n_cells": 30956259,
+    "n_connectivity_values": 339307388,
+    "n_fan_triangles": 277394870,
+    "n_points": 138703002
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.230532021702513e-11,
+    "float64_area_closure_relative": 1.8012279260393778e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277394870,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938932.6604210911,
+    "surface_area_float64_in2": 1938932.6605031183,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938932.6605031148,
+    "zero_area_triangles": 233526,
+    "zero_weight_points": 5465
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC094_AoA_16.json b/surface_dual_areas/cases/geo_LHC094_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..9dedbba443ecacb6a39c7fa2bdb46c780d63427e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC094_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC094_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC094_AoA_16/boundary_dual_area_geo_LHC094_AoA_16.npy",
+    "sha256": "ff7520a49f52de0b060c09ff1f61bd1f1bbf0e05a329444c6ebb0ed0a27b89fc",
+    "shape": [
+      145173356
+    ],
+    "size_bytes": 580693552
+  },
+  "runtime": {
+    "accumulation_seconds": 10.986187780974433,
+    "completed_at_utc": "2026-08-07T07:45:36.333489Z",
+    "elapsed_seconds": 21.133765468141064,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.232605635887012,
+    "geometry_read_seconds": 2.140403914032504,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:45:15.199632Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC094_AoA_16/boundary_geo_LHC094_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC094_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624403000000000,
+    "extracted_vtu_size_bytes": 22304881349,
+    "geometry_sha256": "138286fee73b5573915fb000a38430bebbf20d3a8c7b0b7b6d1b0ac5b4e81fe4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4164119,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1358198,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2696376,
+      "13": 843328,
+      "14": 1321910,
+      "15": 459089,
+      "16": 902198,
+      "17": 348756,
+      "18": 745976,
+      "19": 301919,
+      "20": 676834,
+      "21": 227350,
+      "22": 374018,
+      "23": 126064,
+      "24": 216102,
+      "25": 72813,
+      "26": 94244,
+      "27": 51995,
+      "28": 124065,
+      "29": 52809,
+      "3": 58321,
+      "30": 115129,
+      "31": 49568,
+      "32": 109933,
+      "33": 39049,
+      "34": 67813,
+      "35": 28198,
+      "36": 62574,
+      "37": 22917,
+      "38": 38238,
+      "39": 16105,
+      "4": 130551,
+      "40": 29066,
+      "41": 10632,
+      "42": 14133,
+      "43": 5790,
+      "44": 7637,
+      "45": 3606,
+      "46": 4115,
+      "47": 2491,
+      "48": 3535,
+      "49": 2119,
+      "5": 948927,
+      "50": 2924,
+      "51": 1861,
+      "52": 2717,
+      "53": 1753,
+      "54": 2457,
+      "55": 1711,
+      "56": 2498,
+      "57": 1748,
+      "58": 2292,
+      "59": 1746,
+      "6": 5240941,
+      "60": 2507,
+      "61": 1628,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2123846,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6441508,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1992743,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 58321,
+      "7": 32583544,
+      "9": 130551
+    },
+    "connectivity_max": 145173355,
+    "connectivity_min": 0,
+    "n_cells": 32772416,
+    "n_connectivity_values": 355880426,
+    "n_fan_triangles": 290335594,
+    "n_points": 145173356
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5736165972910204e-11,
+    "float64_area_closure_relative": 1.1608168628054202e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290335594,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945575.8403644043,
+    "surface_area_float64_in2": 1945575.8404339317,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945575.8404339543,
+    "zero_area_triangles": 236121,
+    "zero_weight_points": 5740
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC094_AoA_18.json b/surface_dual_areas/cases/geo_LHC094_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..83c04e7e0a8e4c6eb687b0a8fcfb96fa9974fadf
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC094_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC094_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC094_AoA_18/boundary_dual_area_geo_LHC094_AoA_18.npy",
+    "sha256": "1787cb3cb893f1e588617f20917c0449268d627edb31fc2612a704adb3accb1b",
+    "shape": [
+      145817911
+    ],
+    "size_bytes": 583271772
+  },
+  "runtime": {
+    "accumulation_seconds": 11.205307117197663,
+    "completed_at_utc": "2026-08-07T07:45:06.963563Z",
+    "elapsed_seconds": 21.496381192002445,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4138099048286676,
+    "geometry_read_seconds": 2.1265554500278085,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:44:45.467077Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC094_AoA_18/boundary_geo_LHC094_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC094_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624612000000000,
+    "extracted_vtu_size_bytes": 22405836639,
+    "geometry_sha256": "320689d45df57ca357dedb9ceaa0f631ca811af9ff7e4a11c5263187fa204360",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4264716,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1394841,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2717426,
+      "13": 836393,
+      "14": 1268286,
+      "15": 440452,
+      "16": 885725,
+      "17": 344576,
+      "18": 746141,
+      "19": 302744,
+      "20": 679765,
+      "21": 228959,
+      "22": 379313,
+      "23": 127567,
+      "24": 218873,
+      "25": 73470,
+      "26": 94481,
+      "27": 52056,
+      "28": 124084,
+      "29": 52806,
+      "3": 58898,
+      "30": 115134,
+      "31": 49563,
+      "32": 109931,
+      "33": 39049,
+      "34": 67811,
+      "35": 28201,
+      "36": 62566,
+      "37": 22912,
+      "38": 38236,
+      "39": 16108,
+      "4": 132325,
+      "40": 29069,
+      "41": 10630,
+      "42": 14138,
+      "43": 5790,
+      "44": 7641,
+      "45": 3608,
+      "46": 4116,
+      "47": 2491,
+      "48": 3535,
+      "49": 2119,
+      "5": 950886,
+      "50": 2924,
+      "51": 1861,
+      "52": 2717,
+      "53": 1753,
+      "54": 2457,
+      "55": 1711,
+      "56": 2498,
+      "57": 1748,
+      "58": 2292,
+      "59": 1746,
+      "6": 5251234,
+      "60": 2507,
+      "61": 1628,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2144885,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6505757,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2040787,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 58898,
+      "7": 32803639,
+      "9": 132325
+    },
+    "connectivity_max": 145817910,
+    "connectivity_min": 0,
+    "n_cells": 32994862,
+    "n_connectivity_values": 357614428,
+    "n_fan_triangles": 291624704,
+    "n_points": 145817911
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.571175410615238e-11,
+    "float64_area_closure_relative": 3.554253811660062e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 291624704,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945575.7755924591,
+    "surface_area_float64_in2": 1945575.775661939,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945575.7756620082,
+    "zero_area_triangles": 237180,
+    "zero_weight_points": 5769
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC096_AoA_18.json b/surface_dual_areas/cases/geo_LHC096_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..81e037c1a28f50e237f8938e3d50791d70fbb072
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC096_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC096_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC096_AoA_18/boundary_dual_area_geo_LHC096_AoA_18.npy",
+    "sha256": "52f040a377ba2b3a7747efb291382d246c9589ed756961e0118a3d4dca5091d2",
+    "shape": [
+      139124526
+    ],
+    "size_bytes": 556498232
+  },
+  "runtime": {
+    "accumulation_seconds": 12.092958013061434,
+    "completed_at_utc": "2026-08-07T08:21:03.687754Z",
+    "elapsed_seconds": 122.43209204007871,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.581802947912365,
+    "geometry_read_seconds": 39.381740919081494,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:19:01.255581Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC096_AoA_18/boundary_geo_LHC096_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC096_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624633000000000,
+    "extracted_vtu_size_bytes": 21366273087,
+    "geometry_sha256": "9889777f49e95e7a4b31200762ce320806fed490d9826c14e2f18a42d8950cbe",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3847627,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1192997,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2591675,
+      "13": 773682,
+      "14": 1345321,
+      "15": 459209,
+      "16": 911878,
+      "17": 352903,
+      "18": 755314,
+      "19": 304598,
+      "20": 676672,
+      "21": 226196,
+      "22": 355878,
+      "23": 123561,
+      "24": 204597,
+      "25": 69414,
+      "26": 95469,
+      "27": 51886,
+      "28": 124989,
+      "29": 52956,
+      "3": 50777,
+      "30": 115265,
+      "31": 49540,
+      "32": 109406,
+      "33": 38927,
+      "34": 67204,
+      "35": 28049,
+      "36": 62090,
+      "37": 23098,
+      "38": 38516,
+      "39": 16094,
+      "4": 112109,
+      "40": 29358,
+      "41": 10707,
+      "42": 14198,
+      "43": 5838,
+      "44": 7698,
+      "45": 3617,
+      "46": 4099,
+      "47": 2467,
+      "48": 3460,
+      "49": 2057,
+      "5": 917448,
+      "50": 2759,
+      "51": 1727,
+      "52": 2522,
+      "53": 1642,
+      "54": 2277,
+      "55": 1611,
+      "56": 2427,
+      "57": 1720,
+      "58": 2259,
+      "59": 1734,
+      "6": 5103371,
+      "60": 2505,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1980303,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5904612,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1776298,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 50777,
+      "7": 30874276,
+      "9": 112109
+    },
+    "connectivity_max": 139124525,
+    "connectivity_min": 0,
+    "n_cells": 31037162,
+    "n_connectivity_values": 340312249,
+    "n_fan_triangles": 278237925,
+    "n_points": 139124526
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.101908590855199e-11,
+    "float64_area_closure_relative": 6.455855290151883e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278237925,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936692.351635067,
+    "surface_area_float64_in2": 1936692.3517145084,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936692.3517143833,
+    "zero_area_triangles": 241286,
+    "zero_weight_points": 5601
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC097_AoA_12.json b/surface_dual_areas/cases/geo_LHC097_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..499436b8c454129ad0b1defec347fe92e9ec2798
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC097_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC097_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC097_AoA_12/boundary_dual_area_geo_LHC097_AoA_12.npy",
+    "sha256": "832d2f1e334b1c0380d5d6c4414ea5e46b28986f3107e7d7c6c59a2d560f90e4",
+    "shape": [
+      139913490
+    ],
+    "size_bytes": 559654088
+  },
+  "runtime": {
+    "accumulation_seconds": 11.784315963974223,
+    "completed_at_utc": "2026-08-07T07:47:34.315648Z",
+    "elapsed_seconds": 31.133369859075174,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.610673332121223,
+    "geometry_read_seconds": 11.070146524114534,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:47:03.182189Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC097_AoA_12/boundary_geo_LHC097_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC097_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624562000000000,
+    "extracted_vtu_size_bytes": 21489458484,
+    "geometry_sha256": "5739e542451e31647ffee50e58004695b82b160a888f4ec69bd4c8848cbb0011",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3679455,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1203098,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2603470,
+      "13": 808831,
+      "14": 1435877,
+      "15": 482202,
+      "16": 949462,
+      "17": 359076,
+      "18": 747180,
+      "19": 300811,
+      "20": 668614,
+      "21": 222780,
+      "22": 346674,
+      "23": 119329,
+      "24": 197614,
+      "25": 66732,
+      "26": 92633,
+      "27": 51060,
+      "28": 124121,
+      "29": 52960,
+      "3": 53329,
+      "30": 114693,
+      "31": 49467,
+      "32": 108462,
+      "33": 38846,
+      "34": 66776,
+      "35": 28146,
+      "36": 63153,
+      "37": 23031,
+      "38": 38998,
+      "39": 16268,
+      "4": 118292,
+      "40": 29388,
+      "41": 10767,
+      "42": 14238,
+      "43": 5750,
+      "44": 7587,
+      "45": 3671,
+      "46": 4245,
+      "47": 2485,
+      "48": 3533,
+      "49": 2143,
+      "5": 939126,
+      "50": 2962,
+      "51": 1841,
+      "52": 2810,
+      "53": 1767,
+      "54": 2401,
+      "55": 1713,
+      "56": 2535,
+      "57": 1734,
+      "58": 2285,
+      "59": 1720,
+      "6": 5193747,
+      "60": 2503,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2024274,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5978840,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1797804,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53329,
+      "7": 31122290,
+      "9": 118292
+    },
+    "connectivity_max": 139913489,
+    "connectivity_min": 0,
+    "n_cells": 31293911,
+    "n_connectivity_values": 342403675,
+    "n_fan_triangles": 279815853,
+    "n_points": 139913490
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.494593540991416e-11,
+    "float64_area_closure_relative": 6.136933897789601e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279815853,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938695.4607059162,
+    "surface_area_float64_in2": 1938695.4607736657,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938695.4607735467,
+    "zero_area_triangles": 237380,
+    "zero_weight_points": 5636
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC098_AoA_20.json b/surface_dual_areas/cases/geo_LHC098_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..06a6f71b834cc802e103b1236b797e4593d07f02
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC098_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC098_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC098_AoA_20/boundary_dual_area_geo_LHC098_AoA_20.npy",
+    "sha256": "286fd21e88ef80b5cd9ecaf9d417838cf8d63a213ef20aef5de46d155f5f1e1d",
+    "shape": [
+      137491077
+    ],
+    "size_bytes": 549964436
+  },
+  "runtime": {
+    "accumulation_seconds": 10.711340078152716,
+    "completed_at_utc": "2026-08-07T08:16:08.274719Z",
+    "elapsed_seconds": 21.377290921052918,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1784433741122484,
+    "geometry_read_seconds": 2.7095330010633916,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:15:46.897346Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC098_AoA_20/boundary_geo_LHC098_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC098_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624401000000000,
+    "extracted_vtu_size_bytes": 21116463575,
+    "geometry_sha256": "6476b70a5e4eb86c0c737da935b6c6d4fb2a80f85baaee9a31b2fb6ffd89cdbb",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3685770,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1165848,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2448474,
+      "13": 759304,
+      "14": 1248605,
+      "15": 451501,
+      "16": 898819,
+      "17": 352704,
+      "18": 748103,
+      "19": 301945,
+      "20": 673827,
+      "21": 227335,
+      "22": 383859,
+      "23": 126761,
+      "24": 218459,
+      "25": 71372,
+      "26": 96849,
+      "27": 52364,
+      "28": 124528,
+      "29": 53023,
+      "3": 49916,
+      "30": 114753,
+      "31": 49525,
+      "32": 109389,
+      "33": 38908,
+      "34": 67038,
+      "35": 28023,
+      "36": 62741,
+      "37": 22884,
+      "38": 38808,
+      "39": 16279,
+      "4": 114448,
+      "40": 29573,
+      "41": 10750,
+      "42": 14278,
+      "43": 5853,
+      "44": 7767,
+      "45": 3642,
+      "46": 4268,
+      "47": 2556,
+      "48": 3541,
+      "49": 2148,
+      "5": 933083,
+      "50": 2893,
+      "51": 1838,
+      "52": 2743,
+      "53": 1755,
+      "54": 2425,
+      "55": 1731,
+      "56": 2577,
+      "57": 1721,
+      "58": 2298,
+      "59": 1698,
+      "6": 5167604,
+      "60": 2446,
+      "61": 1665,
+      "62": 2198,
+      "63": 1587,
+      "64": 2149,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2014194,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5896395,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1772431,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49916,
+      "7": 30550434,
+      "9": 114448
+    },
+    "connectivity_max": 137491076,
+    "connectivity_min": 0,
+    "n_cells": 30714798,
+    "n_connectivity_values": 336400628,
+    "n_fan_triangles": 274971032,
+    "n_points": 137491077
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.008244740909798e-11,
+    "float64_area_closure_relative": 1.080071709837782e-13,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274971032,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935815.150868055,
+    "surface_area_float64_in2": 1935815.1509456472,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935815.1509458562,
+    "zero_area_triangles": 234029,
+    "zero_weight_points": 5406
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC099_AoA_12.json b/surface_dual_areas/cases/geo_LHC099_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..cd4eb0e19f098dada261231710c5f5b2cfb5bc88
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC099_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC099_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC099_AoA_12/boundary_dual_area_geo_LHC099_AoA_12.npy",
+    "sha256": "f0c21b67330d8c09e76421bbbef0f2efcfaf110fae4207d6d570da6751164788",
+    "shape": [
+      143899235
+    ],
+    "size_bytes": 575597068
+  },
+  "runtime": {
+    "accumulation_seconds": 10.988160948036239,
+    "completed_at_utc": "2026-08-07T07:47:04.123041Z",
+    "elapsed_seconds": 21.054561611963436,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2937269010581076,
+    "geometry_read_seconds": 2.0673605538904667,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:46:43.068386Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC099_AoA_12/boundary_geo_LHC099_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC099_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624689000000000,
+    "extracted_vtu_size_bytes": 22104600398,
+    "geometry_sha256": "971729f6895ed5f2a99d9befa550260313e9226f3d7f1490918967de14811f91",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3928135,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1250053,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2759452,
+      "13": 819950,
+      "14": 1473381,
+      "15": 476534,
+      "16": 956463,
+      "17": 354198,
+      "18": 745657,
+      "19": 299636,
+      "20": 670290,
+      "21": 223970,
+      "22": 361969,
+      "23": 123166,
+      "24": 208909,
+      "25": 71523,
+      "26": 93559,
+      "27": 52437,
+      "28": 123902,
+      "29": 53274,
+      "3": 56377,
+      "30": 115491,
+      "31": 49492,
+      "32": 107720,
+      "33": 38648,
+      "34": 66272,
+      "35": 28060,
+      "36": 62356,
+      "37": 23024,
+      "38": 38515,
+      "39": 16191,
+      "4": 127266,
+      "40": 29381,
+      "41": 10701,
+      "42": 14238,
+      "43": 5793,
+      "44": 7634,
+      "45": 3597,
+      "46": 4113,
+      "47": 2499,
+      "48": 3500,
+      "49": 2103,
+      "5": 936204,
+      "50": 2936,
+      "51": 1862,
+      "52": 2769,
+      "53": 1768,
+      "54": 2445,
+      "55": 1717,
+      "56": 2532,
+      "57": 1748,
+      "58": 2287,
+      "59": 1745,
+      "6": 5251350,
+      "60": 2508,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2039981,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6322281,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1849859,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 56377,
+      "7": 32120330,
+      "9": 127266
+    },
+    "connectivity_max": 143899234,
+    "connectivity_min": 0,
+    "n_cells": 32303973,
+    "n_connectivity_values": 352395302,
+    "n_fan_triangles": 287787356,
+    "n_points": 143899235
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.026244329972702e-11,
+    "float64_area_closure_relative": 1.830959632170059e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 287787356,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945596.6069217585,
+    "surface_area_float64_in2": 1945596.607000093,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945596.6070000574,
+    "zero_area_triangles": 271833,
+    "zero_weight_points": 6014
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC099_AoA_8.json b/surface_dual_areas/cases/geo_LHC099_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..6675d567bc1fa66a9982872bc7b4109e1f00ecd9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC099_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC099_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC099_AoA_8/boundary_dual_area_geo_LHC099_AoA_8.npy",
+    "sha256": "def5aa517fa1b509756478f54f05022208ccf2217ca3435a1a36c888d3be640c",
+    "shape": [
+      138046333
+    ],
+    "size_bytes": 552185460
+  },
+  "runtime": {
+    "accumulation_seconds": 10.691365611972287,
+    "completed_at_utc": "2026-08-07T08:17:47.907252Z",
+    "elapsed_seconds": 53.83079238794744,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.260752516100183,
+    "geometry_read_seconds": 35.17879135790281,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:16:54.076377Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC099_AoA_8/boundary_geo_LHC099_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC099_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624387000000000,
+    "extracted_vtu_size_bytes": 21194627102,
+    "geometry_sha256": "187eed394f8ea92dcc2343b90d7bb1ff03fedf632f9b84ce570ef535c610540c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3163589,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 994250,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2391397,
+      "13": 790452,
+      "14": 1714813,
+      "15": 550417,
+      "16": 1036764,
+      "17": 376972,
+      "18": 747822,
+      "19": 300552,
+      "20": 668909,
+      "21": 223932,
+      "22": 361837,
+      "23": 123201,
+      "24": 209304,
+      "25": 71597,
+      "26": 93766,
+      "27": 52474,
+      "28": 123954,
+      "29": 53280,
+      "3": 53027,
+      "30": 115498,
+      "31": 49499,
+      "32": 107719,
+      "33": 38645,
+      "34": 66271,
+      "35": 28060,
+      "36": 62360,
+      "37": 23021,
+      "38": 38513,
+      "39": 16197,
+      "4": 125425,
+      "40": 29381,
+      "41": 10701,
+      "42": 14240,
+      "43": 5793,
+      "44": 7634,
+      "45": 3596,
+      "46": 4112,
+      "47": 2499,
+      "48": 3500,
+      "49": 2103,
+      "5": 933980,
+      "50": 2936,
+      "51": 1862,
+      "52": 2769,
+      "53": 1768,
+      "54": 2445,
+      "55": 1717,
+      "56": 2532,
+      "57": 1748,
+      "58": 2287,
+      "59": 1745,
+      "6": 5247805,
+      "60": 2508,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1944963,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5939635,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1585893,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53027,
+      "7": 30375769,
+      "9": 125425
+    },
+    "connectivity_max": 138046332,
+    "connectivity_min": 0,
+    "n_cells": 30554221,
+    "n_connectivity_values": 337189994,
+    "n_fan_triangles": 276081552,
+    "n_points": 138046333
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.931677823277448e-11,
+    "float64_area_closure_relative": 4.344038356891094e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276081552,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945598.0058039483,
+    "surface_area_float64_in2": 1945598.005880443,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945598.0058805274,
+    "zero_area_triangles": 261853,
+    "zero_weight_points": 5297
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC100_AoA_12.json b/surface_dual_areas/cases/geo_LHC100_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..e38ef8a1d283f05d5d30a2422131d74ecacc23f2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC100_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC100_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC100_AoA_12/boundary_dual_area_geo_LHC100_AoA_12.npy",
+    "sha256": "9714338cbf8eb036e5b30e07fbc8331b161a620803d31839c49f09f28d1c1cc3",
+    "shape": [
+      148349679
+    ],
+    "size_bytes": 593398844
+  },
+  "runtime": {
+    "accumulation_seconds": 11.489420305937529,
+    "completed_at_utc": "2026-08-07T08:18:10.936049Z",
+    "elapsed_seconds": 22.039879343938082,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.322238663909957,
+    "geometry_read_seconds": 2.298592329956591,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:17:48.896077Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC100_AoA_12/boundary_geo_LHC100_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC100_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624561000000000,
+    "extracted_vtu_size_bytes": 22794648656,
+    "geometry_sha256": "0463a94d9f339d457a052d6bde13ec0c6fce2f134f6a3520a3883f189b65c8c5",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4334947,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1364885,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3093677,
+      "13": 866328,
+      "14": 1393346,
+      "15": 478253,
+      "16": 954363,
+      "17": 368854,
+      "18": 748114,
+      "19": 306143,
+      "20": 665809,
+      "21": 220755,
+      "22": 335026,
+      "23": 115884,
+      "24": 185987,
+      "25": 66608,
+      "26": 88462,
+      "27": 50735,
+      "28": 123125,
+      "29": 52668,
+      "3": 57788,
+      "30": 114403,
+      "31": 49135,
+      "32": 109668,
+      "33": 38589,
+      "34": 66718,
+      "35": 27599,
+      "36": 62570,
+      "37": 22794,
+      "38": 38835,
+      "39": 16222,
+      "4": 131585,
+      "40": 30046,
+      "41": 11001,
+      "42": 14424,
+      "43": 5931,
+      "44": 7930,
+      "45": 3767,
+      "46": 4284,
+      "47": 2536,
+      "48": 3626,
+      "49": 2203,
+      "5": 945561,
+      "50": 2902,
+      "51": 1790,
+      "52": 2627,
+      "53": 1715,
+      "54": 2363,
+      "55": 1696,
+      "56": 2514,
+      "57": 1757,
+      "58": 2263,
+      "59": 1691,
+      "6": 5249295,
+      "60": 2465,
+      "61": 1653,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2131720,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6561623,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1990981,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57788,
+      "7": 33369906,
+      "9": 131585
+    },
+    "connectivity_max": 148349678,
+    "connectivity_min": 0,
+    "n_cells": 33559279,
+    "n_connectivity_values": 363806789,
+    "n_fan_triangles": 296688231,
+    "n_points": 148349679
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9539934140272513e-11,
+    "float64_area_closure_relative": 2.393255664790666e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296688231,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945723.1174257249,
+    "surface_area_float64_in2": 1945723.1175026586,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945723.117502659,
+    "zero_area_triangles": 244733,
+    "zero_weight_points": 6168
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC101_AoA_20.json b/surface_dual_areas/cases/geo_LHC101_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc74b00d1dc17934bcb1555816955876bb0e44f2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC101_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC101_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC101_AoA_20/boundary_dual_area_geo_LHC101_AoA_20.npy",
+    "sha256": "a9134a4fb431fbdfa1a57b5ef7ad96f5491665e8016ea0344d340f512a820576",
+    "shape": [
+      149035272
+    ],
+    "size_bytes": 596141216
+  },
+  "runtime": {
+    "accumulation_seconds": 11.41431358200498,
+    "completed_at_utc": "2026-08-07T07:48:12.610090Z",
+    "elapsed_seconds": 22.554129028925672,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.333365862024948,
+    "geometry_read_seconds": 2.791665649972856,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:47:50.055867Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC101_AoA_20/boundary_geo_LHC101_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC101_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624690000000000,
+    "extracted_vtu_size_bytes": 22904544810,
+    "geometry_sha256": "7f2030cc4d72698d737229243a696b578e72ee136e1795c7a40f1f1677d65eda",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4602235,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1439107,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2969822,
+      "13": 841192,
+      "14": 1224852,
+      "15": 433530,
+      "16": 888700,
+      "17": 346493,
+      "18": 751418,
+      "19": 300876,
+      "20": 682967,
+      "21": 223597,
+      "22": 369261,
+      "23": 122799,
+      "24": 211613,
+      "25": 71543,
+      "26": 92202,
+      "27": 52095,
+      "28": 124044,
+      "29": 53139,
+      "3": 61668,
+      "30": 114825,
+      "31": 49424,
+      "32": 108545,
+      "33": 38788,
+      "34": 66292,
+      "35": 27946,
+      "36": 61662,
+      "37": 22894,
+      "38": 38489,
+      "39": 16297,
+      "4": 139744,
+      "40": 29293,
+      "41": 10743,
+      "42": 14320,
+      "43": 5848,
+      "44": 7669,
+      "45": 3627,
+      "46": 4155,
+      "47": 2469,
+      "48": 3515,
+      "49": 2097,
+      "5": 953434,
+      "50": 2894,
+      "51": 1852,
+      "52": 2778,
+      "53": 1776,
+      "54": 2466,
+      "55": 1703,
+      "56": 2536,
+      "57": 1759,
+      "58": 2287,
+      "59": 1750,
+      "6": 5283841,
+      "60": 2509,
+      "61": 1626,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2141346,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6756752,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2084384,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 61668,
+      "7": 33695001,
+      "9": 139744
+    },
+    "connectivity_max": 149035271,
+    "connectivity_min": 0,
+    "n_cells": 33896413,
+    "n_connectivity_values": 365852248,
+    "n_fan_triangles": 298059422,
+    "n_points": 149035272
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.7412467455702814e-11,
+    "float64_area_closure_relative": 2.175970636977995e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 298059422,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947414.9339749312,
+    "surface_area_float64_in2": 1947414.9340477888,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947414.9340477465,
+    "zero_area_triangles": 241759,
+    "zero_weight_points": 6026
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC102_AoA_18.json b/surface_dual_areas/cases/geo_LHC102_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..e185b1ef1ad43d2cd44777b53b4666f85dbe30c6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC102_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC102_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC102_AoA_18/boundary_dual_area_geo_LHC102_AoA_18.npy",
+    "sha256": "2b1393e2e4b954a980adba676b252aab2356551f11f75e411cd9eb76a399604e",
+    "shape": [
+      142098122
+    ],
+    "size_bytes": 568392616
+  },
+  "runtime": {
+    "accumulation_seconds": 10.952466804999858,
+    "completed_at_utc": "2026-08-07T08:23:51.164745Z",
+    "elapsed_seconds": 23.21078816591762,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.304220660123974,
+    "geometry_read_seconds": 3.1078815450891852,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:23:27.953877Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC102_AoA_18/boundary_geo_LHC102_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC102_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624600000000000,
+    "extracted_vtu_size_bytes": 21833440753,
+    "geometry_sha256": "86bc411f80f5111b559e6d40ce73ea25a138d19f03f4c799389e3c5b908f64c9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4192259,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1257027,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2671974,
+      "13": 754770,
+      "14": 1191353,
+      "15": 433216,
+      "16": 892405,
+      "17": 356816,
+      "18": 752424,
+      "19": 306926,
+      "20": 669748,
+      "21": 226152,
+      "22": 361376,
+      "23": 122537,
+      "24": 203837,
+      "25": 69136,
+      "26": 94365,
+      "27": 52086,
+      "28": 124755,
+      "29": 53167,
+      "3": 51935,
+      "30": 115226,
+      "31": 49126,
+      "32": 107842,
+      "33": 38302,
+      "34": 65131,
+      "35": 27560,
+      "36": 62190,
+      "37": 22947,
+      "38": 39510,
+      "39": 16514,
+      "4": 123266,
+      "40": 30461,
+      "41": 11055,
+      "42": 14518,
+      "43": 5993,
+      "44": 7917,
+      "45": 3740,
+      "46": 4288,
+      "47": 2533,
+      "48": 3560,
+      "49": 2187,
+      "5": 941820,
+      "50": 2931,
+      "51": 1852,
+      "52": 2736,
+      "53": 1772,
+      "54": 2436,
+      "55": 1737,
+      "56": 2569,
+      "57": 1781,
+      "58": 2280,
+      "59": 1690,
+      "6": 5273387,
+      "60": 2467,
+      "61": 1651,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2064324,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6315096,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1888465,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51935,
+      "7": 31944963,
+      "9": 123266
+    },
+    "connectivity_max": 142098121,
+    "connectivity_min": 0,
+    "n_cells": 32120164,
+    "n_connectivity_values": 348425496,
+    "n_fan_triangles": 284185168,
+    "n_points": 142098122
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1214215082457866e-11,
+    "float64_area_closure_relative": 6.124178060426601e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284185168,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938931.6752082729,
+    "surface_area_float64_in2": 1938931.675268795,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938931.675268807,
+    "zero_area_triangles": 234625,
+    "zero_weight_points": 5393
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC103_AoA_22.json b/surface_dual_areas/cases/geo_LHC103_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..f6986a371209ae754b4ff5e7f11a3929103354ae
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC103_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC103_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC103_AoA_22/boundary_dual_area_geo_LHC103_AoA_22.npy",
+    "sha256": "2a8f66583e69494a0136c297753c11fae136690a1f3dda6b5a28b7b22c0ebb8c",
+    "shape": [
+      143121676
+    ],
+    "size_bytes": 572486832
+  },
+  "runtime": {
+    "accumulation_seconds": 10.880874183960259,
+    "completed_at_utc": "2026-08-07T08:24:39.726600Z",
+    "elapsed_seconds": 22.28521126206033,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2236211749259382,
+    "geometry_read_seconds": 3.4041760182008147,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:24:17.441290Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC103_AoA_22/boundary_geo_LHC103_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC103_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624639000000000,
+    "extracted_vtu_size_bytes": 21985197834,
+    "geometry_sha256": "0fc75330544c992c773f9ac1aa05d0cff4e433be63d58ee120067c8cdd584606",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3944662,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1305292,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2651361,
+      "13": 837010,
+      "14": 1372056,
+      "15": 470971,
+      "16": 916129,
+      "17": 347736,
+      "18": 741521,
+      "19": 298720,
+      "20": 673915,
+      "21": 227662,
+      "22": 378325,
+      "23": 127622,
+      "24": 216441,
+      "25": 72715,
+      "26": 94461,
+      "27": 51974,
+      "28": 123824,
+      "29": 52533,
+      "3": 56936,
+      "30": 114906,
+      "31": 48980,
+      "32": 109573,
+      "33": 38675,
+      "34": 66923,
+      "35": 28159,
+      "36": 63608,
+      "37": 23081,
+      "38": 38919,
+      "39": 16138,
+      "4": 128243,
+      "40": 29266,
+      "41": 10626,
+      "42": 13985,
+      "43": 5782,
+      "44": 7745,
+      "45": 3672,
+      "46": 4230,
+      "47": 2529,
+      "48": 3576,
+      "49": 2198,
+      "5": 938367,
+      "50": 2900,
+      "51": 1855,
+      "52": 2723,
+      "53": 1734,
+      "54": 2362,
+      "55": 1720,
+      "56": 2525,
+      "57": 1753,
+      "58": 2263,
+      "59": 1687,
+      "6": 5205553,
+      "60": 2469,
+      "61": 1652,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1377,
+      "66": 1811,
+      "67": 1113,
+      "68": 1527,
+      "69": 920,
+      "7": 2077033,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6227176,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1915531,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56936,
+      "7": 31945842,
+      "9": 128243
+    },
+    "connectivity_max": 143121675,
+    "connectivity_min": 0,
+    "n_cells": 32131021,
+    "n_connectivity_values": 350494276,
+    "n_fan_triangles": 286232234,
+    "n_points": 143121676
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.108967962240642e-11,
+    "float64_area_closure_relative": 1.1360957815020173e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 286232234,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946923.0945639831,
+    "surface_area_float64_in2": 1946923.0946245124,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946923.0946244902,
+    "zero_area_triangles": 235552,
+    "zero_weight_points": 5562
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC103_AoA_8.json b/surface_dual_areas/cases/geo_LHC103_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..e4ea95eb4ca9aa683b08fe82c1c67e3fcf722553
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC103_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC103_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC103_AoA_8/boundary_dual_area_geo_LHC103_AoA_8.npy",
+    "sha256": "5c86182bd344a1669371d06b9ae31745e6112325bc3a6abd71e3c36c923ae6c9",
+    "shape": [
+      133676947
+    ],
+    "size_bytes": 534707916
+  },
+  "runtime": {
+    "accumulation_seconds": 10.167099687969312,
+    "completed_at_utc": "2026-08-07T07:48:08.112065Z",
+    "elapsed_seconds": 19.769464862067252,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9114440518897027,
+    "geometry_read_seconds": 2.1166250901296735,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:47:48.342504Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC103_AoA_8/boundary_geo_LHC103_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC103_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624593000000000,
+    "extracted_vtu_size_bytes": 20516113041,
+    "geometry_sha256": "64b9935258c80a6014a5ffc4bfbbb9b87c19e2635a02c06d2b87f6ab0faf3185",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2726776,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 951894,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2064242,
+      "13": 798746,
+      "14": 1768849,
+      "15": 573337,
+      "16": 1024871,
+      "17": 375662,
+      "18": 749441,
+      "19": 301307,
+      "20": 676485,
+      "21": 228346,
+      "22": 380559,
+      "23": 127431,
+      "24": 215445,
+      "25": 72537,
+      "26": 93852,
+      "27": 51895,
+      "28": 123816,
+      "29": 52521,
+      "3": 54630,
+      "30": 114895,
+      "31": 48974,
+      "32": 109560,
+      "33": 38677,
+      "34": 66913,
+      "35": 28163,
+      "36": 63605,
+      "37": 23083,
+      "38": 38941,
+      "39": 16141,
+      "4": 123257,
+      "40": 29269,
+      "41": 10631,
+      "42": 13983,
+      "43": 5782,
+      "44": 7751,
+      "45": 3671,
+      "46": 4230,
+      "47": 2529,
+      "48": 3576,
+      "49": 2197,
+      "5": 930504,
+      "50": 2900,
+      "51": 1856,
+      "52": 2723,
+      "53": 1734,
+      "54": 2362,
+      "55": 1720,
+      "56": 2525,
+      "57": 1753,
+      "58": 2263,
+      "59": 1687,
+      "6": 5177589,
+      "60": 2469,
+      "61": 1652,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1377,
+      "66": 1811,
+      "67": 1113,
+      "68": 1527,
+      "69": 920,
+      "7": 1926649,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5491355,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1541176,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54630,
+      "7": 29102538,
+      "9": 123257
+    },
+    "connectivity_max": 133676946,
+    "connectivity_min": 0,
+    "n_cells": 29280425,
+    "n_connectivity_values": 325903626,
+    "n_fan_triangles": 267342776,
+    "n_points": 133676947
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.167646696394883e-11,
+    "float64_area_closure_relative": 7.0557447235065984e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 267342776,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946925.308873148,
+    "surface_area_float64_in2": 1946925.3089348197,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946925.3089348334,
+    "zero_area_triangles": 222273,
+    "zero_weight_points": 4593
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC104_AoA_4.json b/surface_dual_areas/cases/geo_LHC104_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b7ced6bce6b920535982f427a7dd99f088baf66
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC104_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC104_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC104_AoA_4/boundary_dual_area_geo_LHC104_AoA_4.npy",
+    "sha256": "381e99cf99dd2852b2438565cdd5d77f393d132950c6125bc429441920aef6e1",
+    "shape": [
+      138509067
+    ],
+    "size_bytes": 554036396
+  },
+  "runtime": {
+    "accumulation_seconds": 12.903361954027787,
+    "completed_at_utc": "2026-08-07T08:20:32.112303Z",
+    "elapsed_seconds": 41.87069419794716,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.7452063360251486,
+    "geometry_read_seconds": 20.28809526702389,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:19:50.241533Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC104_AoA_4/boundary_geo_LHC104_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC104_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624680000000000,
+    "extracted_vtu_size_bytes": 21266533335,
+    "geometry_sha256": "674125a3e5908d637b6cb1280102fd115cdf440205d809771f6681f02f875d2b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3071930,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 991151,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2317911,
+      "13": 772584,
+      "14": 1748020,
+      "15": 551603,
+      "16": 1052114,
+      "17": 381340,
+      "18": 755696,
+      "19": 302162,
+      "20": 681412,
+      "21": 227707,
+      "22": 380311,
+      "23": 125707,
+      "24": 205509,
+      "25": 69973,
+      "26": 90521,
+      "27": 51317,
+      "28": 123319,
+      "29": 53113,
+      "3": 57464,
+      "30": 114829,
+      "31": 49427,
+      "32": 109423,
+      "33": 39043,
+      "34": 67113,
+      "35": 28136,
+      "36": 63131,
+      "37": 23013,
+      "38": 38883,
+      "39": 16245,
+      "4": 133412,
+      "40": 29318,
+      "41": 10633,
+      "42": 14004,
+      "43": 5752,
+      "44": 7591,
+      "45": 3651,
+      "46": 4276,
+      "47": 2568,
+      "48": 3564,
+      "49": 2121,
+      "5": 943080,
+      "50": 2931,
+      "51": 1803,
+      "52": 2602,
+      "53": 1668,
+      "54": 2252,
+      "55": 1637,
+      "56": 2440,
+      "57": 1708,
+      "58": 2255,
+      "59": 1717,
+      "6": 5282870,
+      "60": 2505,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2016848,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5971514,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1655657,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57464,
+      "7": 30500210,
+      "9": 133412
+    },
+    "connectivity_max": 138509066,
+    "connectivity_min": 0,
+    "n_cells": 30691086,
+    "n_connectivity_values": 338389189,
+    "n_fan_triangles": 277007017,
+    "n_points": 138509067
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.8240702553381936e-11,
+    "float64_area_closure_relative": 9.207711612653333e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277007017,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947059.195036647,
+    "surface_area_float64_in2": 1947059.1951111038,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947059.195111086,
+    "zero_area_triangles": 228337,
+    "zero_weight_points": 5088
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC105_AoA_10.json b/surface_dual_areas/cases/geo_LHC105_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..59acc6cd99a974319919e7474fb65d10282f5908
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC105_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC105_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC105_AoA_10/boundary_dual_area_geo_LHC105_AoA_10.npy",
+    "sha256": "8373254141badaae3353c49ad9b3dce1d2ce95e86d01bcd529b27236ffa1ae39",
+    "shape": [
+      135733802
+    ],
+    "size_bytes": 542935336
+  },
+  "runtime": {
+    "accumulation_seconds": 10.845336897065863,
+    "completed_at_utc": "2026-08-07T08:24:18.689564Z",
+    "elapsed_seconds": 50.73560934700072,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1905294901225716,
+    "geometry_read_seconds": 32.52594125107862,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:23:27.953847Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC105_AoA_10/boundary_geo_LHC105_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC105_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624706000000000,
+    "extracted_vtu_size_bytes": 20833983356,
+    "geometry_sha256": "a6cad6be1f08302ac3e8d0964bb36e5aee7e1bddb5827e08cfce67e2322211a7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2872995,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 998878,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2169266,
+      "13": 838127,
+      "14": 1771616,
+      "15": 594588,
+      "16": 1025116,
+      "17": 385160,
+      "18": 744293,
+      "19": 299415,
+      "20": 667652,
+      "21": 223181,
+      "22": 367399,
+      "23": 124447,
+      "24": 214960,
+      "25": 72842,
+      "26": 94189,
+      "27": 52394,
+      "28": 123470,
+      "29": 53046,
+      "3": 54119,
+      "30": 115277,
+      "31": 49675,
+      "32": 109543,
+      "33": 39038,
+      "34": 67105,
+      "35": 28004,
+      "36": 62296,
+      "37": 22785,
+      "38": 38267,
+      "39": 15978,
+      "4": 124631,
+      "40": 29053,
+      "41": 10567,
+      "42": 14184,
+      "43": 5813,
+      "44": 7603,
+      "45": 3617,
+      "46": 4135,
+      "47": 2502,
+      "48": 3500,
+      "49": 2076,
+      "5": 931618,
+      "50": 2826,
+      "51": 1783,
+      "52": 2639,
+      "53": 1702,
+      "54": 2373,
+      "55": 1676,
+      "56": 2482,
+      "57": 1726,
+      "58": 2281,
+      "59": 1743,
+      "6": 5127489,
+      "60": 2507,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 1951152,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5674122,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1587184,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 54119,
+      "7": 29639906,
+      "9": 124631
+    },
+    "connectivity_max": 135733801,
+    "connectivity_min": 0,
+    "n_cells": 29818656,
+    "n_connectivity_values": 331093798,
+    "n_fan_triangles": 271456486,
+    "n_points": 135733802
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.304797609477915e-11,
+    "float64_area_closure_relative": 3.3397062850208504e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 271456486,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945073.7290278713,
+    "surface_area_float64_in2": 1945073.7291116028,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945073.7291116677,
+    "zero_area_triangles": 222432,
+    "zero_weight_points": 4748
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC106_AoA_10.json b/surface_dual_areas/cases/geo_LHC106_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..d0a910c392ecb927705cbc085a550ada87c53204
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC106_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC106_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC106_AoA_10/boundary_dual_area_geo_LHC106_AoA_10.npy",
+    "sha256": "5f1196c9ef81080ddc40009395874fedfe2e1be19f3515cbababe7d897b36791",
+    "shape": [
+      134636915
+    ],
+    "size_bytes": 538547788
+  },
+  "runtime": {
+    "accumulation_seconds": 10.42256281315349,
+    "completed_at_utc": "2026-08-07T08:25:55.127246Z",
+    "elapsed_seconds": 20.52984037809074,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1994983539916575,
+    "geometry_read_seconds": 2.1206181389279664,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:25:34.597322Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC106_AoA_10/boundary_geo_LHC106_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC106_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624658000000000,
+    "extracted_vtu_size_bytes": 20665710294,
+    "geometry_sha256": "8425d2cf2d495f4e9ef9d7e1d886b8816a88c2b95083b61bee1b6cf66336d8e7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2749006,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1011492,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2034066,
+      "13": 819045,
+      "14": 1732896,
+      "15": 569330,
+      "16": 1026768,
+      "17": 379160,
+      "18": 759383,
+      "19": 303755,
+      "20": 685909,
+      "21": 227897,
+      "22": 380143,
+      "23": 126487,
+      "24": 213751,
+      "25": 72089,
+      "26": 93303,
+      "27": 52176,
+      "28": 124526,
+      "29": 53015,
+      "3": 53759,
+      "30": 115809,
+      "31": 49656,
+      "32": 109554,
+      "33": 39074,
+      "34": 68065,
+      "35": 28203,
+      "36": 62112,
+      "37": 22522,
+      "38": 37786,
+      "39": 15966,
+      "4": 125781,
+      "40": 28697,
+      "41": 10472,
+      "42": 14135,
+      "43": 5785,
+      "44": 7799,
+      "45": 3649,
+      "46": 4346,
+      "47": 2573,
+      "48": 3521,
+      "49": 2093,
+      "5": 943653,
+      "50": 2794,
+      "51": 1733,
+      "52": 2429,
+      "53": 1589,
+      "54": 2161,
+      "55": 1587,
+      "56": 2440,
+      "57": 1669,
+      "58": 2275,
+      "59": 1680,
+      "6": 5156125,
+      "60": 2441,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1370,
+      "66": 1770,
+      "67": 1096,
+      "68": 1503,
+      "69": 880,
+      "7": 1978208,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5621657,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1612888,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53759,
+      "7": 29401770,
+      "9": 125781
+    },
+    "connectivity_max": 134636914,
+    "connectivity_min": 0,
+    "n_cells": 29581310,
+    "n_connectivity_values": 328425315,
+    "n_fan_triangles": 269262695,
+    "n_points": 134636915
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.920229100604137e-11,
+    "float64_area_closure_relative": 1.9160220919119447e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 269262695,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944283.5831806676,
+    "surface_area_float64_in2": 1944283.583256888,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944283.5832569252,
+    "zero_area_triangles": 223112,
+    "zero_weight_points": 4733
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC106_AoA_12.json b/surface_dual_areas/cases/geo_LHC106_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..fb68ffbf22e27ddf11787584de09e62accab52c9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC106_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC106_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC106_AoA_12/boundary_dual_area_geo_LHC106_AoA_12.npy",
+    "sha256": "f2de3d5a8ae5797cda273d618c5cd575d0f0a4eee9e941ca053f7c48817d25f9",
+    "shape": [
+      137148438
+    ],
+    "size_bytes": 548593880
+  },
+  "runtime": {
+    "accumulation_seconds": 10.508922185050324,
+    "completed_at_utc": "2026-08-07T08:21:35.781832Z",
+    "elapsed_seconds": 21.19374145101756,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1126101720146835,
+    "geometry_read_seconds": 2.9710473001468927,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:21:14.588001Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC106_AoA_12/boundary_geo_LHC106_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC106_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624451000000000,
+    "extracted_vtu_size_bytes": 21055918599,
+    "geometry_sha256": "a36f5ea912308c8b10aed1ec739817e2cb1c419a1f572af8bb1658fd156549c9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3050911,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1106933,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2216634,
+      "13": 833949,
+      "14": 1627276,
+      "15": 541952,
+      "16": 1001836,
+      "17": 371889,
+      "18": 757670,
+      "19": 302648,
+      "20": 684021,
+      "21": 227227,
+      "22": 378210,
+      "23": 126122,
+      "24": 213148,
+      "25": 72000,
+      "26": 93232,
+      "27": 52158,
+      "28": 124512,
+      "29": 53020,
+      "3": 52564,
+      "30": 115813,
+      "31": 49629,
+      "32": 109580,
+      "33": 39088,
+      "34": 68072,
+      "35": 28199,
+      "36": 62131,
+      "37": 22526,
+      "38": 37789,
+      "39": 15976,
+      "4": 124731,
+      "40": 28687,
+      "41": 10476,
+      "42": 14139,
+      "43": 5795,
+      "44": 7798,
+      "45": 3648,
+      "46": 4347,
+      "47": 2577,
+      "48": 3523,
+      "49": 2094,
+      "5": 941264,
+      "50": 2794,
+      "51": 1734,
+      "52": 2429,
+      "53": 1587,
+      "54": 2161,
+      "55": 1588,
+      "56": 2440,
+      "57": 1669,
+      "58": 2275,
+      "59": 1680,
+      "6": 5153017,
+      "60": 2441,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1370,
+      "66": 1770,
+      "67": 1096,
+      "68": 1503,
+      "69": 880,
+      "7": 2015761,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5814997,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1708632,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52564,
+      "7": 30144131,
+      "9": 124731
+    },
+    "connectivity_max": 137148437,
+    "connectivity_min": 0,
+    "n_cells": 30321426,
+    "n_connectivity_values": 334928593,
+    "n_fan_triangles": 274285741,
+    "n_points": 137148438
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9632333774891766e-11,
+    "float64_area_closure_relative": 6.885707096300937e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274285741,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944282.819807851,
+    "surface_area_float64_in2": 1944282.8198849075,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944282.8198850413,
+    "zero_area_triangles": 226843,
+    "zero_weight_points": 5007
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC106_AoA_6.json b/surface_dual_areas/cases/geo_LHC106_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..2db6e8da659cf1a6ceebab2e4e05e81df69f4ac6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC106_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC106_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC106_AoA_6/boundary_dual_area_geo_LHC106_AoA_6.npy",
+    "sha256": "57bded3405147d21a0a8d70fdee7d70e74189eeba7b0c2bfd01242d0b1a02318",
+    "shape": [
+      134309605
+    ],
+    "size_bytes": 537238548
+  },
+  "runtime": {
+    "accumulation_seconds": 10.354118924820796,
+    "completed_at_utc": "2026-08-07T08:24:48.741460Z",
+    "elapsed_seconds": 19.83647446008399,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.963124447967857,
+    "geometry_read_seconds": 2.1183097190223634,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:24:28.904898Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC106_AoA_6/boundary_geo_LHC106_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC106_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624711000000000,
+    "extracted_vtu_size_bytes": 20614302514,
+    "geometry_sha256": "6c0122d475febc2671e1f48e4dfeb3ba1d87dbd83cd473067ae6a8ae67de38a0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2759860,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1008540,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2078415,
+      "13": 817227,
+      "14": 1697642,
+      "15": 565096,
+      "16": 1021925,
+      "17": 379451,
+      "18": 761619,
+      "19": 304472,
+      "20": 687578,
+      "21": 228529,
+      "22": 381079,
+      "23": 126806,
+      "24": 214118,
+      "25": 72176,
+      "26": 93242,
+      "27": 52137,
+      "28": 124439,
+      "29": 53001,
+      "3": 55215,
+      "30": 115816,
+      "31": 49619,
+      "32": 109573,
+      "33": 39101,
+      "34": 68091,
+      "35": 28200,
+      "36": 62133,
+      "37": 22518,
+      "38": 37784,
+      "39": 15978,
+      "4": 124708,
+      "40": 28702,
+      "41": 10479,
+      "42": 14139,
+      "43": 5797,
+      "44": 7802,
+      "45": 3650,
+      "46": 4346,
+      "47": 2576,
+      "48": 3524,
+      "49": 2095,
+      "5": 937914,
+      "50": 2793,
+      "51": 1734,
+      "52": 2430,
+      "53": 1587,
+      "54": 2161,
+      "55": 1588,
+      "56": 2440,
+      "57": 1669,
+      "58": 2275,
+      "59": 1680,
+      "6": 5128038,
+      "60": 2441,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1370,
+      "66": 1770,
+      "67": 1096,
+      "68": 1503,
+      "69": 880,
+      "7": 1967860,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5544061,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1602378,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 55215,
+      "7": 29282751,
+      "9": 124708
+    },
+    "connectivity_max": 134309604,
+    "connectivity_min": 0,
+    "n_cells": 29462674,
+    "n_connectivity_values": 327533423,
+    "n_fan_triangles": 268608075,
+    "n_points": 134309605
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.953688542784147e-11,
+    "float64_area_closure_relative": 1.2094892227999892e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 268608075,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944283.137444695,
+    "surface_area_float64_in2": 1944283.137521566,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944283.1375215894,
+    "zero_area_triangles": 225002,
+    "zero_weight_points": 4752
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC107_AoA_4.json b/surface_dual_areas/cases/geo_LHC107_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..77cd73c092cc4926e41a1cb0337c011d8167ce05
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC107_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC107_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC107_AoA_4/boundary_dual_area_geo_LHC107_AoA_4.npy",
+    "sha256": "e85e9d7763dcf882ce48b337ab0f411b4bc1fbc1542ee416aace692ac38ed6be",
+    "shape": [
+      134220339
+    ],
+    "size_bytes": 536881484
+  },
+  "runtime": {
+    "accumulation_seconds": 10.330729590030387,
+    "completed_at_utc": "2026-08-07T07:50:34.531896Z",
+    "elapsed_seconds": 20.92527986317873,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.041217806050554,
+    "geometry_read_seconds": 2.135908780153841,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:50:13.606504Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC107_AoA_4/boundary_geo_LHC107_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC107_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624398000000000,
+    "extracted_vtu_size_bytes": 20607001273,
+    "geometry_sha256": "fd0bdb06005162dfa8863b9437b24a22ddeecb2d460896b99a3a922c4a14e915",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2918908,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 955298,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2175111,
+      "13": 762013,
+      "14": 1617889,
+      "15": 544618,
+      "16": 1041547,
+      "17": 391440,
+      "18": 762396,
+      "19": 308830,
+      "20": 665079,
+      "21": 224354,
+      "22": 349202,
+      "23": 119916,
+      "24": 193746,
+      "25": 67278,
+      "26": 92592,
+      "27": 51469,
+      "28": 124325,
+      "29": 53207,
+      "3": 48294,
+      "30": 115270,
+      "31": 49450,
+      "32": 107725,
+      "33": 38579,
+      "34": 66276,
+      "35": 27782,
+      "36": 62738,
+      "37": 22812,
+      "38": 39073,
+      "39": 16389,
+      "4": 113588,
+      "40": 30081,
+      "41": 10943,
+      "42": 14509,
+      "43": 5874,
+      "44": 7657,
+      "45": 3659,
+      "46": 4231,
+      "47": 2533,
+      "48": 3510,
+      "49": 2128,
+      "5": 929313,
+      "50": 2935,
+      "51": 1849,
+      "52": 2771,
+      "53": 1783,
+      "54": 2396,
+      "55": 1723,
+      "56": 2525,
+      "57": 1746,
+      "58": 2290,
+      "59": 1728,
+      "6": 5339685,
+      "60": 2509,
+      "61": 1658,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 1927553,
+      "70": 1022,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5710548,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1534795,
+      "90": 59,
+      "91": 56,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 48294,
+      "7": 29537191,
+      "9": 113588
+    },
+    "connectivity_max": 134220338,
+    "connectivity_min": 0,
+    "n_cells": 29699073,
+    "n_connectivity_values": 327827708,
+    "n_fan_triangles": 268429562,
+    "n_points": 134220339
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.398905837884064e-11,
+    "float64_area_closure_relative": 2.715433603037989e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 268429562,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937801.95564774,
+    "surface_area_float64_in2": 1937801.955713604,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937801.9557135515,
+    "zero_area_triangles": 225550,
+    "zero_weight_points": 4810
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC107_AoA_8.json b/surface_dual_areas/cases/geo_LHC107_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..d5c1d7cc57e56d534703e8fd818556bf5bbb9474
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC107_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC107_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC107_AoA_8/boundary_dual_area_geo_LHC107_AoA_8.npy",
+    "sha256": "b84c105964168b156b316fdfc4ce858ecd54446b0b82ba447e6ce6e89a24e2b9",
+    "shape": [
+      140082896
+    ],
+    "size_bytes": 560331712
+  },
+  "runtime": {
+    "accumulation_seconds": 11.070731279905885,
+    "completed_at_utc": "2026-08-07T08:20:12.543029Z",
+    "elapsed_seconds": 22.301420727046207,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2995209631044418,
+    "geometry_read_seconds": 2.7928404801059514,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:19:50.241521Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC107_AoA_8/boundary_geo_LHC107_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC107_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624463000000000,
+    "extracted_vtu_size_bytes": 21518199335,
+    "geometry_sha256": "8163dcaa82b377738484aff2fb488c6c248311e4928c8c0a460b0ab3877436f6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3676038,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1142127,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2587779,
+      "13": 798372,
+      "14": 1415541,
+      "15": 498073,
+      "16": 966888,
+      "17": 374881,
+      "18": 754426,
+      "19": 306321,
+      "20": 660987,
+      "21": 222262,
+      "22": 343873,
+      "23": 118133,
+      "24": 191250,
+      "25": 66543,
+      "26": 92183,
+      "27": 51298,
+      "28": 124223,
+      "29": 53148,
+      "3": 52069,
+      "30": 115259,
+      "31": 49439,
+      "32": 107704,
+      "33": 38583,
+      "34": 66280,
+      "35": 27784,
+      "36": 62760,
+      "37": 22811,
+      "38": 39074,
+      "39": 16393,
+      "4": 119212,
+      "40": 30090,
+      "41": 10944,
+      "42": 14509,
+      "43": 5874,
+      "44": 7660,
+      "45": 3659,
+      "46": 4232,
+      "47": 2533,
+      "48": 3508,
+      "49": 2126,
+      "5": 937835,
+      "50": 2936,
+      "51": 1849,
+      "52": 2771,
+      "53": 1783,
+      "54": 2396,
+      "55": 1723,
+      "56": 2525,
+      "57": 1746,
+      "58": 2290,
+      "59": 1728,
+      "6": 5362285,
+      "60": 2509,
+      "61": 1658,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 1998620,
+      "70": 1022,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6126689,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1723519,
+      "90": 59,
+      "91": 56,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52069,
+      "7": 31269377,
+      "9": 119212
+    },
+    "connectivity_max": 140082895,
+    "connectivity_min": 0,
+    "n_cells": 31440658,
+    "n_connectivity_values": 343035992,
+    "n_fan_triangles": 280154676,
+    "n_points": 140082896
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.393633624011265e-11,
+    "float64_area_closure_relative": 3.5805300853453134e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280154676,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937800.5533448001,
+    "surface_area_float64_in2": 1937800.553410562,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937800.5534106314,
+    "zero_area_triangles": 236678,
+    "zero_weight_points": 5484
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC108_AoA_20.json b/surface_dual_areas/cases/geo_LHC108_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..4dfa7ebc5af11f004145a7c07453a2cc0479be12
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC108_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC108_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC108_AoA_20/boundary_dual_area_geo_LHC108_AoA_20.npy",
+    "sha256": "85eef84fa963c2be880e06afd884504b3004fbd7cfa0ca8ab61df77ae8866d7a",
+    "shape": [
+      142716504
+    ],
+    "size_bytes": 570866144
+  },
+  "runtime": {
+    "accumulation_seconds": 11.18225236912258,
+    "completed_at_utc": "2026-08-07T08:23:22.946442Z",
+    "elapsed_seconds": 31.64863788592629,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2982051570434123,
+    "geometry_read_seconds": 12.213289669947699,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:22:51.297721Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC108_AoA_20/boundary_geo_LHC108_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC108_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624528000000000,
+    "extracted_vtu_size_bytes": 21926155788,
+    "geometry_sha256": "6d87aaf0e029ca93ab234875a7a73b254826b8d9a0a5caa2fe918c24601f6b96",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4113496,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1290817,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2769936,
+      "13": 796749,
+      "14": 1276058,
+      "15": 435258,
+      "16": 897230,
+      "17": 345390,
+      "18": 743567,
+      "19": 299947,
+      "20": 667622,
+      "21": 225336,
+      "22": 361680,
+      "23": 124462,
+      "24": 204687,
+      "25": 71575,
+      "26": 93399,
+      "27": 52438,
+      "28": 124470,
+      "29": 53273,
+      "3": 54719,
+      "30": 114300,
+      "31": 49063,
+      "32": 107262,
+      "33": 38590,
+      "34": 66613,
+      "35": 28050,
+      "36": 63041,
+      "37": 22985,
+      "38": 38947,
+      "39": 16279,
+      "4": 120749,
+      "40": 29615,
+      "41": 10734,
+      "42": 14107,
+      "43": 5796,
+      "44": 7847,
+      "45": 3701,
+      "46": 4205,
+      "47": 2525,
+      "48": 3614,
+      "49": 2204,
+      "5": 940251,
+      "50": 2929,
+      "51": 1835,
+      "52": 2715,
+      "53": 1756,
+      "54": 2386,
+      "55": 1702,
+      "56": 2489,
+      "57": 1766,
+      "58": 2272,
+      "59": 1687,
+      "6": 5217618,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2071725,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6233535,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1907802,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54719,
+      "7": 31992491,
+      "9": 120749
+    },
+    "connectivity_max": 142716503,
+    "connectivity_min": 0,
+    "n_cells": 32167959,
+    "n_connectivity_values": 349757803,
+    "n_fan_triangles": 285421885,
+    "n_points": 142716504
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.217015117117215e-11,
+    "float64_area_closure_relative": 4.1541165842721586e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285421885,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939266.7747133551,
+    "surface_area_float64_in2": 1939266.7747757416,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939266.7747758222,
+    "zero_area_triangles": 240810,
+    "zero_weight_points": 5746
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC108_AoA_22.json b/surface_dual_areas/cases/geo_LHC108_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..2541878c29e518273e606506189da13f17771682
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC108_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC108_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC108_AoA_22/boundary_dual_area_geo_LHC108_AoA_22.npy",
+    "sha256": "c34c9633b9f5254b69712f2a8f436e8ea05aeb6b2ee54b592251cce13336109c",
+    "shape": [
+      142577993
+    ],
+    "size_bytes": 570312100
+  },
+  "runtime": {
+    "accumulation_seconds": 11.402886708965525,
+    "completed_at_utc": "2026-08-07T08:26:07.268888Z",
+    "elapsed_seconds": 54.96771139302291,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2680262881331146,
+    "geometry_read_seconds": 35.63413036405109,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:25:12.301058Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC108_AoA_22/boundary_geo_LHC108_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC108_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624679000000000,
+    "extracted_vtu_size_bytes": 21905338435,
+    "geometry_sha256": "04e3a836893ffef65a35a1d7f4cbb8961c2c87cd232118319429e7fbbd8c7bfa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4097404,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1303608,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2728137,
+      "13": 791585,
+      "14": 1271667,
+      "15": 427470,
+      "16": 895337,
+      "17": 341893,
+      "18": 742031,
+      "19": 298893,
+      "20": 665452,
+      "21": 225722,
+      "22": 366063,
+      "23": 125586,
+      "24": 209068,
+      "25": 72612,
+      "26": 94078,
+      "27": 52646,
+      "28": 124580,
+      "29": 53293,
+      "3": 54371,
+      "30": 114319,
+      "31": 49059,
+      "32": 107267,
+      "33": 38597,
+      "34": 66602,
+      "35": 28052,
+      "36": 63037,
+      "37": 22977,
+      "38": 38945,
+      "39": 16265,
+      "4": 120903,
+      "40": 29609,
+      "41": 10734,
+      "42": 14106,
+      "43": 5796,
+      "44": 7844,
+      "45": 3699,
+      "46": 4207,
+      "47": 2528,
+      "48": 3614,
+      "49": 2203,
+      "5": 943041,
+      "50": 2929,
+      "51": 1835,
+      "52": 2716,
+      "53": 1756,
+      "54": 2384,
+      "55": 1702,
+      "56": 2489,
+      "57": 1766,
+      "58": 2272,
+      "59": 1687,
+      "6": 5229869,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2081946,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6236547,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1927297,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54371,
+      "7": 31979976,
+      "9": 120903
+    },
+    "connectivity_max": 142577992,
+    "connectivity_min": 0,
+    "n_cells": 32155250,
+    "n_connectivity_values": 349455363,
+    "n_fan_triangles": 285144863,
+    "n_points": 142577993
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.222933879887216e-11,
+    "float64_area_closure_relative": 3.3497064624574236e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285144863,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939266.926979626,
+    "surface_area_float64_in2": 1939266.9270421274,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939266.9270421923,
+    "zero_area_triangles": 240197,
+    "zero_weight_points": 5696
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC110_AoA_6.json b/surface_dual_areas/cases/geo_LHC110_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..cf11ef397ec9c858cac44935c03460105f0760f8
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC110_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC110_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC110_AoA_6/boundary_dual_area_geo_LHC110_AoA_6.npy",
+    "sha256": "f3b371cf9fd7902ef078fc15d7d6ba37894362896eb55dc90bb83c00a3f372b4",
+    "shape": [
+      136259628
+    ],
+    "size_bytes": 545038640
+  },
+  "runtime": {
+    "accumulation_seconds": 11.4081671689637,
+    "completed_at_utc": "2026-08-07T08:26:55.725139Z",
+    "elapsed_seconds": 22.474143787054345,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1404916860628873,
+    "geometry_read_seconds": 3.1672105870675296,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:26:33.250909Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC110_AoA_6/boundary_geo_LHC110_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC110_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624443000000000,
+    "extracted_vtu_size_bytes": 20921027347,
+    "geometry_sha256": "d2ddbeb03e5d9e5eb9e187c834c4b2d1e7ef6142b17bb7c6fbb2fa5bb3260ea0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3214227,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1050297,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2378013,
+      "13": 785059,
+      "14": 1598114,
+      "15": 514589,
+      "16": 998843,
+      "17": 368403,
+      "18": 748950,
+      "19": 301234,
+      "20": 664253,
+      "21": 222753,
+      "22": 352052,
+      "23": 121065,
+      "24": 199703,
+      "25": 67544,
+      "26": 94160,
+      "27": 51634,
+      "28": 124808,
+      "29": 53155,
+      "3": 51527,
+      "30": 115873,
+      "31": 49616,
+      "32": 109303,
+      "33": 38787,
+      "34": 65759,
+      "35": 27988,
+      "36": 62120,
+      "37": 23026,
+      "38": 38505,
+      "39": 16258,
+      "4": 115776,
+      "40": 29400,
+      "41": 10677,
+      "42": 14252,
+      "43": 5783,
+      "44": 7695,
+      "45": 3620,
+      "46": 4262,
+      "47": 2563,
+      "48": 3553,
+      "49": 2132,
+      "5": 928823,
+      "50": 2929,
+      "51": 1856,
+      "52": 2714,
+      "53": 1745,
+      "54": 2413,
+      "55": 1682,
+      "56": 2557,
+      "57": 1711,
+      "58": 2306,
+      "59": 1694,
+      "6": 5204405,
+      "60": 2439,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1370,
+      "66": 1770,
+      "67": 1096,
+      "68": 1503,
+      "69": 880,
+      "7": 1951426,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5725864,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1625204,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51527,
+      "7": 30020223,
+      "9": 115776
+    },
+    "connectivity_max": 136259627,
+    "connectivity_min": 0,
+    "n_cells": 30187526,
+    "n_connectivity_values": 332883189,
+    "n_fan_triangles": 272508137,
+    "n_points": 136259628
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.084967272452485e-11,
+    "float64_area_closure_relative": 5.6570965249042064e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272508137,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938507.371667067,
+    "surface_area_float64_in2": 1938507.3717268694,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938507.371726979,
+    "zero_area_triangles": 232067,
+    "zero_weight_points": 5299
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC110_AoA_8.json b/surface_dual_areas/cases/geo_LHC110_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f6d9dbe5bd5e182beb82b10620969b5e2626217
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC110_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC110_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC110_AoA_8/boundary_dual_area_geo_LHC110_AoA_8.npy",
+    "sha256": "bc7273210acdb86172bbff8b5ecd1efda0a85f5318f89f6e8692dfa77bd657a2",
+    "shape": [
+      137726606
+    ],
+    "size_bytes": 550906552
+  },
+  "runtime": {
+    "accumulation_seconds": 10.863416861975566,
+    "completed_at_utc": "2026-08-07T07:50:44.381143Z",
+    "elapsed_seconds": 20.272835186915472,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.042778881965205,
+    "geometry_read_seconds": 1.7286374738905579,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:50:24.108215Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC110_AoA_8/boundary_geo_LHC110_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC110_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624399000000000,
+    "extracted_vtu_size_bytes": 21148642191,
+    "geometry_sha256": "c3a7b07ccd332174d9cc4ffc2cdc84eb713b8d7048b7eb506daf19385977fc1c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3389393,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1102580,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2483849,
+      "13": 796351,
+      "14": 1564358,
+      "15": 504804,
+      "16": 982608,
+      "17": 363942,
+      "18": 746316,
+      "19": 299780,
+      "20": 660910,
+      "21": 221861,
+      "22": 349143,
+      "23": 120420,
+      "24": 198510,
+      "25": 67274,
+      "26": 94084,
+      "27": 51564,
+      "28": 124763,
+      "29": 53116,
+      "3": 51873,
+      "30": 115849,
+      "31": 49605,
+      "32": 109275,
+      "33": 38784,
+      "34": 65748,
+      "35": 27982,
+      "36": 62135,
+      "37": 23035,
+      "38": 38536,
+      "39": 16253,
+      "4": 116760,
+      "40": 29413,
+      "41": 10683,
+      "42": 14260,
+      "43": 5784,
+      "44": 7699,
+      "45": 3620,
+      "46": 4263,
+      "47": 2562,
+      "48": 3558,
+      "49": 2131,
+      "5": 928805,
+      "50": 2929,
+      "51": 1858,
+      "52": 2716,
+      "53": 1745,
+      "54": 2411,
+      "55": 1682,
+      "56": 2557,
+      "57": 1711,
+      "58": 2306,
+      "59": 1695,
+      "6": 5199620,
+      "60": 2439,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 1968173,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5813824,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1677279,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51873,
+      "7": 30438977,
+      "9": 116760
+    },
+    "connectivity_max": 137726605,
+    "connectivity_min": 0,
+    "n_cells": 30607610,
+    "n_connectivity_values": 336657313,
+    "n_fan_triangles": 275442093,
+    "n_points": 137726606
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.0724405506075756e-11,
+    "float64_area_closure_relative": 6.305681997564471e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275442093,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938507.015763542,
+    "surface_area_float64_in2": 1938507.0158231014,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938507.0158232236,
+    "zero_area_triangles": 234843,
+    "zero_weight_points": 5419
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC111_AoA_18.json b/surface_dual_areas/cases/geo_LHC111_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..74f293bc1da9a471e681e63abac15e4cf7860af0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC111_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC111_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC111_AoA_18/boundary_dual_area_geo_LHC111_AoA_18.npy",
+    "sha256": "380ee39317b52e0eab851a84c34c9a58381fa84da4d87036c5d27e8b001ecdb3",
+    "shape": [
+      146343449
+    ],
+    "size_bytes": 585373924
+  },
+  "runtime": {
+    "accumulation_seconds": 11.258949851850048,
+    "completed_at_utc": "2026-08-07T07:51:58.334087Z",
+    "elapsed_seconds": 24.258380847983062,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4580552058760077,
+    "geometry_read_seconds": 4.338377352105454,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:51:34.075606Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC111_AoA_18/boundary_geo_LHC111_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC111_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624412000000000,
+    "extracted_vtu_size_bytes": 22486762273,
+    "geometry_sha256": "f6e46c5bc1fd9e5cfa4d0c6a73a17d0d56907e2ae7337e85ea1b2e7a1d2c3148",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4310137,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1368804,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2824288,
+      "13": 829345,
+      "14": 1275546,
+      "15": 448388,
+      "16": 897944,
+      "17": 349978,
+      "18": 750478,
+      "19": 301456,
+      "20": 682616,
+      "21": 224030,
+      "22": 366741,
+      "23": 122699,
+      "24": 214734,
+      "25": 71986,
+      "26": 94166,
+      "27": 51958,
+      "28": 123913,
+      "29": 52809,
+      "3": 58961,
+      "30": 115005,
+      "31": 49574,
+      "32": 109781,
+      "33": 39109,
+      "34": 67426,
+      "35": 28178,
+      "36": 62458,
+      "37": 22922,
+      "38": 38474,
+      "39": 16248,
+      "4": 132949,
+      "40": 29366,
+      "41": 10696,
+      "42": 14271,
+      "43": 5892,
+      "44": 7684,
+      "45": 3607,
+      "46": 4277,
+      "47": 2551,
+      "48": 3550,
+      "49": 2141,
+      "5": 953344,
+      "50": 2947,
+      "51": 1882,
+      "52": 2770,
+      "53": 1777,
+      "54": 2435,
+      "55": 1708,
+      "56": 2568,
+      "57": 1729,
+      "58": 2291,
+      "59": 1701,
+      "6": 5252870,
+      "60": 2451,
+      "61": 1667,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2118232,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6557848,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2006586,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58961,
+      "7": 32928794,
+      "9": 132949
+    },
+    "connectivity_max": 146343448,
+    "connectivity_min": 0,
+    "n_cells": 33120704,
+    "n_connectivity_values": 358917183,
+    "n_fan_triangles": 292675775,
+    "n_points": 146343449
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.048641846398824e-11,
+    "float64_area_closure_relative": 8.854302637780183e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 292675775,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945886.4615913224,
+    "surface_area_float64_in2": 1945886.4616701044,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945886.4616700872,
+    "zero_area_triangles": 240239,
+    "zero_weight_points": 6054
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC111_AoA_22.json b/surface_dual_areas/cases/geo_LHC111_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..2025e4295d4dbe11a155ea9ee5a4087bf6b12b6a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC111_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC111_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC111_AoA_22/boundary_dual_area_geo_LHC111_AoA_22.npy",
+    "sha256": "75ef42987c96d8fb03300eb43a8c85de8353ab7de2147233554b89f0ef0e1dd6",
+    "shape": [
+      147657119
+    ],
+    "size_bytes": 590628604
+  },
+  "runtime": {
+    "accumulation_seconds": 12.460843533044681,
+    "completed_at_utc": "2026-08-07T08:25:04.435438Z",
+    "elapsed_seconds": 23.869079012889415,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.423221913166344,
+    "geometry_read_seconds": 2.969686792930588,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:24:40.566249Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC111_AoA_22/boundary_geo_LHC111_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC111_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624499000000000,
+    "extracted_vtu_size_bytes": 22692072050,
+    "geometry_sha256": "d77d22b638bcc4d169a9e3cb210768279947186b9cdd836b4b969d57cc601225",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4411370,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1401995,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2864218,
+      "13": 840498,
+      "14": 1273427,
+      "15": 446751,
+      "16": 888351,
+      "17": 345653,
+      "18": 740720,
+      "19": 297897,
+      "20": 674395,
+      "21": 222513,
+      "22": 365826,
+      "23": 123102,
+      "24": 218217,
+      "25": 72684,
+      "26": 94625,
+      "27": 52056,
+      "28": 123955,
+      "29": 52803,
+      "3": 60510,
+      "30": 114999,
+      "31": 49585,
+      "32": 109787,
+      "33": 39099,
+      "34": 67426,
+      "35": 28184,
+      "36": 62457,
+      "37": 22917,
+      "38": 38472,
+      "39": 16252,
+      "4": 137216,
+      "40": 29366,
+      "41": 10696,
+      "42": 14273,
+      "43": 5891,
+      "44": 7685,
+      "45": 3603,
+      "46": 4274,
+      "47": 2551,
+      "48": 3549,
+      "49": 2142,
+      "5": 968297,
+      "50": 2947,
+      "51": 1882,
+      "52": 2769,
+      "53": 1777,
+      "54": 2437,
+      "55": 1708,
+      "56": 2568,
+      "57": 1729,
+      "58": 2291,
+      "59": 1701,
+      "6": 5313604,
+      "60": 2451,
+      "61": 1667,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2152343,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6683031,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2052215,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60510,
+      "7": 33358443,
+      "9": 137216
+    },
+    "connectivity_max": 147657118,
+    "connectivity_min": 0,
+    "n_cells": 33556169,
+    "n_connectivity_values": 362415452,
+    "n_fan_triangles": 295303114,
+    "n_points": 147657119
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9317299030314164e-11,
+    "float64_area_closure_relative": 1.1606317825713944e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295303114,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945886.0917543531,
+    "surface_area_float64_in2": 1945886.0918308601,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945886.0918308375,
+    "zero_area_triangles": 241473,
+    "zero_weight_points": 6107
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC111_AoA_6.json b/surface_dual_areas/cases/geo_LHC111_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..2e62a09bfe2466ceaeb6a7bd376bb8ac7221e897
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC111_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC111_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC111_AoA_6/boundary_dual_area_geo_LHC111_AoA_6.npy",
+    "sha256": "c1b39604736bb9a25dde1583a76412052af728f96e9631f42e4f06afaf13e35d",
+    "shape": [
+      137329098
+    ],
+    "size_bytes": 549316520
+  },
+  "runtime": {
+    "accumulation_seconds": 10.695204828865826,
+    "completed_at_utc": "2026-08-07T08:30:01.795315Z",
+    "elapsed_seconds": 23.046979586128145,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.091494061984122,
+    "geometry_read_seconds": 3.9614412491209805,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:29:38.748243Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC111_AoA_6/boundary_geo_LHC111_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC111_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624570000000000,
+    "extracted_vtu_size_bytes": 21083909867,
+    "geometry_sha256": "24b44076371ec5981f48ad9d95fcacdd8bc8104dbd62a0eddae3fd330942f23d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3016353,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 974392,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2272948,
+      "13": 797535,
+      "14": 1779486,
+      "15": 573346,
+      "16": 1050503,
+      "17": 386778,
+      "18": 747968,
+      "19": 301924,
+      "20": 670475,
+      "21": 222027,
+      "22": 351026,
+      "23": 121150,
+      "24": 207330,
+      "25": 71184,
+      "26": 93421,
+      "27": 51821,
+      "28": 123894,
+      "29": 52780,
+      "3": 57124,
+      "30": 115015,
+      "31": 49581,
+      "32": 109791,
+      "33": 39100,
+      "34": 67424,
+      "35": 28182,
+      "36": 62460,
+      "37": 22913,
+      "38": 38470,
+      "39": 16254,
+      "4": 128864,
+      "40": 29365,
+      "41": 10699,
+      "42": 14272,
+      "43": 5890,
+      "44": 7686,
+      "45": 3602,
+      "46": 4276,
+      "47": 2550,
+      "48": 3550,
+      "49": 2143,
+      "5": 955227,
+      "50": 2947,
+      "51": 1882,
+      "52": 2769,
+      "53": 1777,
+      "54": 2437,
+      "55": 1708,
+      "56": 2568,
+      "57": 1729,
+      "58": 2291,
+      "59": 1701,
+      "6": 5261390,
+      "60": 2451,
+      "61": 1667,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 1975731,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5852663,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1596314,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57124,
+      "7": 30185578,
+      "9": 128864
+    },
+    "connectivity_max": 137329097,
+    "connectivity_min": 0,
+    "n_cells": 30371566,
+    "n_connectivity_values": 335390204,
+    "n_fan_triangles": 274647072,
+    "n_points": 137329098
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.0831337980096386e-11,
+    "float64_area_closure_relative": 8.375683616968099e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274647072,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945888.3358592214,
+    "surface_area_float64_in2": 1945888.3359386746,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945888.3359386583,
+    "zero_area_triangles": 224931,
+    "zero_weight_points": 5068
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC112_AoA_22.json b/surface_dual_areas/cases/geo_LHC112_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..e021d3d4f748ec53eab8fb48678e01b0e16cfd05
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC112_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC112_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC112_AoA_22/boundary_dual_area_geo_LHC112_AoA_22.npy",
+    "sha256": "07ce9c3e954d8fc9b01ca4ee45a9be8c24b9a7fc807a25ab41186fd4fdc2b53e",
+    "shape": [
+      142597755
+    ],
+    "size_bytes": 570391148
+  },
+  "runtime": {
+    "accumulation_seconds": 11.052379884989932,
+    "completed_at_utc": "2026-08-07T07:52:20.971172Z",
+    "elapsed_seconds": 21.663184591103345,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2121786770876497,
+    "geometry_read_seconds": 2.2850988681893796,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:51:59.307898Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC112_AoA_22/boundary_geo_LHC112_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC112_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624468000000000,
+    "extracted_vtu_size_bytes": 21907734597,
+    "geometry_sha256": "b7fe5a84fba5f6b12591f1daadc7261be0a08445da939be8c1f68bbb63f2cfcc",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4060442,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1293194,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2721210,
+      "13": 807036,
+      "14": 1301405,
+      "15": 458486,
+      "16": 922033,
+      "17": 357125,
+      "18": 732887,
+      "19": 298050,
+      "20": 652883,
+      "21": 222645,
+      "22": 354306,
+      "23": 123394,
+      "24": 206895,
+      "25": 70795,
+      "26": 95077,
+      "27": 52543,
+      "28": 124532,
+      "29": 53103,
+      "3": 53607,
+      "30": 114445,
+      "31": 49305,
+      "32": 107709,
+      "33": 38533,
+      "34": 66322,
+      "35": 27736,
+      "36": 62534,
+      "37": 22797,
+      "38": 38915,
+      "39": 16389,
+      "4": 120381,
+      "40": 29991,
+      "41": 10835,
+      "42": 14585,
+      "43": 5985,
+      "44": 7793,
+      "45": 3656,
+      "46": 4277,
+      "47": 2561,
+      "48": 3527,
+      "49": 2139,
+      "5": 942913,
+      "50": 2888,
+      "51": 1852,
+      "52": 2736,
+      "53": 1765,
+      "54": 2411,
+      "55": 1703,
+      "56": 2593,
+      "57": 1713,
+      "58": 2310,
+      "59": 1696,
+      "6": 5220365,
+      "60": 2452,
+      "61": 1667,
+      "62": 2199,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 881,
+      "7": 2089271,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 446,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6204383,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1920564,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53607,
+      "7": 31960120,
+      "9": 120381
+    },
+    "connectivity_max": 142597754,
+    "connectivity_min": 0,
+    "n_cells": 32134108,
+    "n_connectivity_values": 349452595,
+    "n_fan_triangles": 285184379,
+    "n_points": 142597755
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.424550608350383e-11,
+    "float64_area_closure_relative": 7.806078389896616e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285184379,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938744.5374070462,
+    "surface_area_float64_in2": 1938744.5374734395,
+    "weight_max_in2": 1.100180399258682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938744.5374734546,
+    "zero_area_triangles": 239281,
+    "zero_weight_points": 5826
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC113_AoA_18.json b/surface_dual_areas/cases/geo_LHC113_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e11304c5f341d4b3236216ed9edd44298b337a9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC113_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC113_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC113_AoA_18/boundary_dual_area_geo_LHC113_AoA_18.npy",
+    "sha256": "527a30069d499556bc0c77b24d072dd884d8f0619e6c3f1766fe40e33bb0b446",
+    "shape": [
+      138632555
+    ],
+    "size_bytes": 554530348
+  },
+  "runtime": {
+    "accumulation_seconds": 10.777332714060321,
+    "completed_at_utc": "2026-08-07T08:30:01.987546Z",
+    "elapsed_seconds": 23.239194297930226,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1135430401191115,
+    "geometry_read_seconds": 4.505924959899858,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:29:38.748261Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC113_AoA_18/boundary_geo_LHC113_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC113_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624584000000000,
+    "extracted_vtu_size_bytes": 21294086221,
+    "geometry_sha256": "5e6e7260771a755a38b947b5c0dae5791679c5a6ab96652ec45778158dc42f03",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3856407,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1199818,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2516980,
+      "13": 760897,
+      "14": 1215308,
+      "15": 439801,
+      "16": 889105,
+      "17": 351836,
+      "18": 754883,
+      "19": 305000,
+      "20": 674377,
+      "21": 227195,
+      "22": 378051,
+      "23": 124361,
+      "24": 213473,
+      "25": 70169,
+      "26": 95305,
+      "27": 52360,
+      "28": 124396,
+      "29": 53195,
+      "3": 51639,
+      "30": 114915,
+      "31": 49395,
+      "32": 108467,
+      "33": 38784,
+      "34": 66593,
+      "35": 28011,
+      "36": 62795,
+      "37": 22939,
+      "38": 39230,
+      "39": 16553,
+      "4": 117283,
+      "40": 29981,
+      "41": 10929,
+      "42": 14367,
+      "43": 5789,
+      "44": 7622,
+      "45": 3706,
+      "46": 4248,
+      "47": 2515,
+      "48": 3538,
+      "49": 2162,
+      "5": 936553,
+      "50": 2940,
+      "51": 1852,
+      "52": 2745,
+      "53": 1786,
+      "54": 2461,
+      "55": 1733,
+      "56": 2538,
+      "57": 1752,
+      "58": 2289,
+      "59": 1732,
+      "6": 5185753,
+      "60": 2509,
+      "61": 1660,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2028154,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5953344,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1809029,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51639,
+      "7": 30893234,
+      "9": 117283
+    },
+    "connectivity_max": 138632554,
+    "connectivity_min": 0,
+    "n_cells": 31062156,
+    "n_connectivity_values": 339378294,
+    "n_fan_triangles": 277253982,
+    "n_points": 138632555
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.119588937023424e-11,
+    "float64_area_closure_relative": 3.534808731369883e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277253982,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936518.0532858481,
+    "surface_area_float64_in2": 1936518.0533462595,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936518.053346328,
+    "zero_area_triangles": 233639,
+    "zero_weight_points": 5565
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC113_AoA_8.json b/surface_dual_areas/cases/geo_LHC113_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..fd4de1ba0d74d7137cd632cea1b0dc3d6084e54f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC113_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC113_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC113_AoA_8/boundary_dual_area_geo_LHC113_AoA_8.npy",
+    "sha256": "0525e1b0b5e858732c9ba8bbcecbc21bb6c5a293af69c25ea69b3cf8d13c0265",
+    "shape": [
+      137980382
+    ],
+    "size_bytes": 551921656
+  },
+  "runtime": {
+    "accumulation_seconds": 10.637740127975121,
+    "completed_at_utc": "2026-08-07T08:25:12.501596Z",
+    "elapsed_seconds": 20.50380862504244,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1467449530027807,
+    "geometry_read_seconds": 2.112138533964753,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:24:51.997692Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC113_AoA_8/boundary_geo_LHC113_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC113_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624470000000000,
+    "extracted_vtu_size_bytes": 21189469017,
+    "geometry_sha256": "b67832e78e1a615e35710ac587f6701d49083dc5cb2d6146bc91f0e0602fa307",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3607429,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1084961,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2479600,
+      "13": 775655,
+      "14": 1482396,
+      "15": 502584,
+      "16": 979877,
+      "17": 372724,
+      "18": 758721,
+      "19": 304392,
+      "20": 659141,
+      "21": 221092,
+      "22": 342848,
+      "23": 118301,
+      "24": 189788,
+      "25": 66840,
+      "26": 91985,
+      "27": 51712,
+      "28": 124009,
+      "29": 53093,
+      "3": 50856,
+      "30": 114911,
+      "31": 49391,
+      "32": 108464,
+      "33": 38785,
+      "34": 66592,
+      "35": 28009,
+      "36": 62799,
+      "37": 22937,
+      "38": 39230,
+      "39": 16552,
+      "4": 114458,
+      "40": 29981,
+      "41": 10930,
+      "42": 14367,
+      "43": 5789,
+      "44": 7622,
+      "45": 3706,
+      "46": 4248,
+      "47": 2515,
+      "48": 3538,
+      "49": 2162,
+      "5": 934175,
+      "50": 2940,
+      "51": 1852,
+      "52": 2745,
+      "53": 1786,
+      "54": 2461,
+      "55": 1733,
+      "56": 2538,
+      "57": 1752,
+      "58": 2289,
+      "59": 1732,
+      "6": 5187375,
+      "60": 2509,
+      "61": 1660,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1988642,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5835136,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1683069,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50856,
+      "7": 30573018,
+      "9": 114458
+    },
+    "connectivity_max": 137980381,
+    "connectivity_min": 0,
+    "n_cells": 30738332,
+    "n_connectivity_values": 337426300,
+    "n_fan_triangles": 275949636,
+    "n_points": 137980382
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.0844220235225396e-11,
+    "float64_area_closure_relative": 5.5547009233157145e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275949636,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936517.534423087,
+    "surface_area_float64_in2": 1936517.5344828174,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936517.534482925,
+    "zero_area_triangles": 233583,
+    "zero_weight_points": 5517
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC114_AoA_12.json b/surface_dual_areas/cases/geo_LHC114_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..2b11aeb7ca6a060c5d0d824d64317f94e3a45052
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC114_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC114_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC114_AoA_12/boundary_dual_area_geo_LHC114_AoA_12.npy",
+    "sha256": "9b33ca873a20ea228ccf10aa15a0c6e5a38584a1164f6987cf866a680f55974f",
+    "shape": [
+      151529957
+    ],
+    "size_bytes": 606119956
+  },
+  "runtime": {
+    "accumulation_seconds": 11.8703881399706,
+    "completed_at_utc": "2026-08-07T08:25:52.445656Z",
+    "elapsed_seconds": 38.43510760203935,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5492944109719247,
+    "geometry_read_seconds": 17.507172607816756,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:25:14.010463Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC114_AoA_12/boundary_geo_LHC114_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC114_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624692000000000,
+    "extracted_vtu_size_bytes": 23289232098,
+    "geometry_sha256": "bd5411cf8e684a53824e0d791788c22269064808b5093b16aaa736737a91d376",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4752456,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1350700,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3307046,
+      "13": 855486,
+      "14": 1392054,
+      "15": 466488,
+      "16": 932188,
+      "17": 354626,
+      "18": 741087,
+      "19": 299180,
+      "20": 663959,
+      "21": 217517,
+      "22": 331813,
+      "23": 114974,
+      "24": 185428,
+      "25": 67185,
+      "26": 87965,
+      "27": 51061,
+      "28": 122933,
+      "29": 52729,
+      "3": 58852,
+      "30": 114522,
+      "31": 49501,
+      "32": 109022,
+      "33": 38815,
+      "34": 66425,
+      "35": 27944,
+      "36": 62009,
+      "37": 23014,
+      "38": 38413,
+      "39": 16384,
+      "4": 131321,
+      "40": 29243,
+      "41": 10750,
+      "42": 14231,
+      "43": 5822,
+      "44": 7763,
+      "45": 3601,
+      "46": 4242,
+      "47": 2540,
+      "48": 3562,
+      "49": 2147,
+      "5": 949215,
+      "50": 2902,
+      "51": 1855,
+      "52": 2774,
+      "53": 1774,
+      "54": 2479,
+      "55": 1716,
+      "56": 2580,
+      "57": 1699,
+      "58": 2311,
+      "59": 1700,
+      "6": 5354181,
+      "60": 2451,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2112824,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6916053,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1971431,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58852,
+      "7": 34325196,
+      "9": 131321
+    },
+    "connectivity_max": 151529956,
+    "connectivity_min": 0,
+    "n_cells": 34515369,
+    "n_connectivity_values": 372079531,
+    "n_fan_triangles": 303048793,
+    "n_points": 151529957
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.706678063742574e-11,
+    "float64_area_closure_relative": 2.836715935672898e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 303048793,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945237.5139152685,
+    "surface_area_float64_in2": 1945237.5139873722,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945237.513987317,
+    "zero_area_triangles": 247499,
+    "zero_weight_points": 6517
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC114_AoA_18.json b/surface_dual_areas/cases/geo_LHC114_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..a217d9b9d219fe2ce39e54a92d55298727f3f8dd
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC114_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC114_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC114_AoA_18/boundary_dual_area_geo_LHC114_AoA_18.npy",
+    "sha256": "4fbd511e63381a166a8b817894036898248f6afdc502c185de05251f52cd3fae",
+    "shape": [
+      149835830
+    ],
+    "size_bytes": 599343448
+  },
+  "runtime": {
+    "accumulation_seconds": 11.88884762302041,
+    "completed_at_utc": "2026-08-07T08:31:47.788249Z",
+    "elapsed_seconds": 59.67114363890141,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5310109071433544,
+    "geometry_read_seconds": 37.094786101952195,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:30:48.117012Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC114_AoA_18/boundary_geo_LHC114_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC114_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624678000000000,
+    "extracted_vtu_size_bytes": 23027585827,
+    "geometry_sha256": "f1af0fcb86eb54125e2d7c284c2c21075cde301db6757812b9a27790b2bda51a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4762659,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1329187,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3211629,
+      "13": 822695,
+      "14": 1244380,
+      "15": 444446,
+      "16": 887573,
+      "17": 348695,
+      "18": 759849,
+      "19": 304335,
+      "20": 684092,
+      "21": 224333,
+      "22": 352605,
+      "23": 120596,
+      "24": 196809,
+      "25": 69622,
+      "26": 88810,
+      "27": 51331,
+      "28": 122957,
+      "29": 52727,
+      "3": 61201,
+      "30": 114532,
+      "31": 49508,
+      "32": 109018,
+      "33": 38819,
+      "34": 66417,
+      "35": 27939,
+      "36": 62013,
+      "37": 23014,
+      "38": 38416,
+      "39": 16378,
+      "4": 135630,
+      "40": 29247,
+      "41": 10751,
+      "42": 14229,
+      "43": 5819,
+      "44": 7766,
+      "45": 3600,
+      "46": 4243,
+      "47": 2539,
+      "48": 3562,
+      "49": 2148,
+      "5": 947546,
+      "50": 2902,
+      "51": 1854,
+      "52": 2773,
+      "53": 1773,
+      "54": 2481,
+      "55": 1716,
+      "56": 2580,
+      "57": 1699,
+      "58": 2311,
+      "59": 1700,
+      "6": 5305034,
+      "60": 2451,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2089112,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6835388,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1950885,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61201,
+      "7": 33881919,
+      "9": 135630
+    },
+    "connectivity_max": 149835829,
+    "connectivity_min": 0,
+    "n_cells": 34078750,
+    "n_connectivity_values": 367818039,
+    "n_fan_triangles": 299660539,
+    "n_points": 149835830
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.67340058498582e-11,
+    "float64_area_closure_relative": 3.890008211455709e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 299660539,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945239.0604700278,
+    "surface_area_float64_in2": 1945239.0605414843,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945239.0605414086,
+    "zero_area_triangles": 246611,
+    "zero_weight_points": 6419
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC115_AoA_12.json b/surface_dual_areas/cases/geo_LHC115_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..0b69c81704a0cae5e0c2d43df48a8fe6a64f82b0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC115_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC115_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC115_AoA_12/boundary_dual_area_geo_LHC115_AoA_12.npy",
+    "sha256": "670ff11e689228964e945713658b8e3cfe3c1b774b7ef93c3905700132d1555f",
+    "shape": [
+      140221066
+    ],
+    "size_bytes": 560884392
+  },
+  "runtime": {
+    "accumulation_seconds": 11.162148911971599,
+    "completed_at_utc": "2026-08-07T07:53:20.232911Z",
+    "elapsed_seconds": 22.04994289809838,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.323024468962103,
+    "geometry_read_seconds": 2.732961531030014,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:52:58.182874Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC115_AoA_12/boundary_geo_LHC115_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC115_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624708000000000,
+    "extracted_vtu_size_bytes": 21538589519,
+    "geometry_sha256": "e7f062a06ef36bc78be42c5faa8db6e6106e097e2f0f3c9f51ba21bdd7921da7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4011575,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1180557,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2677390,
+      "13": 758696,
+      "14": 1306647,
+      "15": 446174,
+      "16": 907597,
+      "17": 349219,
+      "18": 749469,
+      "19": 301699,
+      "20": 666484,
+      "21": 225689,
+      "22": 361836,
+      "23": 124979,
+      "24": 200859,
+      "25": 69789,
+      "26": 93417,
+      "27": 52043,
+      "28": 124554,
+      "29": 53204,
+      "3": 51530,
+      "30": 114269,
+      "31": 49108,
+      "32": 107308,
+      "33": 38462,
+      "34": 66587,
+      "35": 27868,
+      "36": 63133,
+      "37": 23066,
+      "38": 39277,
+      "39": 16326,
+      "4": 115511,
+      "40": 29516,
+      "41": 10784,
+      "42": 14119,
+      "43": 5806,
+      "44": 7788,
+      "45": 3709,
+      "46": 4199,
+      "47": 2524,
+      "48": 3576,
+      "49": 2193,
+      "5": 916776,
+      "50": 2972,
+      "51": 1847,
+      "52": 2706,
+      "53": 1722,
+      "54": 2426,
+      "55": 1699,
+      "56": 2546,
+      "57": 1756,
+      "58": 2263,
+      "59": 1688,
+      "6": 5190372,
+      "60": 2465,
+      "61": 1652,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1982449,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6072619,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1772764,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51530,
+      "7": 31271257,
+      "9": 115511
+    },
+    "connectivity_max": 140221065,
+    "connectivity_min": 0,
+    "n_cells": 31438298,
+    "n_connectivity_values": 343307615,
+    "n_fan_triangles": 280431019,
+    "n_points": 140221066
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.9153656184241765e-11,
+    "float64_area_closure_relative": 6.252356492143557e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280431019,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936420.8494607806,
+    "surface_area_float64_in2": 1936420.8495172344,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936420.8495171133,
+    "zero_area_triangles": 237911,
+    "zero_weight_points": 5453
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC115_AoA_16.json b/surface_dual_areas/cases/geo_LHC115_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..86559e84f24f2b4772e44334eab56a99e29918de
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC115_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC115_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC115_AoA_16/boundary_dual_area_geo_LHC115_AoA_16.npy",
+    "sha256": "84c0895cce41897ad08f26bb3bc13121febb03c0123e9d911c5d667ce5f13367",
+    "shape": [
+      140110323
+    ],
+    "size_bytes": 560441420
+  },
+  "runtime": {
+    "accumulation_seconds": 11.026843389961869,
+    "completed_at_utc": "2026-08-07T08:26:17.266659Z",
+    "elapsed_seconds": 21.640550815034658,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.401302234036848,
+    "geometry_read_seconds": 2.353993684053421,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:25:55.626017Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC115_AoA_16/boundary_geo_LHC115_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC115_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624494000000000,
+    "extracted_vtu_size_bytes": 21522534022,
+    "geometry_sha256": "421edfdb50135e081ee23ef5707e1566350c3b2931958853b6cb25b3d0657f28",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4053457,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1203697,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2679811,
+      "13": 756491,
+      "14": 1219084,
+      "15": 433395,
+      "16": 872808,
+      "17": 343194,
+      "18": 748059,
+      "19": 301355,
+      "20": 670930,
+      "21": 228397,
+      "22": 375523,
+      "23": 127807,
+      "24": 208815,
+      "25": 71063,
+      "26": 94566,
+      "27": 52342,
+      "28": 124768,
+      "29": 53260,
+      "3": 50452,
+      "30": 114273,
+      "31": 49112,
+      "32": 107299,
+      "33": 38472,
+      "34": 66592,
+      "35": 27875,
+      "36": 63126,
+      "37": 23062,
+      "38": 39273,
+      "39": 16324,
+      "4": 116335,
+      "40": 29518,
+      "41": 10784,
+      "42": 14119,
+      "43": 5810,
+      "44": 7787,
+      "45": 3706,
+      "46": 4197,
+      "47": 2523,
+      "48": 3579,
+      "49": 2193,
+      "5": 918237,
+      "50": 2971,
+      "51": 1848,
+      "52": 2706,
+      "53": 1722,
+      "54": 2426,
+      "55": 1699,
+      "56": 2546,
+      "57": 1756,
+      "58": 2263,
+      "59": 1688,
+      "6": 5194112,
+      "60": 2465,
+      "61": 1652,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1989812,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6091426,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1798075,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50452,
+      "7": 31284890,
+      "9": 116335
+    },
+    "connectivity_max": 140110322,
+    "connectivity_min": 0,
+    "n_cells": 31451677,
+    "n_connectivity_values": 343112886,
+    "n_fan_triangles": 280209532,
+    "n_points": 140110323
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.982878434483464e-11,
+    "float64_area_closure_relative": 5.4828345713290744e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280209532,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936421.2456488747,
+    "surface_area_float64_in2": 1936421.2457066358,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936421.2457065296,
+    "zero_area_triangles": 236959,
+    "zero_weight_points": 5501
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC115_AoA_4.json b/surface_dual_areas/cases/geo_LHC115_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..aba7996b45f761247753efe7d4cf08545d2370cb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC115_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC115_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC115_AoA_4/boundary_dual_area_geo_LHC115_AoA_4.npy",
+    "sha256": "a8c870f4a8900a6af7974079be51014575602f4f3b09290b0dbf84491569be6d",
+    "shape": [
+      136145714
+    ],
+    "size_bytes": 544582984
+  },
+  "runtime": {
+    "accumulation_seconds": 10.508170941844583,
+    "completed_at_utc": "2026-08-07T07:52:15.841398Z",
+    "elapsed_seconds": 20.290063071995974,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.026621980126947,
+    "geometry_read_seconds": 2.1626888120081276,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:51:55.551243Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC115_AoA_4/boundary_geo_LHC115_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC115_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624383000000000,
+    "extracted_vtu_size_bytes": 20903756273,
+    "geometry_sha256": "0c6c3c7a19130165350c4bce19a214094e182006bac940e95ca1710db7a0af06",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3288245,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1002483,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2428415,
+      "13": 759543,
+      "14": 1586078,
+      "15": 519869,
+      "16": 1001427,
+      "17": 372074,
+      "18": 748178,
+      "19": 300816,
+      "20": 658646,
+      "21": 221676,
+      "22": 347481,
+      "23": 120539,
+      "24": 193124,
+      "25": 67920,
+      "26": 92917,
+      "27": 51873,
+      "28": 124597,
+      "29": 53219,
+      "3": 49034,
+      "30": 114268,
+      "31": 49083,
+      "32": 107287,
+      "33": 38458,
+      "34": 66587,
+      "35": 27861,
+      "36": 63131,
+      "37": 23068,
+      "38": 39291,
+      "39": 16331,
+      "4": 111193,
+      "40": 29523,
+      "41": 10799,
+      "42": 14123,
+      "43": 5811,
+      "44": 7791,
+      "45": 3710,
+      "46": 4200,
+      "47": 2523,
+      "48": 3576,
+      "49": 2193,
+      "5": 913502,
+      "50": 2971,
+      "51": 1849,
+      "52": 2706,
+      "53": 1722,
+      "54": 2425,
+      "55": 1699,
+      "56": 2546,
+      "57": 1756,
+      "58": 2263,
+      "59": 1688,
+      "6": 5204430,
+      "60": 2465,
+      "61": 1652,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1925618,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5770104,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1583655,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49034,
+      "7": 30010825,
+      "9": 111193
+    },
+    "connectivity_max": 136145713,
+    "connectivity_min": 0,
+    "n_cells": 30171052,
+    "n_connectivity_values": 332622419,
+    "n_fan_triangles": 272280315,
+    "n_points": 136145714
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.947119889580407e-11,
+    "float64_area_closure_relative": 1.8035640755791775e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272280315,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936421.1685041385,
+    "surface_area_float64_in2": 1936421.1685612071,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936421.1685612036,
+    "zero_area_triangles": 229156,
+    "zero_weight_points": 5027
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC115_AoA_8.json b/surface_dual_areas/cases/geo_LHC115_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..b8dd8f5160219c22017d99bae4f32cdf7e40da30
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC115_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC115_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC115_AoA_8/boundary_dual_area_geo_LHC115_AoA_8.npy",
+    "sha256": "b53b3ae2a4f65a7d1f8e5e945f0c4f613b78fdd19d84792fa3f05fc54a70d740",
+    "shape": [
+      139943246
+    ],
+    "size_bytes": 559773112
+  },
+  "runtime": {
+    "accumulation_seconds": 11.06712011108175,
+    "completed_at_utc": "2026-08-07T07:51:50.086356Z",
+    "elapsed_seconds": 21.047139309113845,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0442564971745014,
+    "geometry_read_seconds": 1.8022298100404441,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:51:29.039131Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC115_AoA_8/boundary_geo_LHC115_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC115_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624530000000000,
+    "extracted_vtu_size_bytes": 21494212434,
+    "geometry_sha256": "9a3529cef905b2a2c399469fef90bcf065f2ef4ffccc90b1d6f9300e9a76fdaf",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3847789,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1132393,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2659213,
+      "13": 773367,
+      "14": 1434917,
+      "15": 482274,
+      "16": 953040,
+      "17": 360008,
+      "18": 745577,
+      "19": 299776,
+      "20": 658049,
+      "21": 221162,
+      "22": 346721,
+      "23": 120217,
+      "24": 191829,
+      "25": 67698,
+      "26": 92639,
+      "27": 51805,
+      "28": 124503,
+      "29": 53187,
+      "3": 50014,
+      "30": 114258,
+      "31": 49088,
+      "32": 107288,
+      "33": 38456,
+      "34": 66583,
+      "35": 27861,
+      "36": 63131,
+      "37": 23069,
+      "38": 39292,
+      "39": 16329,
+      "4": 113910,
+      "40": 29523,
+      "41": 10800,
+      "42": 14123,
+      "43": 5810,
+      "44": 7791,
+      "45": 3710,
+      "46": 4200,
+      "47": 2523,
+      "48": 3576,
+      "49": 2193,
+      "5": 917434,
+      "50": 2971,
+      "51": 1849,
+      "52": 2706,
+      "53": 1722,
+      "54": 2425,
+      "55": 1699,
+      "56": 2546,
+      "57": 1756,
+      "58": 2263,
+      "59": 1688,
+      "6": 5216507,
+      "60": 2465,
+      "61": 1652,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1972640,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6025498,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1721356,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50014,
+      "7": 31143985,
+      "9": 113910
+    },
+    "connectivity_max": 139943245,
+    "connectivity_min": 0,
+    "n_cells": 31307909,
+    "n_connectivity_values": 342491197,
+    "n_fan_triangles": 279875379,
+    "n_points": 139943246
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.9866071272072146e-11,
+    "float64_area_closure_relative": 3.871652448390943e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279875379,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936420.3851888883,
+    "surface_area_float64_in2": 1936420.3852467216,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936420.3852466466,
+    "zero_area_triangles": 236289,
+    "zero_weight_points": 5415
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC116_AoA_14.json b/surface_dual_areas/cases/geo_LHC116_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..4011fc1022adfaf76364c0e1f2e6c155e0fd14fa
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC116_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC116_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC116_AoA_14/boundary_dual_area_geo_LHC116_AoA_14.npy",
+    "sha256": "f9c1ce39ef813d9f91070cbbea55f9f356555ad6b6e480c2f791bac1f3ae7dbb",
+    "shape": [
+      147187742
+    ],
+    "size_bytes": 588751096
+  },
+  "runtime": {
+    "accumulation_seconds": 11.276993256993592,
+    "completed_at_utc": "2026-08-07T07:53:30.839207Z",
+    "elapsed_seconds": 21.383406535023823,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.261289694812149,
+    "geometry_read_seconds": 1.936261601978913,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:53:09.455707Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC116_AoA_14/boundary_geo_LHC116_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC116_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624708000000000,
+    "extracted_vtu_size_bytes": 22615271737,
+    "geometry_sha256": "4c106557247f76a739d1f5a413e01a660a96ea771734974958a0a969e563b522",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4315308,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1369133,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2927528,
+      "13": 825268,
+      "14": 1380210,
+      "15": 444701,
+      "16": 911495,
+      "17": 349411,
+      "18": 752387,
+      "19": 303672,
+      "20": 673971,
+      "21": 226100,
+      "22": 365371,
+      "23": 123203,
+      "24": 205271,
+      "25": 70936,
+      "26": 91282,
+      "27": 52126,
+      "28": 123665,
+      "29": 53232,
+      "3": 56939,
+      "30": 114355,
+      "31": 49240,
+      "32": 108129,
+      "33": 38863,
+      "34": 67076,
+      "35": 28004,
+      "36": 63019,
+      "37": 23089,
+      "38": 38704,
+      "39": 16020,
+      "4": 130806,
+      "40": 29112,
+      "41": 10645,
+      "42": 14013,
+      "43": 5816,
+      "44": 7869,
+      "45": 3730,
+      "46": 4274,
+      "47": 2527,
+      "48": 3659,
+      "49": 2163,
+      "5": 941372,
+      "50": 2831,
+      "51": 1758,
+      "52": 2545,
+      "53": 1648,
+      "54": 2210,
+      "55": 1614,
+      "56": 2428,
+      "57": 1720,
+      "58": 2246,
+      "59": 1681,
+      "6": 5238471,
+      "60": 2463,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 921,
+      "7": 2127847,
+      "70": 991,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6509106,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2019917,
+      "90": 58,
+      "91": 57,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56939,
+      "7": 33075123,
+      "9": 130806
+    },
+    "connectivity_max": 147187741,
+    "connectivity_min": 0,
+    "n_cells": 33262868,
+    "n_connectivity_values": 360890097,
+    "n_fan_triangles": 294364361,
+    "n_points": 147187742
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3603904458792176e-11,
+    "float64_area_closure_relative": 1.4363405124400923e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294364361,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945198.7182385346,
+    "surface_area_float64_in2": 1945198.718303901,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945198.718303873,
+    "zero_area_triangles": 243793,
+    "zero_weight_points": 6101
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC116_AoA_8.json b/surface_dual_areas/cases/geo_LHC116_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..b7a04458d89d52dd1cc701d2a1bb3f6957e68d6e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC116_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC116_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC116_AoA_8/boundary_dual_area_geo_LHC116_AoA_8.npy",
+    "sha256": "920ab25f5d9cc3c552e3aabd6d231cecad674c11ae30593a32575552549d872d",
+    "shape": [
+      139816948
+    ],
+    "size_bytes": 559267920
+  },
+  "runtime": {
+    "accumulation_seconds": 10.719412023900077,
+    "completed_at_utc": "2026-08-07T07:52:38.897568Z",
+    "elapsed_seconds": 21.908321843016893,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0884047059807926,
+    "geometry_read_seconds": 3.272845725994557,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:52:16.989161Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC116_AoA_8/boundary_geo_LHC116_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC116_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624451000000000,
+    "extracted_vtu_size_bytes": 21470370650,
+    "geometry_sha256": "e2c17fcc894443f30ee77d14ed14b4c11f3a67bb6db13c1b7a6712179f991fba",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3309055,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1046283,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2435145,
+      "13": 781369,
+      "14": 1667771,
+      "15": 529550,
+      "16": 1021880,
+      "17": 375676,
+      "18": 761461,
+      "19": 306041,
+      "20": 676418,
+      "21": 227178,
+      "22": 367522,
+      "23": 124155,
+      "24": 205903,
+      "25": 71267,
+      "26": 91313,
+      "27": 52109,
+      "28": 123710,
+      "29": 53218,
+      "3": 53312,
+      "30": 114378,
+      "31": 49221,
+      "32": 108153,
+      "33": 38870,
+      "34": 67116,
+      "35": 28023,
+      "36": 63055,
+      "37": 23092,
+      "38": 38720,
+      "39": 16025,
+      "4": 128143,
+      "40": 29114,
+      "41": 10647,
+      "42": 14022,
+      "43": 5818,
+      "44": 7869,
+      "45": 3734,
+      "46": 4276,
+      "47": 2529,
+      "48": 3660,
+      "49": 2163,
+      "5": 943142,
+      "50": 2831,
+      "51": 1758,
+      "52": 2544,
+      "53": 1648,
+      "54": 2210,
+      "55": 1614,
+      "56": 2428,
+      "57": 1720,
+      "58": 2246,
+      "59": 1681,
+      "6": 5275660,
+      "60": 2463,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 921,
+      "7": 2023173,
+      "70": 991,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6081689,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1695465,
+      "90": 58,
+      "91": 57,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53312,
+      "7": 30920470,
+      "9": 128143
+    },
+    "connectivity_max": 139816947,
+    "connectivity_min": 0,
+    "n_cells": 31101925,
+    "n_connectivity_values": 341826623,
+    "n_fan_triangles": 279622773,
+    "n_points": 139816948
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.562061525775323e-11,
+    "float64_area_closure_relative": 1.158647005813442e-13,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279622773,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945200.4097717998,
+    "surface_area_float64_in2": 1945200.409841089,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945200.4098408637,
+    "zero_area_triangles": 229984,
+    "zero_weight_points": 5219
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC118_AoA_12.json b/surface_dual_areas/cases/geo_LHC118_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..62308973336cf9a5aa837291a38dfd9faf4069a6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC118_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC118_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC118_AoA_12/boundary_dual_area_geo_LHC118_AoA_12.npy",
+    "sha256": "2d59e0fa30370af61db9c908258885df1725a500fb640552d3586699b2fa475a",
+    "shape": [
+      143237740
+    ],
+    "size_bytes": 572951088
+  },
+  "runtime": {
+    "accumulation_seconds": 11.590612340020016,
+    "completed_at_utc": "2026-08-07T08:29:18.197358Z",
+    "elapsed_seconds": 23.521959190024063,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.450766006950289,
+    "geometry_read_seconds": 3.4520301478914917,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:28:54.675310Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC118_AoA_12/boundary_geo_LHC118_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC118_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624501000000000,
+    "extracted_vtu_size_bytes": 22007167368,
+    "geometry_sha256": "c22dc746ed834b95a1dab73262826918d43dcc160900a38046447ddd39b9173c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4180477,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1236537,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2764036,
+      "13": 799222,
+      "14": 1351660,
+      "15": 468293,
+      "16": 945397,
+      "17": 365229,
+      "18": 755479,
+      "19": 303486,
+      "20": 658011,
+      "21": 219765,
+      "22": 339885,
+      "23": 117410,
+      "24": 184827,
+      "25": 65792,
+      "26": 90384,
+      "27": 51416,
+      "28": 124353,
+      "29": 53218,
+      "3": 55400,
+      "30": 114070,
+      "31": 48872,
+      "32": 107659,
+      "33": 38498,
+      "34": 66115,
+      "35": 27685,
+      "36": 63341,
+      "37": 22834,
+      "38": 39443,
+      "39": 16337,
+      "4": 122865,
+      "40": 29980,
+      "41": 10917,
+      "42": 14354,
+      "43": 5858,
+      "44": 7934,
+      "45": 3741,
+      "46": 4251,
+      "47": 2513,
+      "48": 3597,
+      "49": 2211,
+      "5": 942020,
+      "50": 2953,
+      "51": 1807,
+      "52": 2703,
+      "53": 1731,
+      "54": 2422,
+      "55": 1696,
+      "56": 2557,
+      "57": 1773,
+      "58": 2289,
+      "59": 1695,
+      "6": 5288428,
+      "60": 2466,
+      "61": 1653,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 921,
+      "7": 2041149,
+      "70": 991,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6281762,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1841202,
+      "90": 58,
+      "91": 57,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 55400,
+      "7": 32144434,
+      "9": 122865
+    },
+    "connectivity_max": 143237739,
+    "connectivity_min": 0,
+    "n_cells": 32322699,
+    "n_connectivity_values": 351109774,
+    "n_fan_triangles": 286464376,
+    "n_points": 143237740
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.080954978824609e-11,
+    "float64_area_closure_relative": 6.670760588127911e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 286464376,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937125.542364711,
+    "surface_area_float64_in2": 1937125.5424437642,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937125.5424438934,
+    "zero_area_triangles": 240651,
+    "zero_weight_points": 5727
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC119_AoA_12.json b/surface_dual_areas/cases/geo_LHC119_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..90043321ac3cb7d14a793125c5280a5c786367ab
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC119_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC119_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC119_AoA_12/boundary_dual_area_geo_LHC119_AoA_12.npy",
+    "sha256": "7a3c6ffb974e077588b19f33803209bd2542502fc89050be3da322bdca7fef33",
+    "shape": [
+      139752200
+    ],
+    "size_bytes": 559008928
+  },
+  "runtime": {
+    "accumulation_seconds": 10.787419118918478,
+    "completed_at_utc": "2026-08-07T08:30:31.624749Z",
+    "elapsed_seconds": 52.87641946505755,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2132770579773933,
+    "geometry_read_seconds": 33.77680974104442,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:29:38.748242Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC119_AoA_12/boundary_geo_LHC119_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC119_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624711000000000,
+    "extracted_vtu_size_bytes": 21465003269,
+    "geometry_sha256": "6b44a6c0a115e516e78c93260f7da8f26bb32e566abf1ec3d4caeff9aadd57d0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3791332,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1172259,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2636349,
+      "13": 776038,
+      "14": 1377601,
+      "15": 461160,
+      "16": 918597,
+      "17": 351067,
+      "18": 748975,
+      "19": 302646,
+      "20": 677894,
+      "21": 226301,
+      "22": 360723,
+      "23": 123419,
+      "24": 201930,
+      "25": 68457,
+      "26": 94074,
+      "27": 51992,
+      "28": 124932,
+      "29": 53318,
+      "3": 52840,
+      "30": 114584,
+      "31": 49262,
+      "32": 108362,
+      "33": 38713,
+      "34": 66462,
+      "35": 28091,
+      "36": 62982,
+      "37": 23072,
+      "38": 38436,
+      "39": 16063,
+      "4": 117468,
+      "40": 29123,
+      "41": 10629,
+      "42": 14079,
+      "43": 5726,
+      "44": 7610,
+      "45": 3692,
+      "46": 4232,
+      "47": 2566,
+      "48": 3544,
+      "49": 2117,
+      "5": 933407,
+      "50": 2940,
+      "51": 1805,
+      "52": 2618,
+      "53": 1703,
+      "54": 2290,
+      "55": 1641,
+      "56": 2455,
+      "57": 1710,
+      "58": 2267,
+      "59": 1716,
+      "6": 5193858,
+      "60": 2503,
+      "61": 1657,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 2006500,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6007374,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1766429,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52840,
+      "7": 31100228,
+      "9": 117468
+    },
+    "connectivity_max": 139752199,
+    "connectivity_min": 0,
+    "n_cells": 31270536,
+    "n_connectivity_values": 342034355,
+    "n_fan_triangles": 279493283,
+    "n_points": 139752200
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1714725248969235e-11,
+    "float64_area_closure_relative": 3.688806626923622e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279493283,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937727.1521300331,
+    "surface_area_float64_in2": 1937727.1521914876,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937727.152191559,
+    "zero_area_triangles": 238166,
+    "zero_weight_points": 5512
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC119_AoA_20.json b/surface_dual_areas/cases/geo_LHC119_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..f1767a8e5f701f93e0d0f21419659d6cb305042b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC119_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC119_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC119_AoA_20/boundary_dual_area_geo_LHC119_AoA_20.npy",
+    "sha256": "54faf66d8d577872f84711b59bec2762a4ab1dffab658a10f5b66520cbd34301",
+    "shape": [
+      139348455
+    ],
+    "size_bytes": 557393948
+  },
+  "runtime": {
+    "accumulation_seconds": 10.625567579874769,
+    "completed_at_utc": "2026-08-07T07:53:49.112759Z",
+    "elapsed_seconds": 20.51705894409679,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1968334862031043,
+    "geometry_read_seconds": 1.88992293109186,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:53:28.595598Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC119_AoA_20/boundary_geo_LHC119_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC119_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624720000000000,
+    "extracted_vtu_size_bytes": 21403082009,
+    "geometry_sha256": "c00f32519d8cfc6cea19fb8d60cfbb7295c98542a77313f64c2e6cd004477baa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3831234,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1161657,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2566408,
+      "13": 753872,
+      "14": 1334376,
+      "15": 455093,
+      "16": 920894,
+      "17": 351411,
+      "18": 753735,
+      "19": 303470,
+      "20": 680091,
+      "21": 227008,
+      "22": 365086,
+      "23": 124486,
+      "24": 206093,
+      "25": 69819,
+      "26": 95249,
+      "27": 52542,
+      "28": 125223,
+      "29": 53429,
+      "3": 51076,
+      "30": 114656,
+      "31": 49263,
+      "32": 108388,
+      "33": 38702,
+      "34": 66456,
+      "35": 28079,
+      "36": 62965,
+      "37": 23067,
+      "38": 38425,
+      "39": 16056,
+      "4": 117256,
+      "40": 29102,
+      "41": 10612,
+      "42": 14069,
+      "43": 5717,
+      "44": 7611,
+      "45": 3683,
+      "46": 4226,
+      "47": 2566,
+      "48": 3542,
+      "49": 2117,
+      "5": 930691,
+      "50": 2939,
+      "51": 1801,
+      "52": 2618,
+      "53": 1701,
+      "54": 2289,
+      "55": 1641,
+      "56": 2455,
+      "57": 1710,
+      "58": 2267,
+      "59": 1716,
+      "6": 5187553,
+      "60": 2503,
+      "61": 1657,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 1999659,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6024489,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1768411,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51076,
+      "7": 31015524,
+      "9": 117256
+    },
+    "connectivity_max": 139348454,
+    "connectivity_min": 0,
+    "n_cells": 31183856,
+    "n_connectivity_values": 341053505,
+    "n_fan_triangles": 278685793,
+    "n_points": 139348455
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.147608499690282e-11,
+    "float64_area_closure_relative": 3.340351592859564e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278685793,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937727.7251921808,
+    "surface_area_float64_in2": 1937727.725253173,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937727.7252532376,
+    "zero_area_triangles": 237683,
+    "zero_weight_points": 5437
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC119_AoA_4.json b/surface_dual_areas/cases/geo_LHC119_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..b80583ddfd38562eeb6b9304eafb65fbbaab8f8f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC119_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC119_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC119_AoA_4/boundary_dual_area_geo_LHC119_AoA_4.npy",
+    "sha256": "b1af43b580a00fa9ee87a23750bbc5cea6757ac19959e37b837c46c0984486d0",
+    "shape": [
+      128934968
+    ],
+    "size_bytes": 515740000
+  },
+  "runtime": {
+    "accumulation_seconds": 10.00421906192787,
+    "completed_at_utc": "2026-08-07T07:54:49.911886Z",
+    "elapsed_seconds": 19.79244933789596,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9080495480448008,
+    "geometry_read_seconds": 2.61051693581976,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:54:30.119351Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC119_AoA_4/boundary_geo_LHC119_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC119_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624574000000000,
+    "extracted_vtu_size_bytes": 19784243499,
+    "geometry_sha256": "ea5c212754b3c44df782b104a5bbd4281e3f9ee977495f832825d36ce26e1388",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2310978,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 796340,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1846749,
+      "13": 711067,
+      "14": 1811550,
+      "15": 559321,
+      "16": 1074111,
+      "17": 384193,
+      "18": 764629,
+      "19": 307433,
+      "20": 682626,
+      "21": 228334,
+      "22": 364909,
+      "23": 124606,
+      "24": 204672,
+      "25": 69080,
+      "26": 94625,
+      "27": 52122,
+      "28": 125105,
+      "29": 53357,
+      "3": 47891,
+      "30": 114614,
+      "31": 49257,
+      "32": 108378,
+      "33": 38692,
+      "34": 66475,
+      "35": 28089,
+      "36": 62978,
+      "37": 23077,
+      "38": 38432,
+      "39": 16058,
+      "4": 111176,
+      "40": 29125,
+      "41": 10621,
+      "42": 14073,
+      "43": 5729,
+      "44": 7608,
+      "45": 3692,
+      "46": 4231,
+      "47": 2564,
+      "48": 3543,
+      "49": 2115,
+      "5": 929320,
+      "50": 2940,
+      "51": 1804,
+      "52": 2619,
+      "53": 1703,
+      "54": 2290,
+      "55": 1641,
+      "56": 2455,
+      "57": 1710,
+      "58": 2267,
+      "59": 1716,
+      "6": 5192694,
+      "60": 2503,
+      "61": 1657,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 1881713,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5280153,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1395803,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 47891,
+      "7": 27919092,
+      "9": 111176
+    },
+    "connectivity_max": 128934967,
+    "connectivity_min": 0,
+    "n_cells": 28078159,
+    "n_connectivity_values": 314015136,
+    "n_fan_triangles": 257858818,
+    "n_points": 128934968
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1027504389972085e-11,
+    "float64_area_closure_relative": 2.763597007928551e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 257858818,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937729.99048322,
+    "surface_area_float64_in2": 1937729.990543343,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937729.9905433964,
+    "zero_area_triangles": 217811,
+    "zero_weight_points": 4261
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC120_AoA_16.json b/surface_dual_areas/cases/geo_LHC120_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..21bab443b116d142fe88cdb9e9a05c3b7b3a79a5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC120_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC120_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC120_AoA_16/boundary_dual_area_geo_LHC120_AoA_16.npy",
+    "sha256": "e9e6c78c904a3a3ae4bfc160f8e810a64c108ba32801da3c16dcaa31918b6ce5",
+    "shape": [
+      152163059
+    ],
+    "size_bytes": 608652364
+  },
+  "runtime": {
+    "accumulation_seconds": 11.978125917026773,
+    "completed_at_utc": "2026-08-07T08:30:56.028785Z",
+    "elapsed_seconds": 23.31305950693786,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3902202770113945,
+    "geometry_read_seconds": 2.34824969409965,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:30:32.715625Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC120_AoA_16/boundary_geo_LHC120_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC120_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624551000000000,
+    "extracted_vtu_size_bytes": 23388012765,
+    "geometry_sha256": "3408fc17da99fee31e4c50a98b042fef152205bc21406cc1a96fff7a7937b4a7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4801700,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1401018,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3335610,
+      "13": 863487,
+      "14": 1333172,
+      "15": 462434,
+      "16": 896997,
+      "17": 355964,
+      "18": 736659,
+      "19": 300757,
+      "20": 662129,
+      "21": 220031,
+      "22": 341876,
+      "23": 116922,
+      "24": 190973,
+      "25": 67974,
+      "26": 89182,
+      "27": 51474,
+      "28": 123649,
+      "29": 52992,
+      "3": 60708,
+      "30": 114590,
+      "31": 48887,
+      "32": 107193,
+      "33": 38354,
+      "34": 65086,
+      "35": 27643,
+      "36": 62371,
+      "37": 22909,
+      "38": 39363,
+      "39": 16515,
+      "4": 137627,
+      "40": 30326,
+      "41": 11084,
+      "42": 14462,
+      "43": 5985,
+      "44": 7879,
+      "45": 3742,
+      "46": 4280,
+      "47": 2490,
+      "48": 3644,
+      "49": 2211,
+      "5": 965718,
+      "50": 2974,
+      "51": 1847,
+      "52": 2763,
+      "53": 1784,
+      "54": 2417,
+      "55": 1708,
+      "56": 2507,
+      "57": 1776,
+      "58": 2275,
+      "59": 1692,
+      "6": 5337410,
+      "60": 2469,
+      "61": 1651,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2159388,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6939053,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2039814,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60708,
+      "7": 34520301,
+      "9": 137627
+    },
+    "connectivity_max": 152163058,
+    "connectivity_min": 0,
+    "n_cells": 34718636,
+    "n_connectivity_values": 373752256,
+    "n_fan_triangles": 304314984,
+    "n_points": 152163059
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.7268240958521736e-11,
+    "float64_area_closure_relative": 4.793150718229326e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 304314984,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947885.5055952189,
+    "surface_area_float64_in2": 1947885.5056678131,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947885.5056679065,
+    "zero_area_triangles": 246429,
+    "zero_weight_points": 6290
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC120_AoA_20.json b/surface_dual_areas/cases/geo_LHC120_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..8474c2baec7be9e1fe909260459f4f76e00072a6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC120_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC120_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC120_AoA_20/boundary_dual_area_geo_LHC120_AoA_20.npy",
+    "sha256": "86f9d825b30376947b40b257d99b75d68b632a28a0a922e1389c5a097ae57425",
+    "shape": [
+      150972281
+    ],
+    "size_bytes": 603889252
+  },
+  "runtime": {
+    "accumulation_seconds": 11.530378185911104,
+    "completed_at_utc": "2026-08-07T08:30:26.893667Z",
+    "elapsed_seconds": 22.987677715020254,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.545503641013056,
+    "geometry_read_seconds": 2.654413955984637,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:30:03.905894Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC120_AoA_20/boundary_geo_LHC120_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC120_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624577000000000,
+    "extracted_vtu_size_bytes": 23203613246,
+    "geometry_sha256": "00c0260f1b219786d12dbc7e338124f755677dc2d68b25f0ec9067bccaf28607",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4761400,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1403179,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3257545,
+      "13": 854725,
+      "14": 1243017,
+      "15": 450393,
+      "16": 879335,
+      "17": 353859,
+      "18": 746957,
+      "19": 303607,
+      "20": 673245,
+      "21": 223340,
+      "22": 352951,
+      "23": 119176,
+      "24": 199378,
+      "25": 68883,
+      "26": 90692,
+      "27": 51647,
+      "28": 123855,
+      "29": 53011,
+      "3": 61439,
+      "30": 114594,
+      "31": 48890,
+      "32": 107189,
+      "33": 38354,
+      "34": 65095,
+      "35": 27641,
+      "36": 62375,
+      "37": 22907,
+      "38": 39363,
+      "39": 16513,
+      "4": 139874,
+      "40": 30324,
+      "41": 11087,
+      "42": 14459,
+      "43": 5983,
+      "44": 7881,
+      "45": 3743,
+      "46": 4281,
+      "47": 2488,
+      "48": 3642,
+      "49": 2211,
+      "5": 958686,
+      "50": 2974,
+      "51": 1847,
+      "52": 2763,
+      "53": 1784,
+      "54": 2417,
+      "55": 1708,
+      "56": 2507,
+      "57": 1776,
+      "58": 2275,
+      "59": 1692,
+      "6": 5292530,
+      "60": 2469,
+      "61": 1651,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2141625,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6881014,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2032774,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61439,
+      "7": 34190748,
+      "9": 139874
+    },
+    "connectivity_max": 150972280,
+    "connectivity_min": 0,
+    "n_cells": 34392061,
+    "n_connectivity_values": 370717550,
+    "n_fan_triangles": 301933428,
+    "n_points": 150972281
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6659691082195085e-11,
+    "float64_area_closure_relative": 2.1515376296613668e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 301933428,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947886.724284545,
+    "surface_area_float64_in2": 1947886.724355954,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947886.724355996,
+    "zero_area_triangles": 245299,
+    "zero_weight_points": 6236
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC120_AoA_6.json b/surface_dual_areas/cases/geo_LHC120_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a7fd1b97893121caad4e6ce0febcfae4a147dba
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC120_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC120_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC120_AoA_6/boundary_dual_area_geo_LHC120_AoA_6.npy",
+    "sha256": "beace13abebe91266f738d9c8a2032b255643d1813f15ec2a973853e519b936d",
+    "shape": [
+      147019837
+    ],
+    "size_bytes": 588079476
+  },
+  "runtime": {
+    "accumulation_seconds": 11.189630603883415,
+    "completed_at_utc": "2026-08-07T07:54:52.223965Z",
+    "elapsed_seconds": 22.10459372214973,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.311914207879454,
+    "geometry_read_seconds": 2.6413908421527594,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:54:30.119283Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC120_AoA_6/boundary_geo_LHC120_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC120_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624408000000000,
+    "extracted_vtu_size_bytes": 22588832334,
+    "geometry_sha256": "0bb1ba03154d8b6226ecfa20119864626658737db10438095eb7b8cba20852df",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3946781,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1201696,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2930862,
+      "13": 844854,
+      "14": 1591648,
+      "15": 522702,
+      "16": 1028723,
+      "17": 380204,
+      "18": 748938,
+      "19": 302754,
+      "20": 661669,
+      "21": 218198,
+      "22": 335737,
+      "23": 114707,
+      "24": 184410,
+      "25": 66615,
+      "26": 87956,
+      "27": 51206,
+      "28": 123587,
+      "29": 52956,
+      "3": 56968,
+      "30": 114588,
+      "31": 48886,
+      "32": 107195,
+      "33": 38354,
+      "34": 65084,
+      "35": 27645,
+      "36": 62372,
+      "37": 22907,
+      "38": 39365,
+      "39": 16513,
+      "4": 133869,
+      "40": 30326,
+      "41": 11086,
+      "42": 14462,
+      "43": 5985,
+      "44": 7879,
+      "45": 3742,
+      "46": 4280,
+      "47": 2490,
+      "48": 3644,
+      "49": 2211,
+      "5": 968677,
+      "50": 2974,
+      "51": 1847,
+      "52": 2763,
+      "53": 1784,
+      "54": 2417,
+      "55": 1708,
+      "56": 2507,
+      "57": 1776,
+      "58": 2275,
+      "59": 1692,
+      "6": 5391964,
+      "60": 2469,
+      "61": 1651,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2100872,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6645383,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1831439,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56968,
+      "7": 33008456,
+      "9": 133869
+    },
+    "connectivity_max": 147019836,
+    "connectivity_min": 0,
+    "n_cells": 33199293,
+    "n_connectivity_values": 360427126,
+    "n_fan_triangles": 294028540,
+    "n_points": 147019837
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6595162953465185e-11,
+    "float64_area_closure_relative": 4.8409620478749275e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294028540,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947885.7661724573,
+    "surface_area_float64_in2": 1947885.7662437405,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947885.7662438347,
+    "zero_area_triangles": 237172,
+    "zero_weight_points": 5747
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC120_AoA_8.json b/surface_dual_areas/cases/geo_LHC120_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..38932a38c08094a8830d8d3379604e85e32c9e26
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC120_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC120_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC120_AoA_8/boundary_dual_area_geo_LHC120_AoA_8.npy",
+    "sha256": "931db7773d706d1c8ef4a7b96ebf8a5d3185154a009a3e41a803ddc345df7277",
+    "shape": [
+      150230566
+    ],
+    "size_bytes": 600922392
+  },
+  "runtime": {
+    "accumulation_seconds": 11.822243054863065,
+    "completed_at_utc": "2026-08-07T07:55:14.024578Z",
+    "elapsed_seconds": 23.1206524358131,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.371164286043495,
+    "geometry_read_seconds": 2.115378070855513,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:54:50.903788Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC120_AoA_8/boundary_geo_LHC120_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC120_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624625000000000,
+    "extracted_vtu_size_bytes": 23087703576,
+    "geometry_sha256": "4cd57786d3215ffcf2e9a1189ce0db71835ae058687f02b3dd6cbd8fb2c2bb3d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4364588,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1327996,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3155924,
+      "13": 864308,
+      "14": 1479438,
+      "15": 488453,
+      "16": 986424,
+      "17": 369064,
+      "18": 742973,
+      "19": 300808,
+      "20": 659549,
+      "21": 217246,
+      "22": 334294,
+      "23": 114095,
+      "24": 183593,
+      "25": 66343,
+      "26": 87784,
+      "27": 51139,
+      "28": 123563,
+      "29": 52945,
+      "3": 60324,
+      "30": 114586,
+      "31": 48884,
+      "32": 107194,
+      "33": 38352,
+      "34": 65085,
+      "35": 27642,
+      "36": 62373,
+      "37": 22907,
+      "38": 39364,
+      "39": 16515,
+      "4": 136803,
+      "40": 30326,
+      "41": 11084,
+      "42": 14464,
+      "43": 5984,
+      "44": 7879,
+      "45": 3743,
+      "46": 4280,
+      "47": 2490,
+      "48": 3644,
+      "49": 2211,
+      "5": 970954,
+      "50": 2974,
+      "51": 1847,
+      "52": 2763,
+      "53": 1784,
+      "54": 2417,
+      "55": 1708,
+      "56": 2507,
+      "57": 1776,
+      "58": 2275,
+      "59": 1692,
+      "6": 5391652,
+      "60": 2469,
+      "61": 1651,
+      "62": 2225,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2146448,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6836008,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1960000,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60324,
+      "7": 33949500,
+      "9": 136803
+    },
+    "connectivity_max": 150230565,
+    "connectivity_min": 0,
+    "n_cells": 34146627,
+    "n_connectivity_values": 368743252,
+    "n_fan_triangles": 300449998,
+    "n_points": 150230566
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.700050606825262e-11,
+    "float64_area_closure_relative": 3.6695704612998075e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 300449998,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947884.8642621366,
+    "surface_area_float64_in2": 1947884.8643342094,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947884.8643342808,
+    "zero_area_triangles": 244008,
+    "zero_weight_points": 6181
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC121_AoA_12.json b/surface_dual_areas/cases/geo_LHC121_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..c20e9c06bd094f71050ae1e9b3b0adbad8207545
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC121_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC121_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC121_AoA_12/boundary_dual_area_geo_LHC121_AoA_12.npy",
+    "sha256": "273eaca9ca4778eed4325671dfefa8b3b4e6c5cc476ef550aa465058d6899d75",
+    "shape": [
+      144100576
+    ],
+    "size_bytes": 576402432
+  },
+  "runtime": {
+    "accumulation_seconds": 11.123537529958412,
+    "completed_at_utc": "2026-08-07T07:55:37.393893Z",
+    "elapsed_seconds": 22.02699112519622,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3389064411167055,
+    "geometry_read_seconds": 2.380335121182725,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:55:15.366816Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC121_AoA_12/boundary_geo_LHC121_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC121_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624405000000000,
+    "extracted_vtu_size_bytes": 22134672377,
+    "geometry_sha256": "dd1b9f42535eaaea7a01fc39029b518feb839a075bb6734c555b08c23c83fa45",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3946839,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1274012,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2818940,
+      "13": 812030,
+      "14": 1462892,
+      "15": 455549,
+      "16": 942328,
+      "17": 345967,
+      "18": 738351,
+      "19": 297694,
+      "20": 669808,
+      "21": 226796,
+      "22": 375997,
+      "23": 127282,
+      "24": 210484,
+      "25": 72242,
+      "26": 92656,
+      "27": 52057,
+      "28": 124192,
+      "29": 53226,
+      "3": 56155,
+      "30": 114879,
+      "31": 49406,
+      "32": 107775,
+      "33": 38662,
+      "34": 66954,
+      "35": 28140,
+      "36": 63619,
+      "37": 23188,
+      "38": 39120,
+      "39": 16378,
+      "4": 125932,
+      "40": 29492,
+      "41": 10686,
+      "42": 14074,
+      "43": 5681,
+      "44": 7571,
+      "45": 3639,
+      "46": 4246,
+      "47": 2504,
+      "48": 3512,
+      "49": 2138,
+      "5": 933967,
+      "50": 3011,
+      "51": 1840,
+      "52": 2698,
+      "53": 1720,
+      "54": 2342,
+      "55": 1678,
+      "56": 2482,
+      "57": 1717,
+      "58": 2273,
+      "59": 1715,
+      "6": 5187813,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2073194,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6263286,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1898984,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56155,
+      "7": 32132829,
+      "9": 125932
+    },
+    "connectivity_max": 144100575,
+    "connectivity_min": 0,
+    "n_cells": 32314916,
+    "n_connectivity_values": 352819862,
+    "n_fan_triangles": 288190030,
+    "n_points": 144100576
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.4198355664432595e-11,
+    "float64_area_closure_relative": 4.044871217729858e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 288190030,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945593.6497206306,
+    "surface_area_float64_in2": 1945593.6498066226,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945593.649806544,
+    "zero_area_triangles": 238331,
+    "zero_weight_points": 5708
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC121_AoA_8.json b/surface_dual_areas/cases/geo_LHC121_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..f7b2367feeb5e96b83dadc9312fe1bc150a3cde9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC121_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC121_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC121_AoA_8/boundary_dual_area_geo_LHC121_AoA_8.npy",
+    "sha256": "2ebf2fd10b025ca9ab5f1ac6e7e56d4c00240302a9bf44f0b28cff7e09ab0535",
+    "shape": [
+      138190194
+    ],
+    "size_bytes": 552760904
+  },
+  "runtime": {
+    "accumulation_seconds": 10.589924426050857,
+    "completed_at_utc": "2026-08-07T07:53:43.216598Z",
+    "elapsed_seconds": 20.113554944982752,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.044310129014775,
+    "geometry_read_seconds": 1.9519517838489264,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:53:23.102960Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC121_AoA_8/boundary_geo_LHC121_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC121_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624490000000000,
+    "extracted_vtu_size_bytes": 21216649566,
+    "geometry_sha256": "b59acae9d2c637cb8eefd2f7cd6b378c60be866890dc2ba0880ca85690af7cce",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3170955,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1015416,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2416263,
+      "13": 772295,
+      "14": 1680135,
+      "15": 523925,
+      "16": 1026218,
+      "17": 369490,
+      "18": 746421,
+      "19": 300345,
+      "20": 672102,
+      "21": 227917,
+      "22": 377974,
+      "23": 128153,
+      "24": 211857,
+      "25": 72661,
+      "26": 93004,
+      "27": 52114,
+      "28": 124278,
+      "29": 53229,
+      "3": 53132,
+      "30": 114883,
+      "31": 49414,
+      "32": 107779,
+      "33": 38655,
+      "34": 66947,
+      "35": 28146,
+      "36": 63623,
+      "37": 23183,
+      "38": 39121,
+      "39": 16378,
+      "4": 124546,
+      "40": 29488,
+      "41": 10683,
+      "42": 14075,
+      "43": 5682,
+      "44": 7572,
+      "45": 3637,
+      "46": 4248,
+      "47": 2504,
+      "48": 3513,
+      "49": 2138,
+      "5": 935361,
+      "50": 3010,
+      "51": 1840,
+      "52": 2698,
+      "53": 1720,
+      "54": 2342,
+      "55": 1677,
+      "56": 2482,
+      "57": 1717,
+      "58": 2273,
+      "59": 1715,
+      "6": 5205476,
+      "60": 2502,
+      "61": 1654,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1989952,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5920372,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1643628,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53132,
+      "7": 30405787,
+      "9": 124546
+    },
+    "connectivity_max": 138190193,
+    "connectivity_min": 0,
+    "n_cells": 30583465,
+    "n_connectivity_values": 337536196,
+    "n_fan_triangles": 276369266,
+    "n_points": 138190194
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.318746685473274e-11,
+    "float64_area_closure_relative": 2.0104671368784325e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276369266,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945595.0020100232,
+    "surface_area_float64_in2": 1945595.0020940485,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945595.0020940877,
+    "zero_area_triangles": 227203,
+    "zero_weight_points": 5102
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC122_AoA_8.json b/surface_dual_areas/cases/geo_LHC122_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..dbcb81764bc73542626df5ce861b294a2ff740b5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC122_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC122_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC122_AoA_8/boundary_dual_area_geo_LHC122_AoA_8.npy",
+    "sha256": "a48a9e551ce50ff7b1f7ff261ba13f17663fdef1d20939dabc10de625d455729",
+    "shape": [
+      136793297
+    ],
+    "size_bytes": 547173316
+  },
+  "runtime": {
+    "accumulation_seconds": 10.805708640953526,
+    "completed_at_utc": "2026-08-07T07:54:34.047868Z",
+    "elapsed_seconds": 20.42187146889046,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.075141991954297,
+    "geometry_read_seconds": 1.9421129249967635,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:54:13.625901Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC122_AoA_8/boundary_geo_LHC122_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC122_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624423000000000,
+    "extracted_vtu_size_bytes": 21003706728,
+    "geometry_sha256": "f08a1cdc5bb8174107a96713668aecf4604e3630412451529de6c0cec1b3e9b7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3472838,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1045747,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2419140,
+      "13": 777839,
+      "14": 1521072,
+      "15": 519597,
+      "16": 986155,
+      "17": 373323,
+      "18": 755113,
+      "19": 303679,
+      "20": 663918,
+      "21": 222499,
+      "22": 346836,
+      "23": 120394,
+      "24": 190418,
+      "25": 66937,
+      "26": 92698,
+      "27": 51270,
+      "28": 124408,
+      "29": 52993,
+      "3": 49010,
+      "30": 114474,
+      "31": 49405,
+      "32": 108829,
+      "33": 39181,
+      "34": 67826,
+      "35": 28156,
+      "36": 63315,
+      "37": 22999,
+      "38": 38733,
+      "39": 16194,
+      "4": 110667,
+      "40": 29237,
+      "41": 10641,
+      "42": 14119,
+      "43": 5716,
+      "44": 7570,
+      "45": 3618,
+      "46": 4261,
+      "47": 2528,
+      "48": 3498,
+      "49": 2108,
+      "5": 930620,
+      "50": 2898,
+      "51": 1791,
+      "52": 2639,
+      "53": 1680,
+      "54": 2287,
+      "55": 1678,
+      "56": 2494,
+      "57": 1726,
+      "58": 2273,
+      "59": 1718,
+      "6": 5114865,
+      "60": 2506,
+      "61": 1656,
+      "62": 2228,
+      "63": 1635,
+      "64": 2178,
+      "65": 1376,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 1973668,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 301,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5724955,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 58,
+      "88": 70,
+      "89": 59,
+      "9": 1648025,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49010,
+      "7": 30175706,
+      "9": 110667
+    },
+    "connectivity_max": 136793296,
+    "connectivity_min": 0,
+    "n_cells": 30335383,
+    "n_connectivity_values": 334246234,
+    "n_fan_triangles": 273575468,
+    "n_points": 136793297
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.4288918812124884e-11,
+    "float64_area_closure_relative": 3.080666895603683e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273575468,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1934796.8083732326,
+    "surface_area_float64_in2": 1934796.8084589227,
+    "weight_max_in2": 1.100800005293373,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1934796.808458863,
+    "zero_area_triangles": 232943,
+    "zero_weight_points": 5220
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC123_AoA_12.json b/surface_dual_areas/cases/geo_LHC123_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..5fc4fde1be9e0e7824473dc8172b8cec2cc44e97
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC123_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC123_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC123_AoA_12/boundary_dual_area_geo_LHC123_AoA_12.npy",
+    "sha256": "32f8fe30010d7f902494b265c6e231d9b4469e698853ac2f9a0256afb87f2e1a",
+    "shape": [
+      147911445
+    ],
+    "size_bytes": 591645908
+  },
+  "runtime": {
+    "accumulation_seconds": 11.281771342968568,
+    "completed_at_utc": "2026-08-07T07:54:57.152394Z",
+    "elapsed_seconds": 21.554509066976607,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.33197356085293,
+    "geometry_read_seconds": 2.029530636034906,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:54:35.597795Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC123_AoA_12/boundary_geo_LHC123_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC123_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624379000000000,
+    "extracted_vtu_size_bytes": 22727420638,
+    "geometry_sha256": "6555d044dfcc7d12627577b1e4f60dc60bb6340fe301930d758c2c60893f952c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4340871,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1386558,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3000897,
+      "13": 859995,
+      "14": 1395844,
+      "15": 464243,
+      "16": 930801,
+      "17": 356649,
+      "18": 740005,
+      "19": 300188,
+      "20": 660214,
+      "21": 219077,
+      "22": 345371,
+      "23": 118255,
+      "24": 203582,
+      "25": 69595,
+      "26": 93045,
+      "27": 51632,
+      "28": 123129,
+      "29": 52658,
+      "3": 58888,
+      "30": 114372,
+      "31": 49254,
+      "32": 108508,
+      "33": 38748,
+      "34": 66992,
+      "35": 28002,
+      "36": 63046,
+      "37": 23026,
+      "38": 38986,
+      "39": 16622,
+      "4": 134268,
+      "40": 30139,
+      "41": 10835,
+      "42": 14567,
+      "43": 5973,
+      "44": 7807,
+      "45": 3697,
+      "46": 4314,
+      "47": 2554,
+      "48": 3552,
+      "49": 2148,
+      "5": 937480,
+      "50": 2908,
+      "51": 1881,
+      "52": 2768,
+      "53": 1800,
+      "54": 2472,
+      "55": 1727,
+      "56": 2571,
+      "57": 1736,
+      "58": 2315,
+      "59": 1697,
+      "6": 5276126,
+      "60": 2447,
+      "61": 1666,
+      "62": 2197,
+      "63": 1588,
+      "64": 2148,
+      "65": 1370,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2093777,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 299,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6586820,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 56,
+      "88": 70,
+      "89": 58,
+      "9": 1986641,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58888,
+      "7": 33271345,
+      "9": 134268
+    },
+    "connectivity_max": 147911444,
+    "connectivity_min": 0,
+    "n_cells": 33464501,
+    "n_connectivity_values": 362740773,
+    "n_fan_triangles": 295811771,
+    "n_points": 147911445
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.801440509301461e-11,
+    "float64_area_closure_relative": 4.592946292996967e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295811771,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946614.6881797693,
+    "surface_area_float64_in2": 1946614.6882537687,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946614.6882538581,
+    "zero_area_triangles": 240401,
+    "zero_weight_points": 6015
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC123_AoA_14.json b/surface_dual_areas/cases/geo_LHC123_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..c1407b24c022c44d266cd98e97edf02dfab5f211
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC123_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC123_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC123_AoA_14/boundary_dual_area_geo_LHC123_AoA_14.npy",
+    "sha256": "fa3b341d879996f26671e328272f780e211015c25370ef5cf612b872d7e5c6bd",
+    "shape": [
+      147674301
+    ],
+    "size_bytes": 590697332
+  },
+  "runtime": {
+    "accumulation_seconds": 11.242428133962676,
+    "completed_at_utc": "2026-08-07T07:56:31.259422Z",
+    "elapsed_seconds": 23.541787893977016,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.300040649017319,
+    "geometry_read_seconds": 3.882757782936096,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:56:07.717557Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC123_AoA_14/boundary_geo_LHC123_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC123_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624554000000000,
+    "extracted_vtu_size_bytes": 22690361968,
+    "geometry_sha256": "3e75a5f76ba5d50307376105807f1102daf91ad3d2446562b1b92e159d3c3fa5",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4364739,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1384372,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2979457,
+      "13": 855651,
+      "14": 1389369,
+      "15": 463943,
+      "16": 919191,
+      "17": 355938,
+      "18": 743732,
+      "19": 301345,
+      "20": 662450,
+      "21": 219987,
+      "22": 346718,
+      "23": 118581,
+      "24": 204198,
+      "25": 69767,
+      "26": 93141,
+      "27": 51646,
+      "28": 123140,
+      "29": 52664,
+      "3": 59171,
+      "30": 114373,
+      "31": 49254,
+      "32": 108506,
+      "33": 38749,
+      "34": 66993,
+      "35": 28002,
+      "36": 63046,
+      "37": 23025,
+      "38": 38986,
+      "39": 16622,
+      "4": 135103,
+      "40": 30139,
+      "41": 10835,
+      "42": 14567,
+      "43": 5973,
+      "44": 7807,
+      "45": 3697,
+      "46": 4314,
+      "47": 2554,
+      "48": 3552,
+      "49": 2148,
+      "5": 932312,
+      "50": 2908,
+      "51": 1881,
+      "52": 2768,
+      "53": 1800,
+      "54": 2472,
+      "55": 1727,
+      "56": 2571,
+      "57": 1736,
+      "58": 2315,
+      "59": 1697,
+      "6": 5248482,
+      "60": 2447,
+      "61": 1666,
+      "62": 2197,
+      "63": 1588,
+      "64": 2148,
+      "65": 1370,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2081369,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 299,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6568050,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 56,
+      "88": 70,
+      "89": 58,
+      "9": 1983639,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59171,
+      "7": 33191773,
+      "9": 135103
+    },
+    "connectivity_max": 147674300,
+    "connectivity_min": 0,
+    "n_cells": 33386047,
+    "n_connectivity_values": 362109576,
+    "n_fan_triangles": 295337482,
+    "n_points": 147674301
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.8605373694283566e-11,
+    "float64_area_closure_relative": 6.41098514098015e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295337482,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946615.414781269,
+    "surface_area_float64_in2": 1946615.4148564187,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946615.4148565435,
+    "zero_area_triangles": 240038,
+    "zero_weight_points": 5978
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC123_AoA_16.json b/surface_dual_areas/cases/geo_LHC123_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d2609ac3c2e3019c429d525f75adc8742da4294
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC123_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC123_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC123_AoA_16/boundary_dual_area_geo_LHC123_AoA_16.npy",
+    "sha256": "172c4f6508d69e69c1be3797c09bf875eac4b71e9718c1c991e067289c0fb1a5",
+    "shape": [
+      147546903
+    ],
+    "size_bytes": 590187740
+  },
+  "runtime": {
+    "accumulation_seconds": 11.21002768096514,
+    "completed_at_utc": "2026-08-07T07:54:28.092698Z",
+    "elapsed_seconds": 22.080035131890327,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.325796318007633,
+    "geometry_read_seconds": 1.966147807892412,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:54:06.012587Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC123_AoA_16/boundary_geo_LHC123_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC123_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624390000000000,
+    "extracted_vtu_size_bytes": 22671600522,
+    "geometry_sha256": "f14054fd895d4429d53377ce8be0e19c2423b9cd3d8a884958be244fec702a02",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4423496,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1386778,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2947154,
+      "13": 843425,
+      "14": 1322597,
+      "15": 455711,
+      "16": 894596,
+      "17": 354889,
+      "18": 750151,
+      "19": 303503,
+      "20": 670058,
+      "21": 222007,
+      "22": 353792,
+      "23": 119638,
+      "24": 210288,
+      "25": 70386,
+      "26": 94077,
+      "27": 51732,
+      "28": 123186,
+      "29": 52669,
+      "3": 59120,
+      "30": 114370,
+      "31": 49252,
+      "32": 108506,
+      "33": 38749,
+      "34": 66996,
+      "35": 28002,
+      "36": 63047,
+      "37": 23025,
+      "38": 38984,
+      "39": 16621,
+      "4": 136173,
+      "40": 30139,
+      "41": 10834,
+      "42": 14567,
+      "43": 5973,
+      "44": 7807,
+      "45": 3698,
+      "46": 4315,
+      "47": 2555,
+      "48": 3552,
+      "49": 2147,
+      "5": 932353,
+      "50": 2908,
+      "51": 1881,
+      "52": 2769,
+      "53": 1800,
+      "54": 2470,
+      "55": 1727,
+      "56": 2571,
+      "57": 1736,
+      "58": 2315,
+      "59": 1697,
+      "6": 5247731,
+      "60": 2447,
+      "61": 1666,
+      "62": 2198,
+      "63": 1588,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2085228,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6605969,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1995189,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59120,
+      "7": 33194492,
+      "9": 136173
+    },
+    "connectivity_max": 147546902,
+    "connectivity_min": 0,
+    "n_cells": 33389785,
+    "n_connectivity_values": 361862257,
+    "n_fan_triangles": 295082687,
+    "n_points": 147546903
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.8849723729730505e-11,
+    "float64_area_closure_relative": 5.741179397821686e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295082687,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946615.8641884457,
+    "surface_area_float64_in2": 1946615.8642640712,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946615.864264183,
+    "zero_area_triangles": 239738,
+    "zero_weight_points": 5969
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC125_AoA_12.json b/surface_dual_areas/cases/geo_LHC125_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..c64a681e5dfe932305b7eb8dbd165e5b6bfa0ac8
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC125_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC125_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC125_AoA_12/boundary_dual_area_geo_LHC125_AoA_12.npy",
+    "sha256": "b851e4cf159063b9ce2bdab2c568f02b66f911bbee51c4dbe88dbc60d5f40087",
+    "shape": [
+      138492853
+    ],
+    "size_bytes": 553971540
+  },
+  "runtime": {
+    "accumulation_seconds": 10.593796365195885,
+    "completed_at_utc": "2026-08-07T08:34:32.478507Z",
+    "elapsed_seconds": 20.793687796918675,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1479168189689517,
+    "geometry_read_seconds": 2.500847788993269,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:34:11.684736Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC125_AoA_12/boundary_geo_LHC125_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC125_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624672000000000,
+    "extracted_vtu_size_bytes": 21270941623,
+    "geometry_sha256": "13ce153d2a005991d14d904c819dce3f90734f6afb13f877d6ac64884f0dd841",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3872463,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1119676,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2537299,
+      "13": 748437,
+      "14": 1275293,
+      "15": 454025,
+      "16": 909908,
+      "17": 354900,
+      "18": 759513,
+      "19": 306258,
+      "20": 675560,
+      "21": 229591,
+      "22": 368896,
+      "23": 127635,
+      "24": 207600,
+      "25": 70747,
+      "26": 95228,
+      "27": 52464,
+      "28": 125045,
+      "29": 53220,
+      "3": 51285,
+      "30": 114893,
+      "31": 49256,
+      "32": 108213,
+      "33": 38677,
+      "34": 65992,
+      "35": 28145,
+      "36": 62437,
+      "37": 23071,
+      "38": 38470,
+      "39": 16428,
+      "4": 115105,
+      "40": 29404,
+      "41": 10638,
+      "42": 14248,
+      "43": 5846,
+      "44": 7736,
+      "45": 3596,
+      "46": 4267,
+      "47": 2539,
+      "48": 3535,
+      "49": 2149,
+      "5": 936559,
+      "50": 2970,
+      "51": 1880,
+      "52": 2713,
+      "53": 1767,
+      "54": 2438,
+      "55": 1686,
+      "56": 2563,
+      "57": 1722,
+      "58": 2296,
+      "59": 1702,
+      "6": 5169979,
+      "60": 2447,
+      "61": 1664,
+      "62": 2198,
+      "63": 1586,
+      "64": 2149,
+      "65": 1369,
+      "66": 1770,
+      "67": 1094,
+      "68": 1505,
+      "69": 880,
+      "7": 1994595,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5947223,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1730753,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51285,
+      "7": 30797016,
+      "9": 115105
+    },
+    "connectivity_max": 138492852,
+    "connectivity_min": 0,
+    "n_cells": 30963406,
+    "n_connectivity_values": 338901396,
+    "n_fan_triangles": 276974584,
+    "n_points": 138492853
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.887978321101673e-11,
+    "float64_area_closure_relative": 7.191942081226183e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276974584,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935954.4797093577,
+    "surface_area_float64_in2": 1935954.4797846272,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935954.4797847664,
+    "zero_area_triangles": 236824,
+    "zero_weight_points": 5520
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC125_AoA_16.json b/surface_dual_areas/cases/geo_LHC125_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..bcdb15820b501bea86f8d4694f82338c856225bd
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC125_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC125_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC125_AoA_16/boundary_dual_area_geo_LHC125_AoA_16.npy",
+    "sha256": "173bb19863463a627bc85c6d9316a13fe2cc39302293b23a92022d0de593ff03",
+    "shape": [
+      138216771
+    ],
+    "size_bytes": 552867212
+  },
+  "runtime": {
+    "accumulation_seconds": 10.69461285811849,
+    "completed_at_utc": "2026-08-07T08:32:08.255646Z",
+    "elapsed_seconds": 21.215736820129678,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.191012696828693,
+    "geometry_read_seconds": 2.4689009089488536,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:31:47.039828Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC125_AoA_16/boundary_geo_LHC125_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC125_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624441000000000,
+    "extracted_vtu_size_bytes": 21228837412,
+    "geometry_sha256": "fcdba5538516933437cc1cfce1fcce93c8e67291758e73941b0eaebb6da003a0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3875609,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1133778,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2510118,
+      "13": 738406,
+      "14": 1230611,
+      "15": 442403,
+      "16": 895495,
+      "17": 350393,
+      "18": 756538,
+      "19": 305422,
+      "20": 679030,
+      "21": 231156,
+      "22": 379482,
+      "23": 129422,
+      "24": 213466,
+      "25": 71720,
+      "26": 95922,
+      "27": 52706,
+      "28": 125216,
+      "29": 53271,
+      "3": 50555,
+      "30": 114940,
+      "31": 49255,
+      "32": 108214,
+      "33": 38681,
+      "34": 65989,
+      "35": 28152,
+      "36": 62428,
+      "37": 23072,
+      "38": 38483,
+      "39": 16421,
+      "4": 116715,
+      "40": 29406,
+      "41": 10642,
+      "42": 14244,
+      "43": 5847,
+      "44": 7727,
+      "45": 3595,
+      "46": 4265,
+      "47": 2539,
+      "48": 3535,
+      "49": 2149,
+      "5": 937290,
+      "50": 2970,
+      "51": 1880,
+      "52": 2711,
+      "53": 1768,
+      "54": 2440,
+      "55": 1686,
+      "56": 2563,
+      "57": 1722,
+      "58": 2296,
+      "59": 1702,
+      "6": 5159786,
+      "60": 2447,
+      "61": 1664,
+      "62": 2198,
+      "63": 1586,
+      "64": 2149,
+      "65": 1369,
+      "66": 1770,
+      "67": 1094,
+      "68": 1505,
+      "69": 880,
+      "7": 2003849,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5945407,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1755683,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50555,
+      "7": 30746373,
+      "9": 116715
+    },
+    "connectivity_max": 138216770,
+    "connectivity_min": 0,
+    "n_cells": 30913643,
+    "n_connectivity_values": 338249706,
+    "n_fan_triangles": 276422420,
+    "n_points": 138216771
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9348342561774043e-11,
+    "float64_area_closure_relative": 6.590609251244643e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276422420,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935954.4444727066,
+    "surface_area_float64_in2": 1935954.4445488832,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935954.4445490108,
+    "zero_area_triangles": 235979,
+    "zero_weight_points": 5496
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC126_AoA_14.json b/surface_dual_areas/cases/geo_LHC126_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc51a588ca6b5ff62489a68f2e3c0b6783714b21
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC126_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC126_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC126_AoA_14/boundary_dual_area_geo_LHC126_AoA_14.npy",
+    "sha256": "73560b41cbcab5f8370856b09e85581a32e3b049608eb070b34319950ffb5296",
+    "shape": [
+      138969549
+    ],
+    "size_bytes": 555878324
+  },
+  "runtime": {
+    "accumulation_seconds": 10.861656170804054,
+    "completed_at_utc": "2026-08-07T08:36:02.283558Z",
+    "elapsed_seconds": 22.283061623806134,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5376702649518847,
+    "geometry_read_seconds": 2.830464388942346,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:35:40.000401Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC126_AoA_14/boundary_geo_LHC126_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC126_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624483000000000,
+    "extracted_vtu_size_bytes": 21344326158,
+    "geometry_sha256": "cdbcb760f922f2bb7ad80efcbdde16cc11881dda4711358faacb42e7a6fa2c90",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3840914,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1190202,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2586085,
+      "13": 753010,
+      "14": 1288036,
+      "15": 437818,
+      "16": 895447,
+      "17": 349667,
+      "18": 750978,
+      "19": 304481,
+      "20": 679176,
+      "21": 228668,
+      "22": 365099,
+      "23": 125040,
+      "24": 212915,
+      "25": 70762,
+      "26": 95383,
+      "27": 51863,
+      "28": 123968,
+      "29": 52760,
+      "3": 51346,
+      "30": 113885,
+      "31": 48943,
+      "32": 107937,
+      "33": 38357,
+      "34": 66794,
+      "35": 27928,
+      "36": 62904,
+      "37": 23144,
+      "38": 39767,
+      "39": 16589,
+      "4": 115744,
+      "40": 30062,
+      "41": 10919,
+      "42": 14302,
+      "43": 5790,
+      "44": 7633,
+      "45": 3706,
+      "46": 4241,
+      "47": 2507,
+      "48": 3522,
+      "49": 2123,
+      "5": 916296,
+      "50": 2971,
+      "51": 1852,
+      "52": 2736,
+      "53": 1785,
+      "54": 2456,
+      "55": 1723,
+      "56": 2552,
+      "57": 1744,
+      "58": 2286,
+      "59": 1726,
+      "6": 5156639,
+      "60": 2505,
+      "61": 1656,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 1991193,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5972371,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1794897,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51346,
+      "7": 30909659,
+      "9": 115744
+    },
+    "connectivity_max": 138969548,
+    "connectivity_min": 0,
+    "n_cells": 31076749,
+    "n_connectivity_values": 340081468,
+    "n_fan_triangles": 277927970,
+    "n_points": 138969549
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.252551361041621e-11,
+    "float64_area_closure_relative": 3.7729110341013143e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277927970,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937729.8177299898,
+    "surface_area_float64_in2": 1937729.8178123927,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937729.8178123196,
+    "zero_area_triangles": 237141,
+    "zero_weight_points": 5444
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC127_AoA_12.json b/surface_dual_areas/cases/geo_LHC127_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..95543d9548038296a0d93323f5976e8fa554fb43
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC127_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC127_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC127_AoA_12/boundary_dual_area_geo_LHC127_AoA_12.npy",
+    "sha256": "29de7160bdc1eae3d2cd6f90fcf8c3e9960f7127bc9d5f036962e0d29848aaae",
+    "shape": [
+      146351222
+    ],
+    "size_bytes": 585405016
+  },
+  "runtime": {
+    "accumulation_seconds": 11.099606376839802,
+    "completed_at_utc": "2026-08-07T07:57:38.604093Z",
+    "elapsed_seconds": 22.414861103054136,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.283964142901823,
+    "geometry_read_seconds": 2.7734855790622532,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:57:16.189135Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC127_AoA_12/boundary_geo_LHC127_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC127_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624471000000000,
+    "extracted_vtu_size_bytes": 22486124051,
+    "geometry_sha256": "b33452f131621df81d225647e98bb3a5953aeb272c5150ce9efac3321cb62350",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4172640,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1322366,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2898791,
+      "13": 833537,
+      "14": 1402341,
+      "15": 460286,
+      "16": 931178,
+      "17": 354564,
+      "18": 747513,
+      "19": 302658,
+      "20": 670214,
+      "21": 224127,
+      "22": 357675,
+      "23": 121744,
+      "24": 207771,
+      "25": 70497,
+      "26": 92603,
+      "27": 51751,
+      "28": 123035,
+      "29": 52760,
+      "3": 57862,
+      "30": 114394,
+      "31": 49428,
+      "32": 108791,
+      "33": 38951,
+      "34": 66909,
+      "35": 28273,
+      "36": 62598,
+      "37": 23111,
+      "38": 38806,
+      "39": 16341,
+      "4": 131019,
+      "40": 29249,
+      "41": 10742,
+      "42": 14221,
+      "43": 5779,
+      "44": 7628,
+      "45": 3605,
+      "46": 4091,
+      "47": 2471,
+      "48": 3498,
+      "49": 2110,
+      "5": 945366,
+      "50": 2911,
+      "51": 1836,
+      "52": 2772,
+      "53": 1764,
+      "54": 2486,
+      "55": 1701,
+      "56": 2528,
+      "57": 1754,
+      "58": 2287,
+      "59": 1749,
+      "6": 5286803,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2087449,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6531795,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1934969,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 57862,
+      "7": 32860277,
+      "9": 131019
+    },
+    "connectivity_max": 146351221,
+    "connectivity_min": 0,
+    "n_cells": 33049158,
+    "n_connectivity_values": 358789640,
+    "n_fan_triangles": 292691324,
+    "n_points": 146351222
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.8926558489327885e-11,
+    "float64_area_closure_relative": 1.903047310020247e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 292691324,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945304.88784856,
+    "surface_area_float64_in2": 1945304.887904831,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945304.887904868,
+    "zero_area_triangles": 238973,
+    "zero_weight_points": 5722
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC127_AoA_18.json b/surface_dual_areas/cases/geo_LHC127_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..1fb61c172e91fdac2db36fec8b6a6f73bbe9d233
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC127_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC127_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC127_AoA_18/boundary_dual_area_geo_LHC127_AoA_18.npy",
+    "sha256": "c84db2acaed1aebdbc593fe3f55a672d3c7d563cee43f60e1bfb2adf6125e12f",
+    "shape": [
+      146745758
+    ],
+    "size_bytes": 586983160
+  },
+  "runtime": {
+    "accumulation_seconds": 11.518331805011258,
+    "completed_at_utc": "2026-08-07T08:36:39.940239Z",
+    "elapsed_seconds": 22.26026383903809,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.346209314186126,
+    "geometry_read_seconds": 2.382586834952235,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:36:17.679901Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC127_AoA_18/boundary_geo_LHC127_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC127_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624700000000000,
+    "extracted_vtu_size_bytes": 22548632154,
+    "geometry_sha256": "7025456411f4622154402a5ea8690768ca3e61fc63519587c73fd9836ef9d626",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4401187,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1374231,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2903386,
+      "13": 813873,
+      "14": 1230107,
+      "15": 421696,
+      "16": 887591,
+      "17": 345308,
+      "18": 761565,
+      "19": 306750,
+      "20": 685153,
+      "21": 229506,
+      "22": 373178,
+      "23": 125996,
+      "24": 215713,
+      "25": 71944,
+      "26": 93120,
+      "27": 51849,
+      "28": 123079,
+      "29": 52784,
+      "3": 59434,
+      "30": 114429,
+      "31": 49423,
+      "32": 108786,
+      "33": 38948,
+      "34": 66893,
+      "35": 28265,
+      "36": 62575,
+      "37": 23087,
+      "38": 38794,
+      "39": 16337,
+      "4": 134338,
+      "40": 29246,
+      "41": 10736,
+      "42": 14222,
+      "43": 5776,
+      "44": 7627,
+      "45": 3605,
+      "46": 4088,
+      "47": 2473,
+      "48": 3495,
+      "49": 2111,
+      "5": 938954,
+      "50": 2910,
+      "51": 1834,
+      "52": 2772,
+      "53": 1763,
+      "54": 2486,
+      "55": 1701,
+      "56": 2528,
+      "57": 1754,
+      "58": 2287,
+      "59": 1749,
+      "6": 5249838,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2090443,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6604369,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1992677,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59434,
+      "7": 33020057,
+      "9": 134338
+    },
+    "connectivity_max": 146745757,
+    "connectivity_min": 0,
+    "n_cells": 33213829,
+    "n_connectivity_values": 359908054,
+    "n_fan_triangles": 293480396,
+    "n_points": 146745758
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.884072552214552e-11,
+    "float64_area_closure_relative": 4.308783926284891e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293480396,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945305.9876512745,
+    "surface_area_float64_in2": 1945305.9877073786,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945305.987707387,
+    "zero_area_triangles": 240071,
+    "zero_weight_points": 5808
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC127_AoA_22.json b/surface_dual_areas/cases/geo_LHC127_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..b0b657841df65f761c119080af8a6be6d42075d2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC127_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC127_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC127_AoA_22/boundary_dual_area_geo_LHC127_AoA_22.npy",
+    "sha256": "3e1c29d6f2535439ddbd78a484c0c32dc917a2238b61a7126172ca19676a8f11",
+    "shape": [
+      147085090
+    ],
+    "size_bytes": 588340488
+  },
+  "runtime": {
+    "accumulation_seconds": 11.313953595934436,
+    "completed_at_utc": "2026-08-07T08:38:37.008708Z",
+    "elapsed_seconds": 23.400228678015992,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3742169928736985,
+    "geometry_read_seconds": 3.230362660018727,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:38:13.608374Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC127_AoA_22/boundary_geo_LHC127_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC127_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624536000000000,
+    "extracted_vtu_size_bytes": 22602437865,
+    "geometry_sha256": "a3c8718f864c7b677770e41cd0b62dfbdc6b16788d19e6f6f1517f3138d13559",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4348505,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1379716,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2916965,
+      "13": 816318,
+      "14": 1226490,
+      "15": 421149,
+      "16": 894632,
+      "17": 346073,
+      "18": 755386,
+      "19": 305012,
+      "20": 681801,
+      "21": 228879,
+      "22": 374723,
+      "23": 126312,
+      "24": 218017,
+      "25": 72533,
+      "26": 93823,
+      "27": 52057,
+      "28": 123159,
+      "29": 52814,
+      "3": 59858,
+      "30": 114422,
+      "31": 49416,
+      "32": 108786,
+      "33": 38950,
+      "34": 66888,
+      "35": 28271,
+      "36": 62572,
+      "37": 23083,
+      "38": 38790,
+      "39": 16337,
+      "4": 135016,
+      "40": 29254,
+      "41": 10734,
+      "42": 14218,
+      "43": 5776,
+      "44": 7629,
+      "45": 3606,
+      "46": 4087,
+      "47": 2472,
+      "48": 3492,
+      "49": 2110,
+      "5": 950889,
+      "50": 2910,
+      "51": 1834,
+      "52": 2771,
+      "53": 1763,
+      "54": 2486,
+      "55": 1701,
+      "56": 2528,
+      "57": 1754,
+      "58": 2287,
+      "59": 1749,
+      "6": 5303099,
+      "60": 2509,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2120733,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6666467,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2011050,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59858,
+      "7": 33162338,
+      "9": 135016
+    },
+    "connectivity_max": 147085089,
+    "connectivity_min": 0,
+    "n_cells": 33357212,
+    "n_connectivity_values": 360873484,
+    "n_fan_triangles": 294159060,
+    "n_points": 147085090
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.9100938266109005e-11,
+    "float64_area_closure_relative": 6.82224357741133e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294159060,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945305.3144901218,
+    "surface_area_float64_in2": 1945305.314546732,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945305.3145467187,
+    "zero_area_triangles": 240637,
+    "zero_weight_points": 5809
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC128_AoA_18.json b/surface_dual_areas/cases/geo_LHC128_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..c76fc638605316d3ef1965cc8c71b6060a3a2699
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC128_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC128_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC128_AoA_18/boundary_dual_area_geo_LHC128_AoA_18.npy",
+    "sha256": "332b43623880aced7a39c47c72c4bba558a4461a62f8a291b3eb57e5bbec4ac0",
+    "shape": [
+      139835523
+    ],
+    "size_bytes": 559342220
+  },
+  "runtime": {
+    "accumulation_seconds": 11.170515939127654,
+    "completed_at_utc": "2026-08-07T08:34:18.835366Z",
+    "elapsed_seconds": 53.90931424405426,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6640000480692834,
+    "geometry_read_seconds": 33.798691562144086,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:33:24.925961Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC128_AoA_18/boundary_geo_LHC128_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC128_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624390000000000,
+    "extracted_vtu_size_bytes": 21477754098,
+    "geometry_sha256": "7e7caf6812edb89b393cb1de5a0dd962cc62a0e78d260107d2c5904271b21d86",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3737519,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1178263,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2587406,
+      "13": 789808,
+      "14": 1404761,
+      "15": 478764,
+      "16": 943413,
+      "17": 357079,
+      "18": 750773,
+      "19": 301293,
+      "20": 666369,
+      "21": 224067,
+      "22": 358186,
+      "23": 122831,
+      "24": 201417,
+      "25": 68490,
+      "26": 93730,
+      "27": 52399,
+      "28": 125133,
+      "29": 53402,
+      "3": 51475,
+      "30": 114961,
+      "31": 49576,
+      "32": 109026,
+      "33": 38892,
+      "34": 67236,
+      "35": 28331,
+      "36": 62380,
+      "37": 22887,
+      "38": 37679,
+      "39": 16066,
+      "4": 119854,
+      "40": 28774,
+      "41": 10527,
+      "42": 14087,
+      "43": 5750,
+      "44": 7640,
+      "45": 3613,
+      "46": 4148,
+      "47": 2493,
+      "48": 3531,
+      "49": 2103,
+      "5": 935979,
+      "50": 2904,
+      "51": 1818,
+      "52": 2646,
+      "53": 1713,
+      "54": 2335,
+      "55": 1647,
+      "56": 2449,
+      "57": 1721,
+      "58": 2274,
+      "59": 1739,
+      "6": 5209253,
+      "60": 2512,
+      "61": 1627,
+      "62": 2260,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2017144,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6011369,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1773108,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51475,
+      "7": 31115968,
+      "9": 119854
+    },
+    "connectivity_max": 139835522,
+    "connectivity_min": 0,
+    "n_cells": 31287297,
+    "n_connectivity_values": 342234523,
+    "n_fan_triangles": 279659929,
+    "n_points": 139835523
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6342684984082925e-11,
+    "float64_area_closure_relative": 2.6803783396173754e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279659929,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937085.9988496152,
+    "surface_area_float64_in2": 1937085.9989200141,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937085.998920066,
+    "zero_area_triangles": 237818,
+    "zero_weight_points": 5426
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC128_AoA_20.json b/surface_dual_areas/cases/geo_LHC128_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7bd2187341de967019b9c9ef9d06c6eab3e1706
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC128_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC128_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC128_AoA_20/boundary_dual_area_geo_LHC128_AoA_20.npy",
+    "sha256": "c24a3624490535cba20e14b163a0ad9a983255f6f9d64575dd265b1b8a392ea5",
+    "shape": [
+      141197709
+    ],
+    "size_bytes": 564790964
+  },
+  "runtime": {
+    "accumulation_seconds": 10.855968710966408,
+    "completed_at_utc": "2026-08-07T08:34:34.791168Z",
+    "elapsed_seconds": 23.106305399909616,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.248138378141448,
+    "geometry_read_seconds": 2.413751680869609,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:34:11.684780Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC128_AoA_20/boundary_geo_LHC128_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC128_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624672000000000,
+    "extracted_vtu_size_bytes": 21689055751,
+    "geometry_sha256": "4ccb5034769f8c4e15fc18591bc6d3edad7dad31c275824b3f42619f8ba619d8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3905355,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1199649,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2693553,
+      "13": 798018,
+      "14": 1402590,
+      "15": 481827,
+      "16": 930860,
+      "17": 356328,
+      "18": 743845,
+      "19": 298617,
+      "20": 658659,
+      "21": 221369,
+      "22": 351438,
+      "23": 121007,
+      "24": 200828,
+      "25": 68443,
+      "26": 94081,
+      "27": 52481,
+      "28": 125196,
+      "29": 53399,
+      "3": 51850,
+      "30": 114975,
+      "31": 49581,
+      "32": 109021,
+      "33": 38895,
+      "34": 67243,
+      "35": 28334,
+      "36": 62374,
+      "37": 22886,
+      "38": 37677,
+      "39": 16066,
+      "4": 121441,
+      "40": 28777,
+      "41": 10522,
+      "42": 14088,
+      "43": 5751,
+      "44": 7641,
+      "45": 3612,
+      "46": 4148,
+      "47": 2495,
+      "48": 3530,
+      "49": 2103,
+      "5": 940083,
+      "50": 2903,
+      "51": 1818,
+      "52": 2646,
+      "53": 1713,
+      "54": 2335,
+      "55": 1647,
+      "56": 2449,
+      "57": 1721,
+      "58": 2274,
+      "59": 1739,
+      "6": 5216844,
+      "60": 2512,
+      "61": 1627,
+      "62": 2260,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2028162,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6086391,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1798878,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51850,
+      "7": 31501931,
+      "9": 121441
+    },
+    "connectivity_max": 141197708,
+    "connectivity_min": 0,
+    "n_cells": 31675222,
+    "n_connectivity_values": 345734745,
+    "n_fan_triangles": 282384301,
+    "n_points": 141197709
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.816955205144753e-11,
+    "float64_area_closure_relative": 5.64922832352322e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282384301,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937085.8504245058,
+    "surface_area_float64_in2": 1937085.8504984435,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937085.850498553,
+    "zero_area_triangles": 239077,
+    "zero_weight_points": 5558
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC128_AoA_6.json b/surface_dual_areas/cases/geo_LHC128_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..fbb801616836d607ff68c81992073387d90d53a1
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC128_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC128_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC128_AoA_6/boundary_dual_area_geo_LHC128_AoA_6.npy",
+    "sha256": "31bb4133362bbca4ce78d6f2770b2afb479aa367e03cb1dfbb8da3e86cdc7ac3",
+    "shape": [
+      132126468
+    ],
+    "size_bytes": 528506000
+  },
+  "runtime": {
+    "accumulation_seconds": 10.212850793031976,
+    "completed_at_utc": "2026-08-07T08:37:45.333772Z",
+    "elapsed_seconds": 22.180394646013156,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0701385950669646,
+    "geometry_read_seconds": 3.756762634962797,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:37:23.153295Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC128_AoA_6/boundary_geo_LHC128_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC128_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624471000000000,
+    "extracted_vtu_size_bytes": 20278956107,
+    "geometry_sha256": "11424d9f9687ca05be1d8477aada219c1b712271d65815d98455c4a99311266d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2731517,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 927989,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2130504,
+      "13": 750850,
+      "14": 1644789,
+      "15": 532976,
+      "16": 1029992,
+      "17": 378649,
+      "18": 767641,
+      "19": 307146,
+      "20": 677725,
+      "21": 227751,
+      "22": 364620,
+      "23": 124656,
+      "24": 202459,
+      "25": 68701,
+      "26": 93441,
+      "27": 52262,
+      "28": 125065,
+      "29": 53361,
+      "3": 48760,
+      "30": 114946,
+      "31": 49569,
+      "32": 109012,
+      "33": 38888,
+      "34": 67238,
+      "35": 28331,
+      "36": 62376,
+      "37": 22890,
+      "38": 37681,
+      "39": 16072,
+      "4": 111936,
+      "40": 28776,
+      "41": 10521,
+      "42": 14087,
+      "43": 5755,
+      "44": 7638,
+      "45": 3611,
+      "46": 4150,
+      "47": 2495,
+      "48": 3531,
+      "49": 2104,
+      "5": 922745,
+      "50": 2908,
+      "51": 1818,
+      "52": 2647,
+      "53": 1713,
+      "54": 2335,
+      "55": 1647,
+      "56": 2449,
+      "57": 1721,
+      "58": 2274,
+      "59": 1739,
+      "6": 5167962,
+      "60": 2512,
+      "61": 1627,
+      "62": 2260,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1910471,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5444098,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1500929,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 48760,
+      "7": 28812287,
+      "9": 111936
+    },
+    "connectivity_max": 132126467,
+    "connectivity_min": 0,
+    "n_cells": 28972983,
+    "n_connectivity_values": 322187785,
+    "n_fan_triangles": 264241819,
+    "n_points": 132126468
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.7079463503371226e-11,
+    "float64_area_closure_relative": 4.639575518346173e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 264241819,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937087.3066227688,
+    "surface_area_float64_in2": 1937087.306694595,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937087.3066946848,
+    "zero_area_triangles": 227210,
+    "zero_weight_points": 4776
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC130_AoA_12.json b/surface_dual_areas/cases/geo_LHC130_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..34cc06d430ec5f8f035f0e8b2ed03f0da2d6626f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC130_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC130_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC130_AoA_12/boundary_dual_area_geo_LHC130_AoA_12.npy",
+    "sha256": "55b5bc6f3045cc7e7c78e2d4ad90068d0fc1ab0704654cf8aa9d24b223912e39",
+    "shape": [
+      140904074
+    ],
+    "size_bytes": 563616424
+  },
+  "runtime": {
+    "accumulation_seconds": 10.976519581163302,
+    "completed_at_utc": "2026-08-07T08:37:02.696172Z",
+    "elapsed_seconds": 117.71780023002066,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4024342191405594,
+    "geometry_read_seconds": 40.25065129692666,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:35:04.978289Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC130_AoA_12/boundary_geo_LHC130_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC130_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624429000000000,
+    "extracted_vtu_size_bytes": 21646827666,
+    "geometry_sha256": "e9dd1546977362bd52c8decf7986320dccfcca18274417df99ced9b80a9a36ce",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3949208,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1240607,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2653859,
+      "13": 772373,
+      "14": 1287185,
+      "15": 443025,
+      "16": 913316,
+      "17": 358773,
+      "18": 754741,
+      "19": 308862,
+      "20": 669208,
+      "21": 225924,
+      "22": 343605,
+      "23": 120887,
+      "24": 200124,
+      "25": 68274,
+      "26": 94684,
+      "27": 51444,
+      "28": 124254,
+      "29": 52601,
+      "3": 51108,
+      "30": 114563,
+      "31": 49246,
+      "32": 108966,
+      "33": 38763,
+      "34": 67109,
+      "35": 27943,
+      "36": 62951,
+      "37": 23063,
+      "38": 39484,
+      "39": 16318,
+      "4": 113346,
+      "40": 29960,
+      "41": 10921,
+      "42": 14422,
+      "43": 5871,
+      "44": 7632,
+      "45": 3697,
+      "46": 4250,
+      "47": 2494,
+      "48": 3510,
+      "49": 2144,
+      "5": 935135,
+      "50": 2972,
+      "51": 1850,
+      "52": 2784,
+      "53": 1782,
+      "54": 2409,
+      "55": 1725,
+      "56": 2537,
+      "57": 1751,
+      "58": 2277,
+      "59": 1733,
+      "6": 5318565,
+      "60": 2500,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2032593,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6117867,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1844624,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51108,
+      "7": 31559967,
+      "9": 113346
+    },
+    "connectivity_max": 140904073,
+    "connectivity_min": 0,
+    "n_cells": 31724421,
+    "n_connectivity_values": 345245863,
+    "n_fan_triangles": 281797021,
+    "n_points": 140904074
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.241481384194417e-11,
+    "float64_area_closure_relative": 1.238261998190205e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281797021,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936710.9973997194,
+    "surface_area_float64_in2": 1936710.9974624976,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936710.9974625215,
+    "zero_area_triangles": 239533,
+    "zero_weight_points": 5729
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC130_AoA_18.json b/surface_dual_areas/cases/geo_LHC130_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..5b4c1899f67416d990451e037b726458b3148d4a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC130_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC130_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC130_AoA_18/boundary_dual_area_geo_LHC130_AoA_18.npy",
+    "sha256": "62c21653728979fa058bd00b6ed520795f09f40abfdd53d92f7993d5f48e53d7",
+    "shape": [
+      139614497
+    ],
+    "size_bytes": 558458116
+  },
+  "runtime": {
+    "accumulation_seconds": 10.628805182874203,
+    "completed_at_utc": "2026-08-07T07:58:43.418383Z",
+    "elapsed_seconds": 21.130284931976348,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.198443102184683,
+    "geometry_read_seconds": 2.174445961834863,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T07:58:22.288010Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC130_AoA_18/boundary_geo_LHC130_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC130_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624599000000000,
+    "extracted_vtu_size_bytes": 21448435795,
+    "geometry_sha256": "3dc260cd36b25dd85758d6278cf77f3e5bcd03024a4db8300bbb92ff0f20440d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3893824,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1200961,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2578641,
+      "13": 745036,
+      "14": 1196103,
+      "15": 433335,
+      "16": 880823,
+      "17": 356036,
+      "18": 750813,
+      "19": 308914,
+      "20": 674785,
+      "21": 230266,
+      "22": 361078,
+      "23": 126477,
+      "24": 215751,
+      "25": 71965,
+      "26": 97920,
+      "27": 52334,
+      "28": 124479,
+      "29": 52664,
+      "3": 50150,
+      "30": 114579,
+      "31": 49247,
+      "32": 108965,
+      "33": 38750,
+      "34": 67109,
+      "35": 27955,
+      "36": 62946,
+      "37": 23058,
+      "38": 39487,
+      "39": 16326,
+      "4": 115136,
+      "40": 29968,
+      "41": 10921,
+      "42": 14423,
+      "43": 5873,
+      "44": 7630,
+      "45": 3697,
+      "46": 4249,
+      "47": 2493,
+      "48": 3510,
+      "49": 2145,
+      "5": 936284,
+      "50": 2972,
+      "51": 1850,
+      "52": 2783,
+      "53": 1782,
+      "54": 2411,
+      "55": 1725,
+      "56": 2537,
+      "57": 1751,
+      "58": 2277,
+      "59": 1733,
+      "6": 5309428,
+      "60": 2500,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2031607,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6131112,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1818866,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50150,
+      "7": 31257756,
+      "9": 115136
+    },
+    "connectivity_max": 139614496,
+    "connectivity_min": 0,
+    "n_cells": 31423042,
+    "n_connectivity_values": 342063951,
+    "n_fan_triangles": 279217867,
+    "n_points": 139614497
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3742150897429597e-11,
+    "float64_area_closure_relative": 5.2896617017322854e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279217867,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936711.4379109826,
+    "surface_area_float64_in2": 1936711.4379763315,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936711.4379763212,
+    "zero_area_triangles": 238496,
+    "zero_weight_points": 5670
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC130_AoA_20.json b/surface_dual_areas/cases/geo_LHC130_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..4562515781eb89687e39ee0f810d2a91a1e23cce
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC130_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC130_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC130_AoA_20/boundary_dual_area_geo_LHC130_AoA_20.npy",
+    "sha256": "7a0885eec3ea5e6657367e377c22538334571543ab05133f19301a559630318d",
+    "shape": [
+      139049397
+    ],
+    "size_bytes": 556197716
+  },
+  "runtime": {
+    "accumulation_seconds": 10.630497025093064,
+    "completed_at_utc": "2026-08-07T07:56:52.570190Z",
+    "elapsed_seconds": 21.249531977111474,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0973284509964287,
+    "geometry_read_seconds": 2.1318421280011535,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:56:31.320571Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC130_AoA_20/boundary_geo_LHC130_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC130_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624555000000000,
+    "extracted_vtu_size_bytes": 21360721520,
+    "geometry_sha256": "c714c2bb8268b98e0b3c2597273d07a62ee3042753fcf1ccf7f02a194d622d27",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3777964,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1177418,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2541179,
+      "13": 748212,
+      "14": 1217436,
+      "15": 444129,
+      "16": 901911,
+      "17": 360412,
+      "18": 749709,
+      "19": 307634,
+      "20": 670774,
+      "21": 229041,
+      "22": 361369,
+      "23": 126418,
+      "24": 215787,
+      "25": 72203,
+      "26": 97985,
+      "27": 52411,
+      "28": 124541,
+      "29": 52698,
+      "3": 49479,
+      "30": 114589,
+      "31": 49258,
+      "32": 108970,
+      "33": 38757,
+      "34": 67107,
+      "35": 27943,
+      "36": 62937,
+      "37": 23051,
+      "38": 39482,
+      "39": 16322,
+      "4": 113760,
+      "40": 29957,
+      "41": 10918,
+      "42": 14420,
+      "43": 5872,
+      "44": 7630,
+      "45": 3697,
+      "46": 4249,
+      "47": 2493,
+      "48": 3510,
+      "49": 2145,
+      "5": 938666,
+      "50": 2972,
+      "51": 1850,
+      "52": 2783,
+      "53": 1782,
+      "54": 2411,
+      "55": 1725,
+      "56": 2537,
+      "57": 1751,
+      "58": 2277,
+      "59": 1733,
+      "6": 5323241,
+      "60": 2500,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2031367,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6100099,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1795790,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49479,
+      "7": 31096624,
+      "9": 113760
+    },
+    "connectivity_max": 139049396,
+    "connectivity_min": 0,
+    "n_cells": 31259863,
+    "n_connectivity_values": 340607393,
+    "n_fan_triangles": 278087667,
+    "n_points": 139049397
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.382522037388518e-11,
+    "float64_area_closure_relative": 2.007666921062128e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278087667,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936711.56709155,
+    "surface_area_float64_in2": 1936711.5671570597,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936711.5671570208,
+    "zero_area_triangles": 237150,
+    "zero_weight_points": 5606
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC131_AoA_14.json b/surface_dual_areas/cases/geo_LHC131_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..05af42e5b7320858638803785a404529a8c2cd0f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC131_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC131_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC131_AoA_14/boundary_dual_area_geo_LHC131_AoA_14.npy",
+    "sha256": "193897612a222562c45698f448774f1a1c3e1c673af3b51636baf61c14acbdc1",
+    "shape": [
+      138405656
+    ],
+    "size_bytes": 553622752
+  },
+  "runtime": {
+    "accumulation_seconds": 10.911778911016881,
+    "completed_at_utc": "2026-08-07T08:40:19.309817Z",
+    "elapsed_seconds": 21.63324185810052,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5393568659201264,
+    "geometry_read_seconds": 1.9991200431250036,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:39:57.676491Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC131_AoA_14/boundary_geo_LHC131_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC131_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624427000000000,
+    "extracted_vtu_size_bytes": 21257675842,
+    "geometry_sha256": "04f0b3dacd105ccdcf74b3d01261de05d45aefe58c48b6e93ac11829f8d0962c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3848535,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1134109,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2528366,
+      "13": 749915,
+      "14": 1282191,
+      "15": 452679,
+      "16": 912843,
+      "17": 354889,
+      "18": 761782,
+      "19": 307389,
+      "20": 678406,
+      "21": 228766,
+      "22": 362405,
+      "23": 125060,
+      "24": 205467,
+      "25": 70212,
+      "26": 94415,
+      "27": 52170,
+      "28": 124772,
+      "29": 53262,
+      "3": 52024,
+      "30": 114597,
+      "31": 49309,
+      "32": 108314,
+      "33": 38869,
+      "34": 66438,
+      "35": 28156,
+      "36": 62629,
+      "37": 22960,
+      "38": 38833,
+      "39": 16091,
+      "4": 115662,
+      "40": 29255,
+      "41": 10676,
+      "42": 14166,
+      "43": 5739,
+      "44": 7568,
+      "45": 3643,
+      "46": 4203,
+      "47": 2516,
+      "48": 3549,
+      "49": 2151,
+      "5": 928398,
+      "50": 2944,
+      "51": 1844,
+      "52": 2784,
+      "53": 1762,
+      "54": 2394,
+      "55": 1715,
+      "56": 2525,
+      "57": 1759,
+      "58": 2281,
+      "59": 1719,
+      "6": 5179164,
+      "60": 2506,
+      "61": 1656,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1981557,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5956348,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1733696,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52024,
+      "7": 30781295,
+      "9": 115662
+    },
+    "connectivity_max": 138405655,
+    "connectivity_min": 0,
+    "n_cells": 30948981,
+    "n_connectivity_values": 338698152,
+    "n_fan_triangles": 276800190,
+    "n_points": 138405656
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.616000390704318e-11,
+    "float64_area_closure_relative": 6.013337752489179e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276800190,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935951.8226717922,
+    "surface_area_float64_in2": 1935951.8227417963,
+    "weight_max_in2": 1.1016537846015613,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935951.8227419127,
+    "zero_area_triangles": 236570,
+    "zero_weight_points": 5395
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC131_AoA_4.json b/surface_dual_areas/cases/geo_LHC131_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..4c1c34068e69cf07454668a41b96c2d2821adb87
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC131_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC131_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC131_AoA_4/boundary_dual_area_geo_LHC131_AoA_4.npy",
+    "sha256": "766e5f669929b1afee1aa62b716106cc9e6bfeb24f01806352e547dd9592d5dd",
+    "shape": [
+      130602054
+    ],
+    "size_bytes": 522408344
+  },
+  "runtime": {
+    "accumulation_seconds": 10.129922291031107,
+    "completed_at_utc": "2026-08-07T07:58:45.635261Z",
+    "elapsed_seconds": 19.455269799102098,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9555987410712987,
+    "geometry_read_seconds": 1.9612177091185004,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:58:26.179903Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC131_AoA_4/boundary_geo_LHC131_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC131_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624687000000000,
+    "extracted_vtu_size_bytes": 20042949695,
+    "geometry_sha256": "e9d20f07107179ec13b154ca32c28cef3dc798110c9638af5a7f7eb2dcde59c8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2588027,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 843448,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1977736,
+      "13": 735680,
+      "14": 1752147,
+      "15": 560941,
+      "16": 1075486,
+      "17": 389220,
+      "18": 767152,
+      "19": 307579,
+      "20": 669402,
+      "21": 224095,
+      "22": 345139,
+      "23": 120099,
+      "24": 195270,
+      "25": 67926,
+      "26": 93701,
+      "27": 52025,
+      "28": 124828,
+      "29": 53252,
+      "3": 46319,
+      "30": 114582,
+      "31": 49310,
+      "32": 108324,
+      "33": 38859,
+      "34": 66428,
+      "35": 28156,
+      "36": 62617,
+      "37": 22963,
+      "38": 38833,
+      "39": 16092,
+      "4": 106891,
+      "40": 29264,
+      "41": 10676,
+      "42": 14179,
+      "43": 5739,
+      "44": 7572,
+      "45": 3646,
+      "46": 4205,
+      "47": 2517,
+      "48": 3548,
+      "49": 2149,
+      "5": 922808,
+      "50": 2944,
+      "51": 1845,
+      "52": 2785,
+      "53": 1762,
+      "54": 2392,
+      "55": 1716,
+      "56": 2525,
+      "57": 1759,
+      "58": 2281,
+      "59": 1719,
+      "6": 5183339,
+      "60": 2506,
+      "61": 1656,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1880667,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5371073,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1428512,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 46319,
+      "7": 28404049,
+      "9": 106891
+    },
+    "connectivity_max": 130602053,
+    "connectivity_min": 0,
+    "n_cells": 28557259,
+    "n_connectivity_values": 318307504,
+    "n_fan_triangles": 261192986,
+    "n_points": 130602054
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.588877120401702e-11,
+    "float64_area_closure_relative": 1.6476531131498048e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 261192986,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935953.5040999383,
+    "surface_area_float64_in2": 1935953.5041694173,
+    "weight_max_in2": 1.1016537846015613,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935953.5041693854,
+    "zero_area_triangles": 221172,
+    "zero_weight_points": 4523
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC132_AoA_18.json b/surface_dual_areas/cases/geo_LHC132_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..1aeb43320d59d10f0dd36cde6ce2390f6093d664
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC132_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC132_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC132_AoA_18/boundary_dual_area_geo_LHC132_AoA_18.npy",
+    "sha256": "882d0c38d58f7a7d065d231a418648098beb22097aba53e696b2970fb4a41629",
+    "shape": [
+      151730163
+    ],
+    "size_bytes": 606920780
+  },
+  "runtime": {
+    "accumulation_seconds": 11.639490532921627,
+    "completed_at_utc": "2026-08-07T08:41:21.356300Z",
+    "elapsed_seconds": 26.476454849820584,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.484071552986279,
+    "geometry_read_seconds": 5.756271191872656,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:40:54.879751Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC132_AoA_18/boundary_geo_LHC132_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC132_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624583000000000,
+    "extracted_vtu_size_bytes": 23322112147,
+    "geometry_sha256": "d3e9cbdaba6fae3f1c807c36483b3f6b6d4b14c4c42ad8053db9f32794b41789",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4806751,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1486572,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3202204,
+      "13": 860250,
+      "14": 1242578,
+      "15": 436512,
+      "16": 885502,
+      "17": 354513,
+      "18": 740876,
+      "19": 303532,
+      "20": 664799,
+      "21": 222940,
+      "22": 349517,
+      "23": 120183,
+      "24": 198836,
+      "25": 69756,
+      "26": 90211,
+      "27": 51433,
+      "28": 123138,
+      "29": 52740,
+      "3": 62877,
+      "30": 114387,
+      "31": 49014,
+      "32": 108410,
+      "33": 38487,
+      "34": 66296,
+      "35": 27701,
+      "36": 63286,
+      "37": 23101,
+      "38": 39583,
+      "39": 16589,
+      "4": 141790,
+      "40": 30396,
+      "41": 11088,
+      "42": 14484,
+      "43": 6000,
+      "44": 7942,
+      "45": 3729,
+      "46": 4272,
+      "47": 2529,
+      "48": 3619,
+      "49": 2200,
+      "5": 958561,
+      "50": 2928,
+      "51": 1868,
+      "52": 2685,
+      "53": 1775,
+      "54": 2423,
+      "55": 1719,
+      "56": 2547,
+      "57": 1771,
+      "58": 2299,
+      "59": 1700,
+      "6": 5311714,
+      "60": 2469,
+      "61": 1652,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2202620,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6867570,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2159390,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 62877,
+      "7": 34440687,
+      "9": 141790
+    },
+    "connectivity_max": 151730162,
+    "connectivity_min": 0,
+    "n_cells": 34645354,
+    "n_connectivity_values": 372739905,
+    "n_fan_triangles": 303449197,
+    "n_points": 151730163
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6258662335943433e-11,
+    "float64_area_closure_relative": 1.7804547542333708e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 303449197,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948477.8156076365,
+    "surface_area_float64_in2": 1948477.8156782857,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948477.8156783204,
+    "zero_area_triangles": 246168,
+    "zero_weight_points": 6355
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC132_AoA_6.json b/surface_dual_areas/cases/geo_LHC132_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..a832c5ae95bab5031ec74083883437fbcaceb99b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC132_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC132_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC132_AoA_6/boundary_dual_area_geo_LHC132_AoA_6.npy",
+    "sha256": "54613fc89aea92a3c26231b0bbf8c4b4fe89d8ece13aa870a14be03fddfb1165",
+    "shape": [
+      142432048
+    ],
+    "size_bytes": 569728320
+  },
+  "runtime": {
+    "accumulation_seconds": 11.288765026954934,
+    "completed_at_utc": "2026-08-07T07:59:01.069006Z",
+    "elapsed_seconds": 21.24463075096719,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0719034019857645,
+    "geometry_read_seconds": 2.1155592808499932,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:58:39.824278Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC132_AoA_6/boundary_geo_LHC132_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC132_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624655000000000,
+    "extracted_vtu_size_bytes": 21876508544,
+    "geometry_sha256": "46f0adcd3e6a754e560a168e4bc9fb62667949d8abc389241a6cb4e1f29bf126",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3411348,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1085052,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2596740,
+      "13": 822321,
+      "14": 1684031,
+      "15": 555477,
+      "16": 1058518,
+      "17": 395246,
+      "18": 753641,
+      "19": 305960,
+      "20": 665466,
+      "21": 220713,
+      "22": 343568,
+      "23": 117395,
+      "24": 191051,
+      "25": 67772,
+      "26": 88454,
+      "27": 50861,
+      "28": 122995,
+      "29": 52687,
+      "3": 56855,
+      "30": 114391,
+      "31": 49023,
+      "32": 108407,
+      "33": 38491,
+      "34": 66287,
+      "35": 27706,
+      "36": 63284,
+      "37": 23097,
+      "38": 39581,
+      "39": 16592,
+      "4": 134518,
+      "40": 30396,
+      "41": 11088,
+      "42": 14485,
+      "43": 6000,
+      "44": 7943,
+      "45": 3730,
+      "46": 4272,
+      "47": 2529,
+      "48": 3619,
+      "49": 2200,
+      "5": 957602,
+      "50": 2928,
+      "51": 1868,
+      "52": 2685,
+      "53": 1775,
+      "54": 2423,
+      "55": 1719,
+      "56": 2547,
+      "57": 1771,
+      "58": 2299,
+      "59": 1700,
+      "6": 5375638,
+      "60": 2469,
+      "61": 1652,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2064522,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6272044,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1737579,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56855,
+      "7": 31674678,
+      "9": 134518
+    },
+    "connectivity_max": 142432047,
+    "connectivity_min": 0,
+    "n_cells": 31866051,
+    "n_connectivity_values": 348585068,
+    "n_fan_triangles": 284852966,
+    "n_points": 142432048
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6776163547106566e-11,
+    "float64_area_closure_relative": 6.321207444729088e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284852966,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948479.172140918,
+    "surface_area_float64_in2": 1948479.1722125756,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948479.1722126987,
+    "zero_area_triangles": 229231,
+    "zero_weight_points": 5306
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC134_AoA_14.json b/surface_dual_areas/cases/geo_LHC134_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..17be9f02fcbd9cb7d9e19e3a582a24a5370eb019
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC134_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC134_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC134_AoA_14/boundary_dual_area_geo_LHC134_AoA_14.npy",
+    "sha256": "6111a56fa3a2ad6aa219ba3c51c672f7b14be0b39612f7600a6ae764d12db11a",
+    "shape": [
+      147587718
+    ],
+    "size_bytes": 590351000
+  },
+  "runtime": {
+    "accumulation_seconds": 11.103127998998389,
+    "completed_at_utc": "2026-08-07T07:59:45.006972Z",
+    "elapsed_seconds": 21.67023341706954,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1386412200517952,
+    "geometry_read_seconds": 2.3360353731550276,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T07:59:23.336651Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC134_AoA_14/boundary_geo_LHC134_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC134_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624633000000000,
+    "extracted_vtu_size_bytes": 22674196894,
+    "geometry_sha256": "2e6fc8a868c67d0896d7adb7ddff8dbac67b9344c0b13c738e41625a6e4b7390",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4244249,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1274486,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3066098,
+      "13": 853919,
+      "14": 1468982,
+      "15": 502432,
+      "16": 949054,
+      "17": 367087,
+      "18": 753540,
+      "19": 305366,
+      "20": 677954,
+      "21": 222751,
+      "22": 350396,
+      "23": 117333,
+      "24": 189801,
+      "25": 66457,
+      "26": 87471,
+      "27": 50981,
+      "28": 123686,
+      "29": 53075,
+      "3": 58932,
+      "30": 115109,
+      "31": 49603,
+      "32": 108729,
+      "33": 39093,
+      "34": 66259,
+      "35": 28009,
+      "36": 62564,
+      "37": 22937,
+      "38": 38347,
+      "39": 16167,
+      "4": 133336,
+      "40": 28756,
+      "41": 10593,
+      "42": 14108,
+      "43": 5801,
+      "44": 7684,
+      "45": 3583,
+      "46": 4120,
+      "47": 2485,
+      "48": 3453,
+      "49": 2055,
+      "5": 948281,
+      "50": 2750,
+      "51": 1732,
+      "52": 2522,
+      "53": 1644,
+      "54": 2272,
+      "55": 1621,
+      "56": 2414,
+      "57": 1717,
+      "58": 2261,
+      "59": 1737,
+      "6": 5213135,
+      "60": 2505,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 2089185,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6514002,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1896847,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 58932,
+      "7": 33059749,
+      "9": 133336
+    },
+    "connectivity_max": 147587717,
+    "connectivity_min": 0,
+    "n_cells": 33252017,
+    "n_connectivity_values": 361668345,
+    "n_fan_triangles": 295164311,
+    "n_points": 147587718
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.802953176660309e-11,
+    "float64_area_closure_relative": 2.4169436684266276e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295164311,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945919.9910484317,
+    "surface_area_float64_in2": 1945919.9911224341,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945919.9911224812,
+    "zero_area_triangles": 244125,
+    "zero_weight_points": 6182
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC134_AoA_16.json b/surface_dual_areas/cases/geo_LHC134_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..62f6e1facd0c5becbc8f74d49e66379599f7cf65
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC134_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC134_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC134_AoA_16/boundary_dual_area_geo_LHC134_AoA_16.npy",
+    "sha256": "3bc67007d64626e016aa6c159e2cd17a597719535fe63a3938981867161a6a2d",
+    "shape": [
+      147850829
+    ],
+    "size_bytes": 591403444
+  },
+  "runtime": {
+    "accumulation_seconds": 13.05173822096549,
+    "completed_at_utc": "2026-08-07T08:00:40.011335Z",
+    "elapsed_seconds": 67.32598350802436,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.280998938018456,
+    "geometry_read_seconds": 45.919181128032506,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T07:59:32.685266Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC134_AoA_16/boundary_geo_LHC134_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC134_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624675000000000,
+    "extracted_vtu_size_bytes": 22715123005,
+    "geometry_sha256": "f1fd3997fe6ab9d41e76516014450ee7d0dfdf31af9b82b8c21b5d8a78b1c278",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4327572,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1290441,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3067484,
+      "13": 845564,
+      "14": 1420414,
+      "15": 491343,
+      "16": 945859,
+      "17": 366069,
+      "18": 762393,
+      "19": 307392,
+      "20": 683068,
+      "21": 223905,
+      "22": 350803,
+      "23": 117624,
+      "24": 189758,
+      "25": 66408,
+      "26": 87458,
+      "27": 50940,
+      "28": 123680,
+      "29": 53079,
+      "3": 59283,
+      "30": 115101,
+      "31": 49581,
+      "32": 108742,
+      "33": 39096,
+      "34": 66262,
+      "35": 28010,
+      "36": 62569,
+      "37": 22940,
+      "38": 38356,
+      "39": 16172,
+      "4": 133424,
+      "40": 28759,
+      "41": 10593,
+      "42": 14111,
+      "43": 5797,
+      "44": 7683,
+      "45": 3585,
+      "46": 4121,
+      "47": 2481,
+      "48": 3455,
+      "49": 2055,
+      "5": 944364,
+      "50": 2749,
+      "51": 1732,
+      "52": 2523,
+      "53": 1644,
+      "54": 2271,
+      "55": 1621,
+      "56": 2414,
+      "57": 1717,
+      "58": 2261,
+      "59": 1737,
+      "6": 5187262,
+      "60": 2505,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 2091789,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6552834,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1918040,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59283,
+      "7": 33138737,
+      "9": 133424
+    },
+    "connectivity_max": 147850828,
+    "connectivity_min": 0,
+    "n_cells": 33331444,
+    "n_connectivity_values": 362353422,
+    "n_fan_triangles": 295690534,
+    "n_points": 147850829
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.7799679809511295e-11,
+    "float64_area_closure_relative": 4.247598683317615e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295690534,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945920.1458608904,
+    "surface_area_float64_in2": 1945920.1459344456,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945920.1459345282,
+    "zero_area_triangles": 245172,
+    "zero_weight_points": 6247
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC134_AoA_8.json b/surface_dual_areas/cases/geo_LHC134_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..215da6d533f4b462e1b428fa90a38d562cd9f7b6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC134_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC134_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC134_AoA_8/boundary_dual_area_geo_LHC134_AoA_8.npy",
+    "sha256": "9dd055f1ecafd854c9f7c3b21ed97d91cc523769b835edd1d2634772beb6e4db",
+    "shape": [
+      141325769
+    ],
+    "size_bytes": 565303204
+  },
+  "runtime": {
+    "accumulation_seconds": 10.69515691511333,
+    "completed_at_utc": "2026-08-07T07:59:27.973876Z",
+    "elapsed_seconds": 20.789066263940185,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.019405544968322,
+    "geometry_read_seconds": 2.2377304278779775,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T07:59:07.184724Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC134_AoA_8/boundary_geo_LHC134_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC134_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624407000000000,
+    "extracted_vtu_size_bytes": 21701155167,
+    "geometry_sha256": "953882c2bc68888d5ac3be6e2cbef5c799db73e9f561a77a0c73cc816faaf4fa",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3372223,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1042308,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2621202,
+      "13": 824884,
+      "14": 1717432,
+      "15": 565229,
+      "16": 1048526,
+      "17": 386512,
+      "18": 762247,
+      "19": 307035,
+      "20": 680276,
+      "21": 223308,
+      "22": 352267,
+      "23": 117798,
+      "24": 190341,
+      "25": 66810,
+      "26": 87576,
+      "27": 51033,
+      "28": 123718,
+      "29": 53084,
+      "3": 55376,
+      "30": 115113,
+      "31": 49617,
+      "32": 108735,
+      "33": 39106,
+      "34": 66254,
+      "35": 28013,
+      "36": 62569,
+      "37": 22944,
+      "38": 38337,
+      "39": 16162,
+      "4": 129877,
+      "40": 28755,
+      "41": 10597,
+      "42": 14111,
+      "43": 5799,
+      "44": 7687,
+      "45": 3585,
+      "46": 4118,
+      "47": 2484,
+      "48": 3454,
+      "49": 2056,
+      "5": 946990,
+      "50": 2750,
+      "51": 1732,
+      "52": 2521,
+      "53": 1645,
+      "54": 2272,
+      "55": 1621,
+      "56": 2414,
+      "57": 1717,
+      "58": 2261,
+      "59": 1737,
+      "6": 5224495,
+      "60": 2505,
+      "61": 1625,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 908,
+      "7": 2007598,
+      "70": 1013,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6114152,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1655567,
+      "90": 57,
+      "91": 56,
+      "92": 55,
+      "93": 51,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 55376,
+      "7": 31215833,
+      "9": 129877
+    },
+    "connectivity_max": 141325768,
+    "connectivity_min": 0,
+    "n_cells": 31401086,
+    "n_connectivity_values": 345442585,
+    "n_fan_triangles": 282640413,
+    "n_points": 141325769
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.805834238675509e-11,
+    "float64_area_closure_relative": 3.098950473992174e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282640413,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945921.2791604453,
+    "surface_area_float64_in2": 1945921.2792345039,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945921.2792344436,
+    "zero_area_triangles": 234160,
+    "zero_weight_points": 5545
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC135_AoA_16.json b/surface_dual_areas/cases/geo_LHC135_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..72cb460a50fab4266f03d04eab74a06bba25b7ec
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC135_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC135_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC135_AoA_16/boundary_dual_area_geo_LHC135_AoA_16.npy",
+    "sha256": "7813ee4ed3a6172e52fb054f35f1bcc1a312950aa1040f7afd4c8cf8aa69c358",
+    "shape": [
+      140217773
+    ],
+    "size_bytes": 560871220
+  },
+  "runtime": {
+    "accumulation_seconds": 10.887079393025488,
+    "completed_at_utc": "2026-08-07T07:58:19.651400Z",
+    "elapsed_seconds": 20.858999026939273,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1271121129393578,
+    "geometry_read_seconds": 2.120918449945748,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T07:57:58.792305Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC135_AoA_16/boundary_geo_LHC135_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC135_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624407000000000,
+    "extracted_vtu_size_bytes": 21538223386,
+    "geometry_sha256": "634ebd45763f68b7a0f4454532bbee0fdf7cf2805d70d8f1518e98768d0198f8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3819572,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1216432,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2602384,
+      "13": 803890,
+      "14": 1331525,
+      "15": 476111,
+      "16": 928840,
+      "17": 360939,
+      "18": 745011,
+      "19": 301447,
+      "20": 661057,
+      "21": 223529,
+      "22": 357609,
+      "23": 122483,
+      "24": 203572,
+      "25": 69239,
+      "26": 94423,
+      "27": 52254,
+      "28": 124822,
+      "29": 53160,
+      "3": 52307,
+      "30": 113962,
+      "31": 48819,
+      "32": 107670,
+      "33": 38404,
+      "34": 66060,
+      "35": 27714,
+      "36": 62794,
+      "37": 22783,
+      "38": 39290,
+      "39": 16402,
+      "4": 120333,
+      "40": 30003,
+      "41": 11032,
+      "42": 14600,
+      "43": 5901,
+      "44": 7659,
+      "45": 3725,
+      "46": 4320,
+      "47": 2501,
+      "48": 3528,
+      "49": 2122,
+      "5": 939314,
+      "50": 2979,
+      "51": 1806,
+      "52": 2714,
+      "53": 1733,
+      "54": 2370,
+      "55": 1718,
+      "56": 2514,
+      "57": 1733,
+      "58": 2282,
+      "59": 1726,
+      "6": 5205208,
+      "60": 2510,
+      "61": 1658,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2025797,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6078253,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1799663,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52307,
+      "7": 31270513,
+      "9": 120333
+    },
+    "connectivity_max": 140217772,
+    "connectivity_min": 0,
+    "n_cells": 31443153,
+    "n_connectivity_values": 343310721,
+    "n_fan_triangles": 280424415,
+    "n_points": 140217773
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.8292880641717047e-11,
+    "float64_area_closure_relative": 3.23138531574804e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280424415,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938222.682262212,
+    "surface_area_float64_in2": 1938222.68231705,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938222.6823171126,
+    "zero_area_triangles": 237635,
+    "zero_weight_points": 5637
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC136_AoA_18.json b/surface_dual_areas/cases/geo_LHC136_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..a65111594832fa52468ab40d36d497dba89653bc
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC136_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC136_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC136_AoA_18/boundary_dual_area_geo_LHC136_AoA_18.npy",
+    "sha256": "f2a2e024b86c9d901a21cb61cd778dee1b76a43406559d23a006659174b1058c",
+    "shape": [
+      141450353
+    ],
+    "size_bytes": 565801540
+  },
+  "runtime": {
+    "accumulation_seconds": 10.96646422194317,
+    "completed_at_utc": "2026-08-07T08:01:22.810629Z",
+    "elapsed_seconds": 21.22348861815408,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.023485329002142,
+    "geometry_read_seconds": 2.3254915541037917,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T08:01:01.587040Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC136_AoA_18/boundary_geo_LHC136_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC136_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624708000000000,
+    "extracted_vtu_size_bytes": 21727415906,
+    "geometry_sha256": "fc98433d03929b29674fd719845d0b9ea5e89ca25929863c287220a58132c698",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4032292,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1221427,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2738207,
+      "13": 767601,
+      "14": 1358705,
+      "15": 446731,
+      "16": 915408,
+      "17": 351390,
+      "18": 749124,
+      "19": 304251,
+      "20": 672613,
+      "21": 225726,
+      "22": 351570,
+      "23": 121715,
+      "24": 201563,
+      "25": 68217,
+      "26": 93294,
+      "27": 51347,
+      "28": 124712,
+      "29": 53072,
+      "3": 51812,
+      "30": 115926,
+      "31": 49719,
+      "32": 109786,
+      "33": 38941,
+      "34": 66326,
+      "35": 27974,
+      "36": 61725,
+      "37": 22857,
+      "38": 38203,
+      "39": 16209,
+      "4": 116643,
+      "40": 29194,
+      "41": 10692,
+      "42": 14239,
+      "43": 5852,
+      "44": 7697,
+      "45": 3638,
+      "46": 4140,
+      "47": 2500,
+      "48": 3551,
+      "49": 2119,
+      "5": 919360,
+      "50": 2928,
+      "51": 1790,
+      "52": 2672,
+      "53": 1694,
+      "54": 2345,
+      "55": 1650,
+      "56": 2449,
+      "57": 1716,
+      "58": 2264,
+      "59": 1735,
+      "6": 5154565,
+      "60": 2507,
+      "61": 1628,
+      "62": 2259,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2006168,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6115780,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1825092,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51812,
+      "7": 31545522,
+      "9": 116643
+    },
+    "connectivity_max": 141450352,
+    "connectivity_min": 0,
+    "n_cells": 31713977,
+    "n_connectivity_values": 346317539,
+    "n_fan_triangles": 282889585,
+    "n_points": 141450353
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.5356446264036007e-11,
+    "float64_area_closure_relative": 2.1617772592840813e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282889585,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938660.2239729862,
+    "surface_area_float64_in2": 1938660.2240221438,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938660.2240221857,
+    "zero_area_triangles": 239672,
+    "zero_weight_points": 5665
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC136_AoA_6.json b/surface_dual_areas/cases/geo_LHC136_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..d145eac33b346f42330f7c64fb5d583189320602
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC136_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC136_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC136_AoA_6/boundary_dual_area_geo_LHC136_AoA_6.npy",
+    "sha256": "a8d6a3aaf5f934805bc90a82d845092a753b663fc80483ad4becd6c2b40b8a40",
+    "shape": [
+      137365254
+    ],
+    "size_bytes": 549461144
+  },
+  "runtime": {
+    "accumulation_seconds": 10.446549429092556,
+    "completed_at_utc": "2026-08-07T08:41:45.690220Z",
+    "elapsed_seconds": 22.441523666959256,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.13022010284476,
+    "geometry_read_seconds": 4.0989235478919,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:41:23.248622Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC136_AoA_6/boundary_geo_LHC136_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC136_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624679000000000,
+    "extracted_vtu_size_bytes": 21093956579,
+    "geometry_sha256": "8debfefbd6f53548baf76453eb644970b041f9c8dc1a6467d9db20ff18f44b33",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3316689,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1084135,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2407372,
+      "13": 752869,
+      "14": 1536056,
+      "15": 481892,
+      "16": 997000,
+      "17": 364760,
+      "18": 757469,
+      "19": 306376,
+      "20": 678863,
+      "21": 227078,
+      "22": 354286,
+      "23": 122182,
+      "24": 200619,
+      "25": 67994,
+      "26": 92462,
+      "27": 51167,
+      "28": 124611,
+      "29": 53066,
+      "3": 50315,
+      "30": 115925,
+      "31": 49731,
+      "32": 109777,
+      "33": 38934,
+      "34": 66331,
+      "35": 27975,
+      "36": 61716,
+      "37": 22861,
+      "38": 38212,
+      "39": 16213,
+      "4": 114680,
+      "40": 29189,
+      "41": 10695,
+      "42": 14246,
+      "43": 5853,
+      "44": 7701,
+      "45": 3640,
+      "46": 4138,
+      "47": 2504,
+      "48": 3551,
+      "49": 2122,
+      "5": 929346,
+      "50": 2927,
+      "51": 1794,
+      "52": 2672,
+      "53": 1695,
+      "54": 2344,
+      "55": 1650,
+      "56": 2449,
+      "57": 1716,
+      "58": 2264,
+      "59": 1735,
+      "6": 5235998,
+      "60": 2507,
+      "61": 1628,
+      "62": 2259,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 1988028,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5895943,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1692513,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 50315,
+      "7": 30394395,
+      "9": 114680
+    },
+    "connectivity_max": 137365253,
+    "connectivity_min": 0,
+    "n_cells": 30559390,
+    "n_connectivity_values": 335838167,
+    "n_fan_triangles": 274719387,
+    "n_points": 137365254
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.6471203909793958e-11,
+    "float64_area_closure_relative": 4.888018797200761e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274719387,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938660.138109211,
+    "surface_area_float64_in2": 1938660.1381605298,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938660.1381606245,
+    "zero_area_triangles": 231335,
+    "zero_weight_points": 5150
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC137_AoA_10.json b/surface_dual_areas/cases/geo_LHC137_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..c4c6296d1d3a4f1f705d00b4a592efd4733b790b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC137_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC137_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC137_AoA_10/boundary_dual_area_geo_LHC137_AoA_10.npy",
+    "sha256": "4ccab1aa570458c654838f940c9873806783cfe2f24ce2b0efd97559b64e2a6b",
+    "shape": [
+      138164990
+    ],
+    "size_bytes": 552660088
+  },
+  "runtime": {
+    "accumulation_seconds": 16.89742495282553,
+    "completed_at_utc": "2026-08-07T08:42:20.441253Z",
+    "elapsed_seconds": 27.17317580897361,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.16034160903655,
+    "geometry_read_seconds": 2.08711725496687,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:41:53.267994Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC137_AoA_10/boundary_geo_LHC137_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC137_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624481000000000,
+    "extracted_vtu_size_bytes": 21220127751,
+    "geometry_sha256": "9ffee14387515e9e0f983874114cb5a1c1e7d5cc5d75ba8ebdd4f31cdcda3ba3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3732820,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1126285,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2523236,
+      "13": 745931,
+      "14": 1352386,
+      "15": 454655,
+      "16": 941244,
+      "17": 356199,
+      "18": 765814,
+      "19": 308237,
+      "20": 674889,
+      "21": 227409,
+      "22": 354794,
+      "23": 123749,
+      "24": 196370,
+      "25": 68854,
+      "26": 92158,
+      "27": 51861,
+      "28": 124433,
+      "29": 53375,
+      "3": 49891,
+      "30": 114582,
+      "31": 49213,
+      "32": 107140,
+      "33": 38626,
+      "34": 66329,
+      "35": 28129,
+      "36": 63136,
+      "37": 23314,
+      "38": 38657,
+      "39": 16093,
+      "4": 113799,
+      "40": 29405,
+      "41": 10686,
+      "42": 14027,
+      "43": 5776,
+      "44": 7724,
+      "45": 3687,
+      "46": 4247,
+      "47": 2517,
+      "48": 3566,
+      "49": 2192,
+      "5": 933965,
+      "50": 2930,
+      "51": 1818,
+      "52": 2729,
+      "53": 1751,
+      "54": 2407,
+      "55": 1679,
+      "56": 2510,
+      "57": 1749,
+      "58": 2256,
+      "59": 1685,
+      "6": 5183726,
+      "60": 2462,
+      "61": 1653,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2002572,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5903261,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1736158,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49891,
+      "7": 30708096,
+      "9": 113799
+    },
+    "connectivity_max": 138164989,
+    "connectivity_min": 0,
+    "n_cells": 30871786,
+    "n_connectivity_values": 338062474,
+    "n_fan_triangles": 276318902,
+    "n_points": 138164990
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.159130397821892e-11,
+    "float64_area_closure_relative": 7.520048821935955e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276318902,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935082.546998798,
+    "surface_area_float64_in2": 1935082.5470599297,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935082.5470600752,
+    "zero_area_triangles": 234907,
+    "zero_weight_points": 5405
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC139_AoA_12.json b/surface_dual_areas/cases/geo_LHC139_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..a8293777620d4434846c0d9d1403e2b24f55b029
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC139_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC139_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC139_AoA_12/boundary_dual_area_geo_LHC139_AoA_12.npy",
+    "sha256": "1135ada5a416a1b322f4fd71655463dd6166f6fe2de2f56da19a7b49aa870663",
+    "shape": [
+      138847701
+    ],
+    "size_bytes": 555390932
+  },
+  "runtime": {
+    "accumulation_seconds": 10.665523370029405,
+    "completed_at_utc": "2026-08-07T08:02:07.864314Z",
+    "elapsed_seconds": 21.30384944798425,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2673103439155966,
+    "geometry_read_seconds": 1.9696384409908205,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T08:01:46.560376Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC139_AoA_12/boundary_geo_LHC139_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC139_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624385000000000,
+    "extracted_vtu_size_bytes": 21323890046,
+    "geometry_sha256": "246e925b35f85a686c199f5e840ff4f987c716cc0b0779047ca9c33c20ac3cc9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3704381,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1179492,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2588822,
+      "13": 784750,
+      "14": 1417380,
+      "15": 465735,
+      "16": 940672,
+      "17": 356032,
+      "18": 748145,
+      "19": 301792,
+      "20": 666513,
+      "21": 222629,
+      "22": 345992,
+      "23": 120037,
+      "24": 200350,
+      "25": 68102,
+      "26": 94645,
+      "27": 51702,
+      "28": 124863,
+      "29": 53075,
+      "3": 51126,
+      "30": 114807,
+      "31": 49359,
+      "32": 107941,
+      "33": 38701,
+      "34": 66518,
+      "35": 28182,
+      "36": 63344,
+      "37": 23043,
+      "38": 39236,
+      "39": 16216,
+      "4": 112588,
+      "40": 29504,
+      "41": 10687,
+      "42": 14045,
+      "43": 5858,
+      "44": 7808,
+      "45": 3696,
+      "46": 4201,
+      "47": 2474,
+      "48": 3591,
+      "49": 2217,
+      "5": 919982,
+      "50": 2922,
+      "51": 1852,
+      "52": 2746,
+      "53": 1763,
+      "54": 2425,
+      "55": 1711,
+      "56": 2521,
+      "57": 1770,
+      "58": 2273,
+      "59": 1689,
+      "6": 5165933,
+      "60": 2466,
+      "61": 1650,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1991068,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5865285,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1763298,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51126,
+      "7": 30816931,
+      "9": 112588
+    },
+    "connectivity_max": 138847700,
+    "connectivity_min": 0,
+    "n_cells": 30980645,
+    "n_connectivity_values": 339645563,
+    "n_fan_triangles": 277684273,
+    "n_points": 138847701
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6281182112082476e-11,
+    "float64_area_closure_relative": 3.60489069880561e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277684273,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937623.049618937,
+    "surface_area_float64_in2": 1937623.0496892363,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937623.0496891665,
+    "zero_area_triangles": 236328,
+    "zero_weight_points": 5552
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC140_AoA_10.json b/surface_dual_areas/cases/geo_LHC140_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..fd41b3eab28fef8e8788fae9b73f1271cc7399ff
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC140_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC140_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC140_AoA_10/boundary_dual_area_geo_LHC140_AoA_10.npy",
+    "sha256": "8cd17ae58c29ff3ffeeb73553dcaac7bacc76fa71faea3cce09d6acd827f7877",
+    "shape": [
+      143212475
+    ],
+    "size_bytes": 572850028
+  },
+  "runtime": {
+    "accumulation_seconds": 10.940627409843728,
+    "completed_at_utc": "2026-08-07T08:02:26.985804Z",
+    "elapsed_seconds": 21.016976284096017,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1275910360272974,
+    "geometry_read_seconds": 2.0443870411254466,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T08:02:05.968731Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC140_AoA_10/boundary_geo_LHC140_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC140_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624622000000000,
+    "extracted_vtu_size_bytes": 22002050357,
+    "geometry_sha256": "036350fd3324b077bc3affbd60607beca3154870f3ada18294d40a28ee308fa2",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4246467,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1245614,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2794032,
+      "13": 783358,
+      "14": 1337660,
+      "15": 448453,
+      "16": 917893,
+      "17": 350538,
+      "18": 753004,
+      "19": 303521,
+      "20": 673371,
+      "21": 223693,
+      "22": 351264,
+      "23": 119085,
+      "24": 187745,
+      "25": 66006,
+      "26": 89925,
+      "27": 51098,
+      "28": 124033,
+      "29": 53117,
+      "3": 52656,
+      "30": 114849,
+      "31": 49386,
+      "32": 108903,
+      "33": 39058,
+      "34": 66488,
+      "35": 28014,
+      "36": 63248,
+      "37": 23156,
+      "38": 38817,
+      "39": 16227,
+      "4": 118419,
+      "40": 29351,
+      "41": 10755,
+      "42": 14021,
+      "43": 5870,
+      "44": 7847,
+      "45": 3715,
+      "46": 4233,
+      "47": 2543,
+      "48": 3638,
+      "49": 2220,
+      "5": 931708,
+      "50": 2920,
+      "51": 1792,
+      "52": 2628,
+      "53": 1670,
+      "54": 2269,
+      "55": 1652,
+      "56": 2456,
+      "57": 1720,
+      "58": 2264,
+      "59": 1681,
+      "6": 5217948,
+      "60": 2462,
+      "61": 1650,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2035680,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6260942,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1853815,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52656,
+      "7": 32096513,
+      "9": 118419
+    },
+    "connectivity_max": 143212474,
+    "connectivity_min": 0,
+    "n_cells": 32267588,
+    "n_connectivity_values": 350949020,
+    "n_fan_triangles": 286413844,
+    "n_points": 143212475
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.946898153537584e-11,
+    "float64_area_closure_relative": 1.7066884912896916e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 286413844,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937198.9420805958,
+    "surface_area_float64_in2": 1937198.942137683,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937198.942137716,
+    "zero_area_triangles": 241549,
+    "zero_weight_points": 5758
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC141_AoA_22.json b/surface_dual_areas/cases/geo_LHC141_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..773a2e7c8c56bb2d158e8184fb8d67864dd4f9d5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC141_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC141_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC141_AoA_22/boundary_dual_area_geo_LHC141_AoA_22.npy",
+    "sha256": "f0112914dc85d62c5a0e4ba413f676b7921e4177fdeb89973b8ce0ffe868e03d",
+    "shape": [
+      147396903
+    ],
+    "size_bytes": 589587740
+  },
+  "runtime": {
+    "accumulation_seconds": 11.248934774892405,
+    "completed_at_utc": "2026-08-07T08:42:45.892562Z",
+    "elapsed_seconds": 24.31835313490592,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.342181044863537,
+    "geometry_read_seconds": 4.714498817920685,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:42:21.574114Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC141_AoA_22/boundary_geo_LHC141_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC141_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624604000000000,
+    "extracted_vtu_size_bytes": 22650067013,
+    "geometry_sha256": "31f7cfcb0d692842e5cd1f93a69d18b9e0089ec753d51fa4c97ecb68c01b70b3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4389325,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1350207,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2885618,
+      "13": 786614,
+      "14": 1254071,
+      "15": 423533,
+      "16": 929473,
+      "17": 354361,
+      "18": 764898,
+      "19": 309930,
+      "20": 687060,
+      "21": 230931,
+      "22": 372881,
+      "23": 126386,
+      "24": 205769,
+      "25": 71353,
+      "26": 90307,
+      "27": 51394,
+      "28": 123487,
+      "29": 52542,
+      "3": 59721,
+      "30": 115062,
+      "31": 49292,
+      "32": 109473,
+      "33": 38878,
+      "34": 67340,
+      "35": 28251,
+      "36": 62752,
+      "37": 22974,
+      "38": 38461,
+      "39": 16244,
+      "4": 133731,
+      "40": 29263,
+      "41": 10718,
+      "42": 14212,
+      "43": 5901,
+      "44": 7646,
+      "45": 3597,
+      "46": 4142,
+      "47": 2491,
+      "48": 3511,
+      "49": 2087,
+      "5": 962838,
+      "50": 2890,
+      "51": 1821,
+      "52": 2779,
+      "53": 1744,
+      "54": 2442,
+      "55": 1683,
+      "56": 2512,
+      "57": 1735,
+      "58": 2282,
+      "59": 1739,
+      "6": 5248157,
+      "60": 2511,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2192379,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6615413,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2067080,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 59721,
+      "7": 33222992,
+      "9": 133731
+    },
+    "connectivity_max": 147396902,
+    "connectivity_min": 0,
+    "n_cells": 33416444,
+    "n_connectivity_values": 361615577,
+    "n_fan_triangles": 294782689,
+    "n_points": 147396903
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.867943807497463e-11,
+    "float64_area_closure_relative": 9.719594636619464e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294782689,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945127.2373781342,
+    "surface_area_float64_in2": 1945127.2374533706,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945127.2374535596,
+    "zero_area_triangles": 245075,
+    "zero_weight_points": 6104
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC141_AoA_4.json b/surface_dual_areas/cases/geo_LHC141_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..ac402354edcf8057c82cc6d87d3f113568d91920
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC141_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC141_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC141_AoA_4/boundary_dual_area_geo_LHC141_AoA_4.npy",
+    "sha256": "e2151fb4764f93b7ff309d266e7185d39951c7c6b9934d679be7eb6bb6dd49f2",
+    "shape": [
+      137716537
+    ],
+    "size_bytes": 550866276
+  },
+  "runtime": {
+    "accumulation_seconds": 10.442010059021413,
+    "completed_at_utc": "2026-08-07T08:44:09.402474Z",
+    "elapsed_seconds": 49.36837328504771,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1073208760935813,
+    "geometry_read_seconds": 31.143688932992518,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:43:20.034013Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC141_AoA_4/boundary_geo_LHC141_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC141_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624452000000000,
+    "extracted_vtu_size_bytes": 21144884470,
+    "geometry_sha256": "f69f9b8f549d620701c7d0e9ce5a5473d405e72f53686aee50c7ff7544958108",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2968920,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 949463,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2233202,
+      "13": 755359,
+      "14": 1760669,
+      "15": 556462,
+      "16": 1093995,
+      "17": 390986,
+      "18": 767718,
+      "19": 309422,
+      "20": 679025,
+      "21": 228093,
+      "22": 363079,
+      "23": 123684,
+      "24": 200754,
+      "25": 70179,
+      "26": 89792,
+      "27": 51222,
+      "28": 123472,
+      "29": 52525,
+      "3": 56997,
+      "30": 115060,
+      "31": 49286,
+      "32": 109462,
+      "33": 38886,
+      "34": 67352,
+      "35": 28260,
+      "36": 62771,
+      "37": 22971,
+      "38": 38465,
+      "39": 16261,
+      "4": 128716,
+      "40": 29267,
+      "41": 10730,
+      "42": 14214,
+      "43": 5895,
+      "44": 7641,
+      "45": 3600,
+      "46": 4140,
+      "47": 2490,
+      "48": 3513,
+      "49": 2088,
+      "5": 966971,
+      "50": 2890,
+      "51": 1822,
+      "52": 2779,
+      "53": 1744,
+      "54": 2444,
+      "55": 1683,
+      "56": 2512,
+      "57": 1735,
+      "58": 2282,
+      "59": 1739,
+      "6": 5305368,
+      "60": 2511,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2048293,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5919798,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1645700,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 56997,
+      "7": 30331196,
+      "9": 128716
+    },
+    "connectivity_max": 137716536,
+    "connectivity_min": 0,
+    "n_cells": 30516909,
+    "n_connectivity_values": 336455775,
+    "n_fan_triangles": 275421957,
+    "n_points": 137716537
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.778260066257989e-11,
+    "float64_area_closure_relative": 7.15801727131748e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275421957,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945129.7701902129,
+    "surface_area_float64_in2": 1945129.770263705,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945129.7702638442,
+    "zero_area_triangles": 227740,
+    "zero_weight_points": 4914
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC142_AoA_14.json b/surface_dual_areas/cases/geo_LHC142_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d3c69c118ce104173f64fc6200e68241a922482
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC142_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC142_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC142_AoA_14/boundary_dual_area_geo_LHC142_AoA_14.npy",
+    "sha256": "f2f7150baf06369f39eed950b749305162fb1068eebe77a22a25f28c26bcb457",
+    "shape": [
+      141694002
+    ],
+    "size_bytes": 566776136
+  },
+  "runtime": {
+    "accumulation_seconds": 10.812719444045797,
+    "completed_at_utc": "2026-08-07T08:45:36.160141Z",
+    "elapsed_seconds": 21.00144164985977,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2037107348442078,
+    "geometry_read_seconds": 2.2461427659727633,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:45:15.158616Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC142_AoA_14/boundary_geo_LHC142_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC142_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624379000000000,
+    "extracted_vtu_size_bytes": 21766855889,
+    "geometry_sha256": "f835d86ad7615a16dd999388d09909f4d108e08b282497d0774b202affda3f27",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4009690,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1227704,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2708708,
+      "13": 797247,
+      "14": 1353741,
+      "15": 462187,
+      "16": 914265,
+      "17": 356438,
+      "18": 744409,
+      "19": 301246,
+      "20": 658450,
+      "21": 222294,
+      "22": 352650,
+      "23": 120510,
+      "24": 204680,
+      "25": 68109,
+      "26": 94786,
+      "27": 51633,
+      "28": 123867,
+      "29": 53043,
+      "3": 54151,
+      "30": 114608,
+      "31": 49251,
+      "32": 107734,
+      "33": 38693,
+      "34": 66383,
+      "35": 27737,
+      "36": 62925,
+      "37": 23018,
+      "38": 39664,
+      "39": 16526,
+      "4": 120922,
+      "40": 30024,
+      "41": 10857,
+      "42": 14381,
+      "43": 5877,
+      "44": 7684,
+      "45": 3667,
+      "46": 4299,
+      "47": 2488,
+      "48": 3520,
+      "49": 2145,
+      "5": 938407,
+      "50": 2996,
+      "51": 1815,
+      "52": 2774,
+      "53": 1749,
+      "54": 2484,
+      "55": 1753,
+      "56": 2569,
+      "57": 1760,
+      "58": 2290,
+      "59": 1730,
+      "6": 5237639,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2028760,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6144067,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1823070,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54151,
+      "7": 31674107,
+      "9": 120922
+    },
+    "connectivity_max": 141694001,
+    "connectivity_min": 0,
+    "n_cells": 31849180,
+    "n_connectivity_values": 347075225,
+    "n_fan_triangles": 283376865,
+    "n_points": 141694002
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.328642680944528e-11,
+    "float64_area_closure_relative": 5.788609179002096e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283376865,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938710.4357191005,
+    "surface_area_float64_in2": 1938710.4358030204,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938710.4358031326,
+    "zero_area_triangles": 238566,
+    "zero_weight_points": 5657
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC142_AoA_16.json b/surface_dual_areas/cases/geo_LHC142_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..5bda91a648d522aaa585cb26e8cc372e03616daa
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC142_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC142_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC142_AoA_16/boundary_dual_area_geo_LHC142_AoA_16.npy",
+    "sha256": "75c27820e48add120271973e2e0051f3de0cf1ea0930d25abf8f857fb8836f9d",
+    "shape": [
+      141803812
+    ],
+    "size_bytes": 567215376
+  },
+  "runtime": {
+    "accumulation_seconds": 10.812192175071687,
+    "completed_at_utc": "2026-08-07T08:02:33.466992Z",
+    "elapsed_seconds": 20.860492055071518,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1335351208690554,
+    "geometry_read_seconds": 1.9275460408534855,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:02:12.606393Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC142_AoA_16/boundary_geo_LHC142_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC142_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624526000000000,
+    "extracted_vtu_size_bytes": 21784523819,
+    "geometry_sha256": "98d8a52607afb9f37317adfa580e992de332c0e3a4c95c426fd218d201c36e00",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4040019,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1237228,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2695085,
+      "13": 790619,
+      "14": 1329477,
+      "15": 453338,
+      "16": 912176,
+      "17": 353652,
+      "18": 747002,
+      "19": 301634,
+      "20": 659425,
+      "21": 222591,
+      "22": 354864,
+      "23": 121280,
+      "24": 206332,
+      "25": 68799,
+      "26": 95085,
+      "27": 51889,
+      "28": 123983,
+      "29": 53088,
+      "3": 53387,
+      "30": 114643,
+      "31": 49252,
+      "32": 107736,
+      "33": 38694,
+      "34": 66382,
+      "35": 27734,
+      "36": 62929,
+      "37": 23019,
+      "38": 39666,
+      "39": 16523,
+      "4": 119618,
+      "40": 30022,
+      "41": 10857,
+      "42": 14381,
+      "43": 5878,
+      "44": 7681,
+      "45": 3669,
+      "46": 4302,
+      "47": 2488,
+      "48": 3521,
+      "49": 2144,
+      "5": 939134,
+      "50": 2997,
+      "51": 1816,
+      "52": 2775,
+      "53": 1749,
+      "54": 2482,
+      "55": 1752,
+      "56": 2568,
+      "57": 1760,
+      "58": 2290,
+      "59": 1730,
+      "6": 5251308,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2037799,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6171226,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1839238,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53387,
+      "7": 31732817,
+      "9": 119618
+    },
+    "connectivity_max": 141803811,
+    "connectivity_min": 0,
+    "n_cells": 31905822,
+    "n_connectivity_values": 347408129,
+    "n_fan_triangles": 283596485,
+    "n_points": 141803812
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.317437440528908e-11,
+    "float64_area_closure_relative": 4.73176732007897e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283596485,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938710.5787385383,
+    "surface_area_float64_in2": 1938710.578822241,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938710.5788223327,
+    "zero_area_triangles": 238296,
+    "zero_weight_points": 5641
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC142_AoA_18.json b/surface_dual_areas/cases/geo_LHC142_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..8977944a4767da3aef6f9daf65d350afe56d1648
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC142_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC142_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC142_AoA_18/boundary_dual_area_geo_LHC142_AoA_18.npy",
+    "sha256": "bd6eb4592ff11b597a8fc1f9dc8cdf62a4afc71b2db91ce72a48e35ef06d8303",
+    "shape": [
+      142687727
+    ],
+    "size_bytes": 570751036
+  },
+  "runtime": {
+    "accumulation_seconds": 11.346346196020022,
+    "completed_at_utc": "2026-08-07T08:04:22.026196Z",
+    "elapsed_seconds": 23.2276850361377,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.290432761190459,
+    "geometry_read_seconds": 3.6634583701379597,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T08:03:58.798416Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC142_AoA_18/boundary_geo_LHC142_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC142_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624515000000000,
+    "extracted_vtu_size_bytes": 21922533314,
+    "geometry_sha256": "b7247c7df88af04c8c7a259f4e6ec7d7bb5835cbd749cfe25971314ca61df12a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4135911,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1282090,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2734267,
+      "13": 790789,
+      "14": 1280190,
+      "15": 435085,
+      "16": 907038,
+      "17": 348490,
+      "18": 746207,
+      "19": 301008,
+      "20": 659627,
+      "21": 223429,
+      "22": 356450,
+      "23": 122625,
+      "24": 207284,
+      "25": 69755,
+      "26": 95508,
+      "27": 52178,
+      "28": 124048,
+      "29": 53110,
+      "3": 53736,
+      "30": 114669,
+      "31": 49257,
+      "32": 107734,
+      "33": 38690,
+      "34": 66388,
+      "35": 27733,
+      "36": 62923,
+      "37": 23020,
+      "38": 39672,
+      "39": 16524,
+      "4": 121354,
+      "40": 30022,
+      "41": 10858,
+      "42": 14382,
+      "43": 5874,
+      "44": 7681,
+      "45": 3670,
+      "46": 4300,
+      "47": 2487,
+      "48": 3520,
+      "49": 2145,
+      "5": 944195,
+      "50": 2995,
+      "51": 1815,
+      "52": 2775,
+      "53": 1749,
+      "54": 2484,
+      "55": 1752,
+      "56": 2568,
+      "57": 1760,
+      "58": 2290,
+      "59": 1730,
+      "6": 5261706,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2066768,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6249577,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1894427,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53736,
+      "7": 32018335,
+      "9": 121354
+    },
+    "connectivity_max": 142687726,
+    "connectivity_min": 0,
+    "n_cells": 32193425,
+    "n_connectivity_values": 349751165,
+    "n_fan_triangles": 285364315,
+    "n_points": 142687727
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.234343505502101e-11,
+    "float64_area_closure_relative": 5.5243986843617964e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285364315,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938710.4768420218,
+    "surface_area_float64_in2": 1938710.4769241135,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938710.4769242206,
+    "zero_area_triangles": 238484,
+    "zero_weight_points": 5686
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC142_AoA_8.json b/surface_dual_areas/cases/geo_LHC142_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..03c3ae4cad85f4eca535cb3f951da8007fd327a9
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC142_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC142_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC142_AoA_8/boundary_dual_area_geo_LHC142_AoA_8.npy",
+    "sha256": "33620c2cde8af4d24156e27670b53ef7384b5bb7aa9a569c62fcaee2e8f03a28",
+    "shape": [
+      140525341
+    ],
+    "size_bytes": 562101492
+  },
+  "runtime": {
+    "accumulation_seconds": 10.94331924780272,
+    "completed_at_utc": "2026-08-07T08:44:42.981842Z",
+    "elapsed_seconds": 22.234740878921002,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6520761870779097,
+    "geometry_read_seconds": 2.6460162750445306,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:44:20.747013Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC142_AoA_8/boundary_geo_LHC142_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC142_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624437000000000,
+    "extracted_vtu_size_bytes": 21584136903,
+    "geometry_sha256": "c78f89c74bb87efc0456b268f16e2837abc048ccdda8812921bad06dbf0aaa05",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3710006,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1176760,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2639973,
+      "13": 806503,
+      "14": 1498857,
+      "15": 486362,
+      "16": 975021,
+      "17": 363464,
+      "18": 743085,
+      "19": 298935,
+      "20": 651701,
+      "21": 219365,
+      "22": 341332,
+      "23": 118411,
+      "24": 195895,
+      "25": 67160,
+      "26": 93323,
+      "27": 51458,
+      "28": 123738,
+      "29": 53010,
+      "3": 52812,
+      "30": 114620,
+      "31": 49249,
+      "32": 107727,
+      "33": 38694,
+      "34": 66387,
+      "35": 27729,
+      "36": 62927,
+      "37": 23017,
+      "38": 39666,
+      "39": 16527,
+      "4": 117901,
+      "40": 30024,
+      "41": 10857,
+      "42": 14381,
+      "43": 5877,
+      "44": 7684,
+      "45": 3667,
+      "46": 4299,
+      "47": 2488,
+      "48": 3520,
+      "49": 2145,
+      "5": 941081,
+      "50": 2996,
+      "51": 1815,
+      "52": 2774,
+      "53": 1749,
+      "54": 2484,
+      "55": 1753,
+      "56": 2569,
+      "57": 1760,
+      "58": 2290,
+      "59": 1730,
+      "6": 5251523,
+      "60": 2504,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2017919,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6024291,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1762497,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52812,
+      "7": 31288181,
+      "9": 117901
+    },
+    "connectivity_max": 140525340,
+    "connectivity_min": 0,
+    "n_cells": 31458894,
+    "n_connectivity_values": 343957330,
+    "n_fan_triangles": 281039542,
+    "n_points": 140525341
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.337458472157176e-11,
+    "float64_area_closure_relative": 7.085643202653436e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281039542,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938710.090544529,
+    "surface_area_float64_in2": 1938710.0906286198,
+    "weight_max_in2": 1.100807408812321,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938710.0906287571,
+    "zero_area_triangles": 235713,
+    "zero_weight_points": 5505
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC143_AoA_14.json b/surface_dual_areas/cases/geo_LHC143_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..9ba145f68327961a2cde4d80d36179614c4b9c81
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC143_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC143_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC143_AoA_14/boundary_dual_area_geo_LHC143_AoA_14.npy",
+    "sha256": "aa2f9d1b63265847040e0cffe94435a9b369b556976b8fdf30fd4e315643d031",
+    "shape": [
+      144442697
+    ],
+    "size_bytes": 577770916
+  },
+  "runtime": {
+    "accumulation_seconds": 11.280430385144427,
+    "completed_at_utc": "2026-08-07T08:46:02.449551Z",
+    "elapsed_seconds": 22.219024755060673,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5089281781110913,
+    "geometry_read_seconds": 2.068078671116382,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:45:40.230436Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC143_AoA_14/boundary_geo_LHC143_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC143_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624712000000000,
+    "extracted_vtu_size_bytes": 22187703174,
+    "geometry_sha256": "36fca6b01551dc0eb9463efdc881f75fee675cd6a9640936a12ad0d6e3c9686e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3850315,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1273494,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2779742,
+      "13": 836198,
+      "14": 1483986,
+      "15": 482673,
+      "16": 953833,
+      "17": 358124,
+      "18": 748951,
+      "19": 302057,
+      "20": 677580,
+      "21": 225469,
+      "22": 371157,
+      "23": 123971,
+      "24": 208608,
+      "25": 69570,
+      "26": 92577,
+      "27": 50955,
+      "28": 124128,
+      "29": 52537,
+      "3": 58722,
+      "30": 115015,
+      "31": 49393,
+      "32": 110365,
+      "33": 39071,
+      "34": 68263,
+      "35": 28267,
+      "36": 63365,
+      "37": 23071,
+      "38": 38155,
+      "39": 16059,
+      "4": 133421,
+      "40": 28838,
+      "41": 10484,
+      "42": 13986,
+      "43": 5807,
+      "44": 7759,
+      "45": 3588,
+      "46": 4297,
+      "47": 2605,
+      "48": 3533,
+      "49": 2126,
+      "5": 944710,
+      "50": 2890,
+      "51": 1782,
+      "52": 2576,
+      "53": 1667,
+      "54": 2243,
+      "55": 1618,
+      "56": 2475,
+      "57": 1674,
+      "58": 2280,
+      "59": 1689,
+      "6": 5236605,
+      "60": 2446,
+      "61": 1664,
+      "62": 2198,
+      "63": 1588,
+      "64": 2149,
+      "65": 1369,
+      "66": 1770,
+      "67": 1094,
+      "68": 1505,
+      "69": 880,
+      "7": 2069039,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6343488,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1881065,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58722,
+      "7": 32218646,
+      "9": 133421
+    },
+    "connectivity_max": 144442696,
+    "connectivity_min": 0,
+    "n_cells": 32410789,
+    "n_connectivity_values": 353695858,
+    "n_fan_triangles": 288874280,
+    "n_points": 144442697
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.722366522950025e-11,
+    "float64_area_closure_relative": 5.26598119784714e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 288874280,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945420.6035861166,
+    "surface_area_float64_in2": 1945420.6036585323,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945420.603658522,
+    "zero_area_triangles": 239186,
+    "zero_weight_points": 5870
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC144_AoA_6.json b/surface_dual_areas/cases/geo_LHC144_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..2299485da0d5773e4e5abe7a01eb88b8062e89ab
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC144_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC144_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC144_AoA_6/boundary_dual_area_geo_LHC144_AoA_6.npy",
+    "sha256": "f819e32b4f91f483935b9bdc79a2e7dc3ae50ded90b92c2477ad4599cf9cdd4e",
+    "shape": [
+      135293590
+    ],
+    "size_bytes": 541174488
+  },
+  "runtime": {
+    "accumulation_seconds": 10.22480849106796,
+    "completed_at_utc": "2026-08-07T08:04:44.625502Z",
+    "elapsed_seconds": 20.763073513051495,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.8920603110454977,
+    "geometry_read_seconds": 3.1414479550439864,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T08:04:23.862340Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC144_AoA_6/boundary_geo_LHC144_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC144_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624447000000000,
+    "extracted_vtu_size_bytes": 20770530915,
+    "geometry_sha256": "3ab25bf0368ac39fd59698033cac6e4e8c070e42a6ba0e72bd7cce475fb1bdb3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3082980,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1027574,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2358227,
+      "13": 783745,
+      "14": 1608110,
+      "15": 523750,
+      "16": 1006934,
+      "17": 375284,
+      "18": 748171,
+      "19": 302092,
+      "20": 669326,
+      "21": 223434,
+      "22": 350409,
+      "23": 119859,
+      "24": 197953,
+      "25": 67304,
+      "26": 92393,
+      "27": 51206,
+      "28": 123612,
+      "29": 52984,
+      "3": 49565,
+      "30": 114121,
+      "31": 49324,
+      "32": 108035,
+      "33": 38819,
+      "34": 66856,
+      "35": 27999,
+      "36": 63389,
+      "37": 23075,
+      "38": 39120,
+      "39": 16350,
+      "4": 113450,
+      "40": 29351,
+      "41": 10673,
+      "42": 14152,
+      "43": 5755,
+      "44": 7528,
+      "45": 3663,
+      "46": 4229,
+      "47": 2485,
+      "48": 3525,
+      "49": 2143,
+      "5": 927673,
+      "50": 2980,
+      "51": 1892,
+      "52": 2722,
+      "53": 1771,
+      "54": 2452,
+      "55": 1734,
+      "56": 2538,
+      "57": 1740,
+      "58": 2274,
+      "59": 1720,
+      "6": 5164307,
+      "60": 2506,
+      "61": 1656,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1376,
+      "66": 1817,
+      "67": 1100,
+      "68": 1464,
+      "69": 904,
+      "7": 1948503,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5634588,
+      "80": 192,
+      "81": 122,
+      "82": 140,
+      "83": 116,
+      "84": 117,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 69,
+      "89": 59,
+      "9": 1607657,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49565,
+      "7": 29723600,
+      "9": 113450
+    },
+    "connectivity_max": 135293589,
+    "connectivity_min": 0,
+    "n_cells": 29886615,
+    "n_connectivity_values": 330349287,
+    "n_fan_triangles": 270576057,
+    "n_points": 135293590
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.929247081543992e-11,
+    "float64_area_closure_relative": 1.608988952703538e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 270576057,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939062.8006469114,
+    "surface_area_float64_in2": 1939062.800723102,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939062.8007230707,
+    "zero_area_triangles": 228936,
+    "zero_weight_points": 4978
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC145_AoA_14.json b/surface_dual_areas/cases/geo_LHC145_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..6c4a7229b555481a1be1f9ecd48b9f077aaa2229
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC145_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC145_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC145_AoA_14/boundary_dual_area_geo_LHC145_AoA_14.npy",
+    "sha256": "bd9edb069143535646b0dd84dd8c2f6e1763a26d6d51f09b104456b8eb172669",
+    "shape": [
+      139456188
+    ],
+    "size_bytes": 557824880
+  },
+  "runtime": {
+    "accumulation_seconds": 10.665499781025574,
+    "completed_at_utc": "2026-08-07T08:45:16.665609Z",
+    "elapsed_seconds": 21.083847588161007,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.120351104065776,
+    "geometry_read_seconds": 2.59165932610631,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:44:55.581663Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC145_AoA_14/boundary_geo_LHC145_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC145_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624454000000000,
+    "extracted_vtu_size_bytes": 21419413275,
+    "geometry_sha256": "f44c7f686c369e4d3432645f2ba0857a16b3d55fc6b8184c4855d28f13bb5d57",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3933350,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1178830,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2610724,
+      "13": 758952,
+      "14": 1312348,
+      "15": 449019,
+      "16": 913805,
+      "17": 353169,
+      "18": 761319,
+      "19": 307747,
+      "20": 681672,
+      "21": 227494,
+      "22": 354118,
+      "23": 122795,
+      "24": 196843,
+      "25": 67885,
+      "26": 91969,
+      "27": 51152,
+      "28": 124311,
+      "29": 53077,
+      "3": 52328,
+      "30": 115719,
+      "31": 49595,
+      "32": 108689,
+      "33": 39140,
+      "34": 67485,
+      "35": 28183,
+      "36": 63135,
+      "37": 23004,
+      "38": 38422,
+      "39": 15978,
+      "4": 116296,
+      "40": 28922,
+      "41": 10522,
+      "42": 13944,
+      "43": 5657,
+      "44": 7572,
+      "45": 3670,
+      "46": 4231,
+      "47": 2546,
+      "48": 3549,
+      "49": 2113,
+      "5": 924636,
+      "50": 2985,
+      "51": 1796,
+      "52": 2634,
+      "53": 1671,
+      "54": 2244,
+      "55": 1641,
+      "56": 2455,
+      "57": 1698,
+      "58": 2266,
+      "59": 1720,
+      "6": 5132128,
+      "60": 2502,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2004556,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5953503,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1789010,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52328,
+      "7": 31030702,
+      "9": 116296
+    },
+    "connectivity_max": 139456187,
+    "connectivity_min": 0,
+    "n_cells": 31199326,
+    "n_connectivity_values": 341299915,
+    "n_fan_triangles": 278901263,
+    "n_points": 139456188
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.468790909534466e-11,
+    "float64_area_closure_relative": 4.4537110534109454e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278901263,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1934282.1551695901,
+    "surface_area_float64_in2": 1934282.1552366863,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1934282.1552367725,
+    "zero_area_triangles": 238590,
+    "zero_weight_points": 5587
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC145_AoA_20.json b/surface_dual_areas/cases/geo_LHC145_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..959d2235f23e5a3bcb32a2237609bcea52ad4dc0
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC145_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC145_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC145_AoA_20/boundary_dual_area_geo_LHC145_AoA_20.npy",
+    "sha256": "5b2900c528149caa906be9aa967942cf4741c723503daaef42335e3269189a69",
+    "shape": [
+      137379539
+    ],
+    "size_bytes": 549518284
+  },
+  "runtime": {
+    "accumulation_seconds": 10.919765752041712,
+    "completed_at_utc": "2026-08-07T08:46:03.710227Z",
+    "elapsed_seconds": 21.23912264709361,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.329934042878449,
+    "geometry_read_seconds": 2.2050637102220207,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:45:42.471010Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC145_AoA_20/boundary_geo_LHC145_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC145_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624401000000000,
+    "extracted_vtu_size_bytes": 21098250298,
+    "geometry_sha256": "0c2be4f5cdfce736dabef53e23ea5eac91d82970730a7e11088f7333c7efaf9a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3670080,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1119832,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2444443,
+      "13": 741202,
+      "14": 1323348,
+      "15": 458558,
+      "16": 935291,
+      "17": 355942,
+      "18": 759467,
+      "19": 306842,
+      "20": 683636,
+      "21": 229320,
+      "22": 365261,
+      "23": 125441,
+      "24": 204012,
+      "25": 69361,
+      "26": 93358,
+      "27": 51546,
+      "28": 124523,
+      "29": 53141,
+      "3": 49177,
+      "30": 115753,
+      "31": 49619,
+      "32": 108692,
+      "33": 39140,
+      "34": 67503,
+      "35": 28183,
+      "36": 63118,
+      "37": 23008,
+      "38": 38409,
+      "39": 15972,
+      "4": 113862,
+      "40": 28907,
+      "41": 10524,
+      "42": 13932,
+      "43": 5644,
+      "44": 7563,
+      "45": 3668,
+      "46": 4231,
+      "47": 2543,
+      "48": 3550,
+      "49": 2108,
+      "5": 930102,
+      "50": 2989,
+      "51": 1794,
+      "52": 2633,
+      "53": 1669,
+      "54": 2243,
+      "55": 1642,
+      "56": 2455,
+      "57": 1698,
+      "58": 2266,
+      "59": 1720,
+      "6": 5164210,
+      "60": 2502,
+      "61": 1654,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 1996641,
+      "70": 1023,
+      "71": 571,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5865778,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1735915,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49177,
+      "7": 30483530,
+      "9": 113862
+    },
+    "connectivity_max": 137379538,
+    "connectivity_min": 0,
+    "n_cells": 30646569,
+    "n_connectivity_values": 336041103,
+    "n_fan_triangles": 274747965,
+    "n_points": 137379539
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4534909884592246e-11,
+    "float64_area_closure_relative": 7.511121719030885e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 274747965,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1934282.6154299444,
+    "surface_area_float64_in2": 1934282.6154967446,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1934282.61549689,
+    "zero_area_triangles": 235433,
+    "zero_weight_points": 5400
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC146_AoA_22.json b/surface_dual_areas/cases/geo_LHC146_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..ffca64796fe6e76d6d9bb4455d6059e097cf56bd
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC146_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC146_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC146_AoA_22/boundary_dual_area_geo_LHC146_AoA_22.npy",
+    "sha256": "6d8e79743010c71444e195bf7c3b21f5dab8ace96b0f1228ac4ede524abeaf49",
+    "shape": [
+      149129892
+    ],
+    "size_bytes": 596519696
+  },
+  "runtime": {
+    "accumulation_seconds": 11.496891462942585,
+    "completed_at_utc": "2026-08-07T08:48:39.477913Z",
+    "elapsed_seconds": 62.52107380400412,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4125373258721083,
+    "geometry_read_seconds": 42.34890543296933,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:47:36.956731Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC146_AoA_22/boundary_geo_LHC146_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC146_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624668000000000,
+    "extracted_vtu_size_bytes": 22918611207,
+    "geometry_sha256": "0d22b0a1d88d67ab8b52aecb6fe16574883ed379b24704460af10b6b2965abb8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4618859,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1508711,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2949529,
+      "13": 875218,
+      "14": 1210562,
+      "15": 441390,
+      "16": 848061,
+      "17": 344172,
+      "18": 738373,
+      "19": 298371,
+      "20": 673571,
+      "21": 223695,
+      "22": 382169,
+      "23": 122861,
+      "24": 216252,
+      "25": 70290,
+      "26": 93461,
+      "27": 51707,
+      "28": 124003,
+      "29": 52698,
+      "3": 62427,
+      "30": 115607,
+      "31": 49340,
+      "32": 108465,
+      "33": 38591,
+      "34": 65931,
+      "35": 27640,
+      "36": 62670,
+      "37": 22893,
+      "38": 39304,
+      "39": 16490,
+      "4": 141885,
+      "40": 29963,
+      "41": 10990,
+      "42": 14560,
+      "43": 5943,
+      "44": 7831,
+      "45": 3677,
+      "46": 4332,
+      "47": 2545,
+      "48": 3506,
+      "49": 2149,
+      "5": 937401,
+      "50": 2887,
+      "51": 1856,
+      "52": 2718,
+      "53": 1804,
+      "54": 2446,
+      "55": 1730,
+      "56": 2606,
+      "57": 1740,
+      "58": 2318,
+      "59": 1696,
+      "6": 5251714,
+      "60": 2442,
+      "61": 1667,
+      "62": 2196,
+      "63": 1588,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2129269,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6732375,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2122798,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 62427,
+      "7": 33694610,
+      "9": 141885
+    },
+    "connectivity_max": 149129891,
+    "connectivity_min": 0,
+    "n_cells": 33898922,
+    "n_connectivity_values": 366046495,
+    "n_fan_triangles": 298248651,
+    "n_points": 149129892
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.874544978943504e-11,
+    "float64_area_closure_relative": 9.559313200355288e-16,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 298248651,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948513.5700853067,
+    "surface_area_float64_in2": 1948513.5701608027,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948513.5701608008,
+    "zero_area_triangles": 240322,
+    "zero_weight_points": 5998
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC148_AoA_20.json b/surface_dual_areas/cases/geo_LHC148_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..75c30dc75e76ce8af041b56e459436b3badb9c88
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC148_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC148_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC148_AoA_20/boundary_dual_area_geo_LHC148_AoA_20.npy",
+    "sha256": "6766cc9a8415f5c1c524ef4a134e0a921c3712ef8e852e7952704cce92607899",
+    "shape": [
+      152247945
+    ],
+    "size_bytes": 608991908
+  },
+  "runtime": {
+    "accumulation_seconds": 11.629897479899228,
+    "completed_at_utc": "2026-08-07T08:02:48.773700Z",
+    "elapsed_seconds": 22.96888619614765,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.346693192142993,
+    "geometry_read_seconds": 2.1562267739791423,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T08:02:25.804722Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC148_AoA_20/boundary_geo_LHC148_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC148_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624410000000000,
+    "extracted_vtu_size_bytes": 23401698439,
+    "geometry_sha256": "e0c9e86feff9cb7e3dafb980ef3ec83cfd846c2a737313672afa67ada49a011e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4729603,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1491142,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3252995,
+      "13": 899940,
+      "14": 1295645,
+      "15": 464894,
+      "16": 896937,
+      "17": 358922,
+      "18": 741663,
+      "19": 301645,
+      "20": 660333,
+      "21": 220680,
+      "22": 343665,
+      "23": 117955,
+      "24": 191142,
+      "25": 68015,
+      "26": 88720,
+      "27": 51332,
+      "28": 123102,
+      "29": 52879,
+      "3": 61817,
+      "30": 114834,
+      "31": 49481,
+      "32": 109328,
+      "33": 38662,
+      "34": 66648,
+      "35": 27653,
+      "36": 62126,
+      "37": 22689,
+      "38": 38598,
+      "39": 16399,
+      "4": 141350,
+      "40": 30167,
+      "41": 10993,
+      "42": 14729,
+      "43": 5995,
+      "44": 7893,
+      "45": 3719,
+      "46": 4393,
+      "47": 2540,
+      "48": 3527,
+      "49": 2078,
+      "5": 978119,
+      "50": 2853,
+      "51": 1779,
+      "52": 2631,
+      "53": 1704,
+      "54": 2329,
+      "55": 1678,
+      "56": 2556,
+      "57": 1701,
+      "58": 2306,
+      "59": 1691,
+      "6": 5329235,
+      "60": 2444,
+      "61": 1664,
+      "62": 2196,
+      "63": 1588,
+      "64": 2151,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2227200,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6847552,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2150500,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61817,
+      "7": 34560367,
+      "9": 141350
+    },
+    "connectivity_max": 152247944,
+    "connectivity_min": 0,
+    "n_cells": 34763534,
+    "n_connectivity_values": 374011836,
+    "n_fan_triangles": 304484768,
+    "n_points": 152247945
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.6003432566275136e-11,
+    "float64_area_closure_relative": 1.232018001598108e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 304484768,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946526.4520597707,
+    "surface_area_float64_in2": 1946526.4521493176,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946526.4521492936,
+    "zero_area_triangles": 248084,
+    "zero_weight_points": 6558
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC148_AoA_22.json b/surface_dual_areas/cases/geo_LHC148_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..27a9bec8a9edeacb0a51ccbdbe73f37ae08b85f2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC148_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC148_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC148_AoA_22/boundary_dual_area_geo_LHC148_AoA_22.npy",
+    "sha256": "d42b31dd1a557fa97fd0358acc574fa7b815be25f3cab471d0af9b73c56566f8",
+    "shape": [
+      152511419
+    ],
+    "size_bytes": 610045804
+  },
+  "runtime": {
+    "accumulation_seconds": 11.54242835380137,
+    "completed_at_utc": "2026-08-07T08:06:53.347942Z",
+    "elapsed_seconds": 24.169600175926462,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.424964829115197,
+    "geometry_read_seconds": 4.132406858028844,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T08:06:29.178251Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC148_AoA_22/boundary_geo_LHC148_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC148_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624553000000000,
+    "extracted_vtu_size_bytes": 23442624616,
+    "geometry_sha256": "3b6559fcc43d526a7ee9cebf6739af05a3b0b7ee5e0ecb4116c8a0b4e56b26d1",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4768341,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1504559,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3268700,
+      "13": 905997,
+      "14": 1272647,
+      "15": 462640,
+      "16": 895092,
+      "17": 356965,
+      "18": 737537,
+      "19": 299916,
+      "20": 659153,
+      "21": 220402,
+      "22": 346472,
+      "23": 118469,
+      "24": 192568,
+      "25": 68392,
+      "26": 88802,
+      "27": 51337,
+      "28": 123098,
+      "29": 52886,
+      "3": 62233,
+      "30": 114828,
+      "31": 49478,
+      "32": 109326,
+      "33": 38649,
+      "34": 66652,
+      "35": 27650,
+      "36": 62135,
+      "37": 22692,
+      "38": 38596,
+      "39": 16395,
+      "4": 141924,
+      "40": 30170,
+      "41": 10996,
+      "42": 14723,
+      "43": 5996,
+      "44": 7894,
+      "45": 3717,
+      "46": 4394,
+      "47": 2538,
+      "48": 3526,
+      "49": 2077,
+      "5": 972915,
+      "50": 2857,
+      "51": 1778,
+      "52": 2631,
+      "53": 1704,
+      "54": 2329,
+      "55": 1678,
+      "56": 2556,
+      "57": 1700,
+      "58": 2306,
+      "59": 1691,
+      "6": 5320771,
+      "60": 2444,
+      "61": 1664,
+      "62": 2196,
+      "63": 1588,
+      "64": 2151,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2223381,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6891363,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2157721,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 62233,
+      "7": 34636658,
+      "9": 141924
+    },
+    "connectivity_max": 152511418,
+    "connectivity_min": 0,
+    "n_cells": 34840815,
+    "n_connectivity_values": 374693346,
+    "n_fan_triangles": 305011716,
+    "n_points": 152511419
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.499042600314573e-11,
+    "float64_area_closure_relative": 5.262989440245478e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 305011716,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946526.4820731862,
+    "surface_area_float64_in2": 1946526.4821607613,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946526.4821607715,
+    "zero_area_triangles": 247892,
+    "zero_weight_points": 6512
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC150_AoA_12.json b/surface_dual_areas/cases/geo_LHC150_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..c18372415dad5fcdae4dfe1b180cc81c4803f410
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC150_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC150_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC150_AoA_12/boundary_dual_area_geo_LHC150_AoA_12.npy",
+    "sha256": "72432a786553d492b7754f56a7c713494108f2260019d992e525874b3c50e562",
+    "shape": [
+      146122133
+    ],
+    "size_bytes": 584488660
+  },
+  "runtime": {
+    "accumulation_seconds": 11.453190512955189,
+    "completed_at_utc": "2026-08-07T08:48:00.008959Z",
+    "elapsed_seconds": 23.052172892028466,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6160323028452694,
+    "geometry_read_seconds": 2.8774887260515243,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:47:36.956712Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC150_AoA_12/boundary_geo_LHC150_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC150_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624625000000000,
+    "extracted_vtu_size_bytes": 22449147679,
+    "geometry_sha256": "f46b07f19338b8988add9d49f247976ecded06f98ec4d25cd93aca8a58b2268e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4161227,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1346820,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2890478,
+      "13": 843618,
+      "14": 1418263,
+      "15": 465284,
+      "16": 924128,
+      "17": 352569,
+      "18": 742016,
+      "19": 300379,
+      "20": 671316,
+      "21": 223717,
+      "22": 362785,
+      "23": 122458,
+      "24": 206035,
+      "25": 71368,
+      "26": 92674,
+      "27": 51923,
+      "28": 123680,
+      "29": 52736,
+      "3": 56124,
+      "30": 115365,
+      "31": 49494,
+      "32": 109340,
+      "33": 38959,
+      "34": 66687,
+      "35": 28210,
+      "36": 63141,
+      "37": 23064,
+      "38": 38622,
+      "39": 16262,
+      "4": 127950,
+      "40": 29159,
+      "41": 10618,
+      "42": 14246,
+      "43": 5788,
+      "44": 7695,
+      "45": 3602,
+      "46": 4179,
+      "47": 2507,
+      "48": 3487,
+      "49": 2067,
+      "5": 945855,
+      "50": 2756,
+      "51": 1754,
+      "52": 2493,
+      "53": 1652,
+      "54": 2216,
+      "55": 1618,
+      "56": 2481,
+      "57": 1675,
+      "58": 2281,
+      "59": 1693,
+      "6": 5216235,
+      "60": 2445,
+      "61": 1665,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2118301,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6386345,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1976043,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56124,
+      "7": 32742236,
+      "9": 127950
+    },
+    "connectivity_max": 146122132,
+    "connectivity_min": 0,
+    "n_cells": 32926310,
+    "n_connectivity_values": 358085766,
+    "n_fan_triangles": 292233146,
+    "n_points": 146122133
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.995393476251195e-11,
+    "float64_area_closure_relative": 6.236648703525111e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 292233146,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945031.235609839,
+    "surface_area_float64_in2": 1945031.2356875506,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945031.235687672,
+    "zero_area_triangles": 245625,
+    "zero_weight_points": 6179
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC150_AoA_8.json b/surface_dual_areas/cases/geo_LHC150_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d40e9409b1f4e5e24aa7c22e49e62bc4b002ab4
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC150_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC150_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC150_AoA_8/boundary_dual_area_geo_LHC150_AoA_8.npy",
+    "sha256": "6b2c419683c037a5a699f7476d85d15da0715524c8529bc7eae5c5899abad087",
+    "shape": [
+      138754669
+    ],
+    "size_bytes": 555018804
+  },
+  "runtime": {
+    "accumulation_seconds": 10.636197190964594,
+    "completed_at_utc": "2026-08-07T08:07:44.313962Z",
+    "elapsed_seconds": 20.921837141970173,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.117376100970432,
+    "geometry_read_seconds": 2.277611810946837,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T08:07:23.392037Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC150_AoA_8/boundary_geo_LHC150_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC150_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624585000000000,
+    "extracted_vtu_size_bytes": 21304656249,
+    "geometry_sha256": "a2046f2fbfd97b6487c33fb2b28a265dec87645eb49e0f80f431846e0ddd981a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3196784,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1038770,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2365667,
+      "13": 799547,
+      "14": 1712458,
+      "15": 553599,
+      "16": 1018974,
+      "17": 379803,
+      "18": 750334,
+      "19": 304077,
+      "20": 674328,
+      "21": 225210,
+      "22": 365091,
+      "23": 123244,
+      "24": 207409,
+      "25": 71803,
+      "26": 92944,
+      "27": 51982,
+      "28": 123738,
+      "29": 52741,
+      "3": 53249,
+      "30": 115363,
+      "31": 49498,
+      "32": 109349,
+      "33": 38953,
+      "34": 66691,
+      "35": 28208,
+      "36": 63135,
+      "37": 23067,
+      "38": 38625,
+      "39": 16271,
+      "4": 127580,
+      "40": 29154,
+      "41": 10622,
+      "42": 14251,
+      "43": 5786,
+      "44": 7694,
+      "45": 3603,
+      "46": 4178,
+      "47": 2505,
+      "48": 3486,
+      "49": 2068,
+      "5": 948345,
+      "50": 2756,
+      "51": 1755,
+      "52": 2493,
+      "53": 1652,
+      "54": 2216,
+      "55": 1618,
+      "56": 2481,
+      "57": 1675,
+      "58": 2281,
+      "59": 1693,
+      "6": 5230803,
+      "60": 2445,
+      "61": 1665,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2017014,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5929526,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1671021,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53249,
+      "7": 30581211,
+      "9": 127580
+    },
+    "connectivity_max": 138754668,
+    "connectivity_min": 0,
+    "n_cells": 30762040,
+    "n_connectivity_values": 339022297,
+    "n_fan_triangles": 277498217,
+    "n_points": 138754669
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.9500804894227425e-11,
+    "float64_area_closure_relative": 4.129829836752225e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277498217,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945033.4573732067,
+    "surface_area_float64_in2": 1945033.4574500371,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945033.4574501175,
+    "zero_area_triangles": 232232,
+    "zero_weight_points": 5325
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC151_AoA_16.json b/surface_dual_areas/cases/geo_LHC151_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e33c175db8dec41012f309c47ea24d125d9014a
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC151_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC151_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC151_AoA_16/boundary_dual_area_geo_LHC151_AoA_16.npy",
+    "sha256": "bf4a1d6de0a6e2e8b02bbe80658a11a7ecad0684fdfa7806bf57487239797276",
+    "shape": [
+      140657294
+    ],
+    "size_bytes": 562629304
+  },
+  "runtime": {
+    "accumulation_seconds": 11.057988606858999,
+    "completed_at_utc": "2026-08-07T08:48:22.794550Z",
+    "elapsed_seconds": 21.83828353486024,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.471465177834034,
+    "geometry_read_seconds": 2.448249773820862,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:48:00.956184Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC151_AoA_16/boundary_geo_LHC151_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC151_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624621000000000,
+    "extracted_vtu_size_bytes": 21606397664,
+    "geometry_sha256": "60c9d78f0e15e94a3ee828f681b798f32f2f8367c2ef26c179ae57d94b7fc550",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4014206,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1225108,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2646090,
+      "13": 784934,
+      "14": 1239880,
+      "15": 447857,
+      "16": 896512,
+      "17": 349680,
+      "18": 752957,
+      "19": 303026,
+      "20": 676828,
+      "21": 225544,
+      "22": 372318,
+      "23": 123118,
+      "24": 209722,
+      "25": 69508,
+      "26": 93627,
+      "27": 51802,
+      "28": 123739,
+      "29": 53027,
+      "3": 52205,
+      "30": 114257,
+      "31": 49313,
+      "32": 107991,
+      "33": 38790,
+      "34": 66545,
+      "35": 28038,
+      "36": 63295,
+      "37": 22956,
+      "38": 39118,
+      "39": 16367,
+      "4": 120329,
+      "40": 29775,
+      "41": 10801,
+      "42": 14269,
+      "43": 5893,
+      "44": 7771,
+      "45": 3730,
+      "46": 4211,
+      "47": 2522,
+      "48": 3593,
+      "49": 2221,
+      "5": 938467,
+      "50": 2871,
+      "51": 1842,
+      "52": 2744,
+      "53": 1765,
+      "54": 2419,
+      "55": 1734,
+      "56": 2557,
+      "57": 1773,
+      "58": 2275,
+      "59": 1691,
+      "6": 5167534,
+      "60": 2463,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2040857,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6076923,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1836077,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52205,
+      "7": 31395621,
+      "9": 120329
+    },
+    "connectivity_max": 140657293,
+    "connectivity_min": 0,
+    "n_cells": 31568155,
+    "n_connectivity_values": 344439782,
+    "n_fan_triangles": 281303472,
+    "n_points": 140657294
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.325394233608185e-11,
+    "float64_area_closure_relative": 4.949540198718858e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281303472,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938083.565965056,
+    "surface_area_float64_in2": 1938083.5660295049,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938083.5660296008,
+    "zero_area_triangles": 236452,
+    "zero_weight_points": 5589
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC151_AoA_20.json b/surface_dual_areas/cases/geo_LHC151_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..b71d1433461582b646f964d7a52837c2a94108ac
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC151_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC151_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC151_AoA_20/boundary_dual_area_geo_LHC151_AoA_20.npy",
+    "sha256": "2aff89865e983b226cdf33600db5dad67b3d9409f092a1567bf096591c1fe103",
+    "shape": [
+      140650212
+    ],
+    "size_bytes": 562600976
+  },
+  "runtime": {
+    "accumulation_seconds": 10.87416568188928,
+    "completed_at_utc": "2026-08-07T08:49:00.983308Z",
+    "elapsed_seconds": 21.437104435870424,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.248704783152789,
+    "geometry_read_seconds": 1.936107851099223,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:48:39.546109Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC151_AoA_20/boundary_geo_LHC151_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC151_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624710000000000,
+    "extracted_vtu_size_bytes": 21606742803,
+    "geometry_sha256": "9dc5aba1fc139924127fbb7deed42f51a17895884180137b175e6cae09f4735f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4045209,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1237136,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2600578,
+      "13": 763167,
+      "14": 1191162,
+      "15": 429494,
+      "16": 892220,
+      "17": 347898,
+      "18": 756466,
+      "19": 305247,
+      "20": 681952,
+      "21": 228712,
+      "22": 379098,
+      "23": 125542,
+      "24": 213286,
+      "25": 70455,
+      "26": 94108,
+      "27": 51967,
+      "28": 123779,
+      "29": 53037,
+      "3": 52418,
+      "30": 114254,
+      "31": 49315,
+      "32": 107984,
+      "33": 38791,
+      "34": 66545,
+      "35": 28039,
+      "36": 63296,
+      "37": 22957,
+      "38": 39118,
+      "39": 16366,
+      "4": 121898,
+      "40": 29775,
+      "41": 10801,
+      "42": 14269,
+      "43": 5893,
+      "44": 7771,
+      "45": 3730,
+      "46": 4211,
+      "47": 2522,
+      "48": 3593,
+      "49": 2221,
+      "5": 943621,
+      "50": 2871,
+      "51": 1842,
+      "52": 2744,
+      "53": 1765,
+      "54": 2419,
+      "55": 1734,
+      "56": 2557,
+      "57": 1773,
+      "58": 2275,
+      "59": 1691,
+      "6": 5194608,
+      "60": 2463,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2056831,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6122543,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1865179,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52418,
+      "7": 31449570,
+      "9": 121898
+    },
+    "connectivity_max": 140650211,
+    "connectivity_min": 0,
+    "n_cells": 31623886,
+    "n_connectivity_values": 344537080,
+    "n_fan_triangles": 281289308,
+    "n_points": 140650212
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4156391617640505e-11,
+    "float64_area_closure_relative": 6.198938538784917e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281289308,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938083.6149545447,
+    "surface_area_float64_in2": 1938083.6150207426,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938083.6150208628,
+    "zero_area_triangles": 235533,
+    "zero_weight_points": 5614
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC153_AoA_10.json b/surface_dual_areas/cases/geo_LHC153_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..cd32437374870e3d14492bcefd29a6cb43b4caac
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC153_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC153_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC153_AoA_10/boundary_dual_area_geo_LHC153_AoA_10.npy",
+    "sha256": "010c03c102046f58dd8afc11d66727383dbb4226500eed76ed464d7058a0e0a5",
+    "shape": [
+      138315515
+    ],
+    "size_bytes": 553262188
+  },
+  "runtime": {
+    "accumulation_seconds": 10.52902149502188,
+    "completed_at_utc": "2026-08-07T08:51:56.292271Z",
+    "elapsed_seconds": 49.92325208615512,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1117825170513242,
+    "geometry_read_seconds": 31.420361193129793,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:51:06.368934Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC153_AoA_10/boundary_geo_LHC153_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC153_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624393000000000,
+    "extracted_vtu_size_bytes": 21240859632,
+    "geometry_sha256": "520e5def152ff57c85a5f5bf2637b4fdceaa53acc4eea11485fdd9316695a259",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3582930,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1100666,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2502174,
+      "13": 789455,
+      "14": 1450128,
+      "15": 507133,
+      "16": 949105,
+      "17": 370944,
+      "18": 761147,
+      "19": 308049,
+      "20": 680614,
+      "21": 226607,
+      "22": 359541,
+      "23": 120321,
+      "24": 191790,
+      "25": 66318,
+      "26": 90530,
+      "27": 51509,
+      "28": 124781,
+      "29": 53372,
+      "3": 52405,
+      "30": 115348,
+      "31": 49637,
+      "32": 108731,
+      "33": 38809,
+      "34": 66368,
+      "35": 28169,
+      "36": 62008,
+      "37": 22921,
+      "38": 37748,
+      "39": 16009,
+      "4": 119730,
+      "40": 28833,
+      "41": 10548,
+      "42": 14176,
+      "43": 5755,
+      "44": 7696,
+      "45": 3637,
+      "46": 4138,
+      "47": 2503,
+      "48": 3468,
+      "49": 2056,
+      "5": 931599,
+      "50": 2768,
+      "51": 1728,
+      "52": 2492,
+      "53": 1629,
+      "54": 2225,
+      "55": 1605,
+      "56": 2413,
+      "57": 1714,
+      "58": 2266,
+      "59": 1734,
+      "6": 5168621,
+      "60": 2507,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1988706,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5896548,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1693053,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52405,
+      "7": 30637832,
+      "9": 119730
+    },
+    "connectivity_max": 138315514,
+    "connectivity_min": 0,
+    "n_cells": 30809967,
+    "n_connectivity_values": 338239843,
+    "n_fan_triangles": 276619909,
+    "n_points": 138315515
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.273144685480734e-11,
+    "float64_area_closure_relative": 4.484863393924517e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276619909,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936420.8550409295,
+    "surface_area_float64_in2": 1936420.8551043114,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936420.8551043982,
+    "zero_area_triangles": 236444,
+    "zero_weight_points": 5472
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC153_AoA_16.json b/surface_dual_areas/cases/geo_LHC153_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..98b4f84b04f104463fad975d5502cee51b69ab11
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC153_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC153_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC153_AoA_16/boundary_dual_area_geo_LHC153_AoA_16.npy",
+    "sha256": "31df858272220d5e581d715200d8a6d63e4b5382456b1d5853b642987648dfb7",
+    "shape": [
+      140212114
+    ],
+    "size_bytes": 560848584
+  },
+  "runtime": {
+    "accumulation_seconds": 10.687035297043622,
+    "completed_at_utc": "2026-08-07T08:05:27.681092Z",
+    "elapsed_seconds": 20.28348002093844,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1104873260483146,
+    "geometry_read_seconds": 1.7797727258875966,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T08:05:07.397527Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC153_AoA_16/boundary_geo_LHC153_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC153_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624566000000000,
+    "extracted_vtu_size_bytes": 21535782484,
+    "geometry_sha256": "d03db96775b07b428b5306d268051f0ce00796f0a9f954ee3d515782a1111b8f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3846426,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1179205,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2612731,
+      "13": 799573,
+      "14": 1385365,
+      "15": 484614,
+      "16": 921601,
+      "17": 362505,
+      "18": 755828,
+      "19": 306563,
+      "20": 678902,
+      "21": 226886,
+      "22": 359730,
+      "23": 120937,
+      "24": 192131,
+      "25": 66622,
+      "26": 90818,
+      "27": 51536,
+      "28": 124792,
+      "29": 53338,
+      "3": 53935,
+      "30": 115319,
+      "31": 49617,
+      "32": 108709,
+      "33": 38797,
+      "34": 66360,
+      "35": 28162,
+      "36": 61999,
+      "37": 22909,
+      "38": 37743,
+      "39": 16005,
+      "4": 121936,
+      "40": 28834,
+      "41": 10546,
+      "42": 14170,
+      "43": 5747,
+      "44": 7694,
+      "45": 3634,
+      "46": 4138,
+      "47": 2506,
+      "48": 3465,
+      "49": 2054,
+      "5": 935009,
+      "50": 2768,
+      "51": 1726,
+      "52": 2492,
+      "53": 1630,
+      "54": 2221,
+      "55": 1605,
+      "56": 2413,
+      "57": 1714,
+      "58": 2266,
+      "59": 1734,
+      "6": 5168021,
+      "60": 2507,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2015305,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6018889,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1773781,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 53935,
+      "7": 31203144,
+      "9": 121936
+    },
+    "connectivity_max": 140212113,
+    "connectivity_min": 0,
+    "n_cells": 31379015,
+    "n_connectivity_values": 343171137,
+    "n_fan_triangles": 280413107,
+    "n_points": 140212114
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.224905670686702e-11,
+    "float64_area_closure_relative": 3.727366729600493e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 280413107,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936420.662801486,
+    "surface_area_float64_in2": 1936420.6628639337,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936420.662863941,
+    "zero_area_triangles": 239415,
+    "zero_weight_points": 5670
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC153_AoA_22.json b/surface_dual_areas/cases/geo_LHC153_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..7bf236398abfae4cbc39dde85897623d0844a2dd
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC153_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC153_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC153_AoA_22/boundary_dual_area_geo_LHC153_AoA_22.npy",
+    "sha256": "c920227a6a75393cc98bf51d11b1ddc7f5f3385ceee907df87891cadaafaa31a",
+    "shape": [
+      139749285
+    ],
+    "size_bytes": 558997268
+  },
+  "runtime": {
+    "accumulation_seconds": 10.709035195875913,
+    "completed_at_utc": "2026-08-07T08:49:20.210209Z",
+    "elapsed_seconds": 21.929103892995045,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.216732014901936,
+    "geometry_read_seconds": 3.0377255799248815,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:48:58.281003Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC153_AoA_22/boundary_geo_LHC153_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC153_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624508000000000,
+    "extracted_vtu_size_bytes": 21465089017,
+    "geometry_sha256": "6a1e94ea793951391332a5c1f69a643fd6d37ed14db9ec4007bbc54e10894e10",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3810839,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1180585,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2504955,
+      "13": 775201,
+      "14": 1374779,
+      "15": 477266,
+      "16": 938346,
+      "17": 364506,
+      "18": 758568,
+      "19": 306871,
+      "20": 678758,
+      "21": 227657,
+      "22": 364326,
+      "23": 121851,
+      "24": 196121,
+      "25": 67154,
+      "26": 91670,
+      "27": 51808,
+      "28": 124992,
+      "29": 53383,
+      "3": 51549,
+      "30": 115319,
+      "31": 49616,
+      "32": 108707,
+      "33": 38793,
+      "34": 66366,
+      "35": 28163,
+      "36": 61999,
+      "37": 22906,
+      "38": 37740,
+      "39": 16002,
+      "4": 119581,
+      "40": 28830,
+      "41": 10549,
+      "42": 14171,
+      "43": 5747,
+      "44": 7692,
+      "45": 3634,
+      "46": 4138,
+      "47": 2501,
+      "48": 3467,
+      "49": 2056,
+      "5": 937539,
+      "50": 2767,
+      "51": 1726,
+      "52": 2491,
+      "53": 1629,
+      "54": 2223,
+      "55": 1605,
+      "56": 2413,
+      "57": 1714,
+      "58": 2266,
+      "59": 1734,
+      "6": 5193482,
+      "60": 2507,
+      "61": 1626,
+      "62": 2257,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2028973,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 303,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6024776,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 55,
+      "88": 72,
+      "89": 59,
+      "9": 1793666,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 52,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51549,
+      "7": 31120094,
+      "9": 119581
+    },
+    "connectivity_max": 139749284,
+    "connectivity_min": 0,
+    "n_cells": 31291224,
+    "n_connectivity_values": 342069897,
+    "n_fan_triangles": 279487449,
+    "n_points": 139749285
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3452032851984904e-11,
+    "float64_area_closure_relative": 1.3707089977306405e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279487449,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936420.7442715834,
+    "surface_area_float64_in2": 1936420.7443363606,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936420.744336334,
+    "zero_area_triangles": 237260,
+    "zero_weight_points": 5458
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC153_AoA_6.json b/surface_dual_areas/cases/geo_LHC153_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..0570c149ddb7090fda0388015f52d40f3fba7807
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC153_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC153_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC153_AoA_6/boundary_dual_area_geo_LHC153_AoA_6.npy",
+    "sha256": "1fa1911731cfb9f7d48c247f2132717a71f63e33965c7105e22ab86dd8fc7f0f",
+    "shape": [
+      133861351
+    ],
+    "size_bytes": 535445532
+  },
+  "runtime": {
+    "accumulation_seconds": 10.264721880899742,
+    "completed_at_utc": "2026-08-07T08:50:27.080050Z",
+    "elapsed_seconds": 24.63255391898565,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9797805468551815,
+    "geometry_read_seconds": 6.677463332889602,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:50:02.447407Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC153_AoA_6/boundary_geo_LHC153_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC153_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624631000000000,
+    "extracted_vtu_size_bytes": 20548459634,
+    "geometry_sha256": "3d5f3fc8701f7e7184b0fc4d742ab27f14d48dbe71e183bb6943e3de20abdfda",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2993403,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 956064,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2227221,
+      "13": 767263,
+      "14": 1591449,
+      "15": 543139,
+      "16": 1000115,
+      "17": 383959,
+      "18": 766508,
+      "19": 309900,
+      "20": 683800,
+      "21": 227968,
+      "22": 363523,
+      "23": 121662,
+      "24": 193968,
+      "25": 66944,
+      "26": 91001,
+      "27": 51654,
+      "28": 124894,
+      "29": 53413,
+      "3": 49983,
+      "30": 115366,
+      "31": 49637,
+      "32": 108724,
+      "33": 38812,
+      "34": 66369,
+      "35": 28170,
+      "36": 62011,
+      "37": 22917,
+      "38": 37749,
+      "39": 16012,
+      "4": 114071,
+      "40": 28835,
+      "41": 10546,
+      "42": 14176,
+      "43": 5758,
+      "44": 7694,
+      "45": 3637,
+      "46": 4141,
+      "47": 2502,
+      "48": 3466,
+      "49": 2057,
+      "5": 926181,
+      "50": 2770,
+      "51": 1727,
+      "52": 2491,
+      "53": 1629,
+      "54": 2225,
+      "55": 1605,
+      "56": 2413,
+      "57": 1714,
+      "58": 2266,
+      "59": 1734,
+      "6": 5150276,
+      "60": 2507,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1935713,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5575863,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1540471,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 49983,
+      "7": 29318564,
+      "9": 114071
+    },
+    "connectivity_max": 133861350,
+    "connectivity_min": 0,
+    "n_cells": 29482618,
+    "n_connectivity_values": 326676817,
+    "n_fan_triangles": 267711581,
+    "n_points": 133861351
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.2961924484732376e-11,
+    "float64_area_closure_relative": 1.0701142770632455e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 267711581,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936421.906394831,
+    "surface_area_float64_in2": 1936421.906458659,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936421.9064586798,
+    "zero_area_triangles": 228601,
+    "zero_weight_points": 4996
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC153_AoA_8.json b/surface_dual_areas/cases/geo_LHC153_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..d55e19667e38055bac748bbb67349e36e8d0f4cb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC153_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC153_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC153_AoA_8/boundary_dual_area_geo_LHC153_AoA_8.npy",
+    "sha256": "4c86e91f24a6d09d3435ce2091b9b0309fbd6f1bd5992b8a9e09ec06b31fdcb8",
+    "shape": [
+      136314083
+    ],
+    "size_bytes": 545256460
+  },
+  "runtime": {
+    "accumulation_seconds": 10.375345340929925,
+    "completed_at_utc": "2026-08-07T08:50:05.197679Z",
+    "elapsed_seconds": 20.10768506792374,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0377434180118144,
+    "geometry_read_seconds": 2.1405448250006884,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:49:45.089912Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC153_AoA_8/boundary_geo_LHC153_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC153_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624564000000000,
+    "extracted_vtu_size_bytes": 20929749113,
+    "geometry_sha256": "a4ec18fb80f263ca62b89c92376c0b69b2c3fd77384b179d4eebdfadfbffe293",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3290055,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1033126,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2381838,
+      "13": 782381,
+      "14": 1519780,
+      "15": 525417,
+      "16": 975787,
+      "17": 377977,
+      "18": 764633,
+      "19": 309099,
+      "20": 682113,
+      "21": 227050,
+      "22": 360246,
+      "23": 120526,
+      "24": 191922,
+      "25": 66320,
+      "26": 90494,
+      "27": 51511,
+      "28": 124792,
+      "29": 53382,
+      "3": 51283,
+      "30": 115347,
+      "31": 49642,
+      "32": 108728,
+      "33": 38810,
+      "34": 66363,
+      "35": 28169,
+      "36": 62006,
+      "37": 22921,
+      "38": 37745,
+      "39": 16012,
+      "4": 117429,
+      "40": 28836,
+      "41": 10546,
+      "42": 14180,
+      "43": 5752,
+      "44": 7695,
+      "45": 3638,
+      "46": 4141,
+      "47": 2502,
+      "48": 3466,
+      "49": 2057,
+      "5": 930459,
+      "50": 2770,
+      "51": 1727,
+      "52": 2491,
+      "53": 1629,
+      "54": 2225,
+      "55": 1605,
+      "56": 2413,
+      "57": 1714,
+      "58": 2266,
+      "59": 1734,
+      "6": 5167451,
+      "60": 2507,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1966839,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5759115,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1620810,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51283,
+      "7": 30045312,
+      "9": 117429
+    },
+    "connectivity_max": 136314082,
+    "connectivity_min": 0,
+    "n_cells": 30214024,
+    "n_connectivity_values": 333045092,
+    "n_fan_triangles": 272617044,
+    "n_points": 136314083
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.221658240390253e-11,
+    "float64_area_closure_relative": 3.390700280248455e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272617044,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936421.2723474577,
+    "surface_area_float64_in2": 1936421.2724098426,
+    "weight_max_in2": 1.1005437673539729,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936421.2724099082,
+    "zero_area_triangles": 232965,
+    "zero_weight_points": 5321
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC154_AoA_10.json b/surface_dual_areas/cases/geo_LHC154_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..215c9c1102ed817479e27a4b4b3fe940bfa44e96
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC154_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC154_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC154_AoA_10/boundary_dual_area_geo_LHC154_AoA_10.npy",
+    "sha256": "9b993e5f0ef39f2a23e7ddba2c5127bf26a6ef5742c8e62f85cd1c92e783b73d",
+    "shape": [
+      138388809
+    ],
+    "size_bytes": 553555364
+  },
+  "runtime": {
+    "accumulation_seconds": 10.611856416100636,
+    "completed_at_utc": "2026-08-07T08:50:52.129694Z",
+    "elapsed_seconds": 21.716576778097078,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.13206749712117,
+    "geometry_read_seconds": 2.712015474913642,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:50:30.413030Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC154_AoA_10/boundary_geo_LHC154_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC154_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624478000000000,
+    "extracted_vtu_size_bytes": 21249808893,
+    "geometry_sha256": "bf5bcabd1b396e5a51ad05ef042519e727bbf50f08c8b0ef6d141ff58ec076e9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3167684,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1099773,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2244196,
+      "13": 820749,
+      "14": 1675322,
+      "15": 537051,
+      "16": 999800,
+      "17": 366817,
+      "18": 748332,
+      "19": 301445,
+      "20": 681529,
+      "21": 226231,
+      "22": 372058,
+      "23": 124537,
+      "24": 213186,
+      "25": 71948,
+      "26": 93385,
+      "27": 52033,
+      "28": 123410,
+      "29": 53033,
+      "3": 54833,
+      "30": 114873,
+      "31": 49701,
+      "32": 109486,
+      "33": 39427,
+      "34": 67357,
+      "35": 28301,
+      "36": 62922,
+      "37": 22971,
+      "38": 38633,
+      "39": 16212,
+      "4": 126493,
+      "40": 29045,
+      "41": 10628,
+      "42": 14055,
+      "43": 5849,
+      "44": 7755,
+      "45": 3596,
+      "46": 4231,
+      "47": 2554,
+      "48": 3604,
+      "49": 2163,
+      "5": 946634,
+      "50": 2935,
+      "51": 1814,
+      "52": 2626,
+      "53": 1716,
+      "54": 2314,
+      "55": 1631,
+      "56": 2501,
+      "57": 1675,
+      "58": 2290,
+      "59": 1689,
+      "6": 5261115,
+      "60": 2445,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1370,
+      "66": 1769,
+      "67": 1096,
+      "68": 1505,
+      "69": 880,
+      "7": 2025134,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 5952767,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 1717115,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54833,
+      "7": 30552710,
+      "9": 126493
+    },
+    "connectivity_max": 138388808,
+    "connectivity_min": 0,
+    "n_cells": 30734036,
+    "n_connectivity_values": 338234572,
+    "n_fan_triangles": 276766500,
+    "n_points": 138388809
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3452337518072675e-11,
+    "float64_area_closure_relative": 8.734291780175633e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276766500,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945966.2459114837,
+    "surface_area_float64_in2": 1945966.2459765808,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945966.2459765978,
+    "zero_area_triangles": 224472,
+    "zero_weight_points": 4850
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC154_AoA_16.json b/surface_dual_areas/cases/geo_LHC154_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..43dcc647d4b1fcac4b4e41ed1f2af4e231de2df2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC154_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC154_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC154_AoA_16/boundary_dual_area_geo_LHC154_AoA_16.npy",
+    "sha256": "37adca5377d0fd1a64d8dc98693a7ef49c8ee47b74fb25a39154b3caf50ddcd7",
+    "shape": [
+      145860847
+    ],
+    "size_bytes": 583443516
+  },
+  "runtime": {
+    "accumulation_seconds": 11.204840967897326,
+    "completed_at_utc": "2026-08-07T08:07:59.258855Z",
+    "elapsed_seconds": 21.683298915158957,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2898546680808067,
+    "geometry_read_seconds": 2.0045699239708483,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:07:37.575467Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC154_AoA_16/boundary_geo_LHC154_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC154_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624373000000000,
+    "extracted_vtu_size_bytes": 22411078842,
+    "geometry_sha256": "055558a2363fbca406b7993796403ea495efc4ec28b5d4abda216453fac4c554",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4211033,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1392568,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2717118,
+      "13": 850836,
+      "14": 1335345,
+      "15": 455556,
+      "16": 914022,
+      "17": 347018,
+      "18": 746016,
+      "19": 300524,
+      "20": 680235,
+      "21": 225554,
+      "22": 369061,
+      "23": 124102,
+      "24": 211668,
+      "25": 71735,
+      "26": 93146,
+      "27": 52021,
+      "28": 123386,
+      "29": 53013,
+      "3": 58700,
+      "30": 114876,
+      "31": 49710,
+      "32": 109469,
+      "33": 39423,
+      "34": 67360,
+      "35": 28299,
+      "36": 62917,
+      "37": 22974,
+      "38": 38634,
+      "39": 16217,
+      "4": 131160,
+      "40": 29040,
+      "41": 10631,
+      "42": 14050,
+      "43": 5846,
+      "44": 7757,
+      "45": 3596,
+      "46": 4231,
+      "47": 2554,
+      "48": 3605,
+      "49": 2162,
+      "5": 942915,
+      "50": 2935,
+      "51": 1814,
+      "52": 2626,
+      "53": 1716,
+      "54": 2314,
+      "55": 1631,
+      "56": 2501,
+      "57": 1675,
+      "58": 2290,
+      "59": 1689,
+      "6": 5222737,
+      "60": 2445,
+      "61": 1664,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1370,
+      "66": 1769,
+      "67": 1096,
+      "68": 1505,
+      "69": 880,
+      "7": 2130123,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6487769,
+      "80": 178,
+      "81": 121,
+      "82": 138,
+      "83": 113,
+      "84": 119,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 69,
+      "89": 58,
+      "9": 2025594,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58700,
+      "7": 32760509,
+      "9": 131160
+    },
+    "connectivity_max": 145860846,
+    "connectivity_min": 0,
+    "n_cells": 32950369,
+    "n_connectivity_values": 357611314,
+    "n_fan_triangles": 291710576,
+    "n_points": 145860847
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.3418508833420576e-11,
+    "float64_area_closure_relative": 3.5894383778516735e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 291710576,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945964.4028109016,
+    "surface_area_float64_in2": 1945964.4028759329,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945964.4028760027,
+    "zero_area_triangles": 235865,
+    "zero_weight_points": 5667
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC155_AoA_10.json b/surface_dual_areas/cases/geo_LHC155_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..a8ea1add0775b52362a8b9fb353796a8d26c26bf
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC155_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC155_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC155_AoA_10/boundary_dual_area_geo_LHC155_AoA_10.npy",
+    "sha256": "394180941ff11589e93e84e07425ff86c53902490d2b4422564f19574852f324",
+    "shape": [
+      148315762
+    ],
+    "size_bytes": 593263176
+  },
+  "runtime": {
+    "accumulation_seconds": 11.723778399871662,
+    "completed_at_utc": "2026-08-07T08:54:12.755719Z",
+    "elapsed_seconds": 22.62403507414274,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.527584526920691,
+    "geometry_read_seconds": 2.4051045840606093,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:53:50.131602Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC155_AoA_10/boundary_geo_LHC155_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC155_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624576000000000,
+    "extracted_vtu_size_bytes": 22791871650,
+    "geometry_sha256": "4e7f61ac3335702109e92f8a76ff65e4c628e78d1f6aa1f9d2d7412fe4a37a93",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4204737,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1332685,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2998900,
+      "13": 856089,
+      "14": 1454793,
+      "15": 479452,
+      "16": 962505,
+      "17": 365882,
+      "18": 746366,
+      "19": 304243,
+      "20": 663159,
+      "21": 220487,
+      "22": 342963,
+      "23": 116948,
+      "24": 193546,
+      "25": 67711,
+      "26": 89797,
+      "27": 51096,
+      "28": 123894,
+      "29": 52525,
+      "3": 59956,
+      "30": 114715,
+      "31": 49130,
+      "32": 108131,
+      "33": 38562,
+      "34": 66229,
+      "35": 27727,
+      "36": 62601,
+      "37": 22943,
+      "38": 39378,
+      "39": 16425,
+      "4": 137233,
+      "40": 30280,
+      "41": 11060,
+      "42": 14444,
+      "43": 5964,
+      "44": 7918,
+      "45": 3744,
+      "46": 4256,
+      "47": 2521,
+      "48": 3585,
+      "49": 2215,
+      "5": 958995,
+      "50": 2911,
+      "51": 1870,
+      "52": 2695,
+      "53": 1762,
+      "54": 2455,
+      "55": 1722,
+      "56": 2552,
+      "57": 1767,
+      "58": 2295,
+      "59": 1700,
+      "6": 5442029,
+      "60": 2473,
+      "61": 1651,
+      "62": 2224,
+      "63": 1601,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2115293,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6681848,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1949135,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59956,
+      "7": 33451800,
+      "9": 137233
+    },
+    "connectivity_max": 148315761,
+    "connectivity_min": 0,
+    "n_cells": 33648989,
+    "n_connectivity_values": 363918370,
+    "n_fan_triangles": 296620392,
+    "n_points": 148315762
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.005651672751501e-11,
+    "float64_area_closure_relative": 6.634882108637898e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296620392,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947600.6522329876,
+    "surface_area_float64_in2": 1947600.6523110017,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947600.652311131,
+    "zero_area_triangles": 242152,
+    "zero_weight_points": 6106
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC155_AoA_14.json b/surface_dual_areas/cases/geo_LHC155_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..2579b0b10bb64b1cd98ecc82c9bdb2da45b8c663
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC155_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC155_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC155_AoA_14/boundary_dual_area_geo_LHC155_AoA_14.npy",
+    "sha256": "904d323c5d88490f39720e35d7cb75d3369e1ff1a2b6eea14ab9b28b2072c791",
+    "shape": [
+      151575710
+    ],
+    "size_bytes": 606302968
+  },
+  "runtime": {
+    "accumulation_seconds": 11.53854434704408,
+    "completed_at_utc": "2026-08-07T08:51:31.409358Z",
+    "elapsed_seconds": 24.601027006981894,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4287321709562093,
+    "geometry_read_seconds": 4.488926202990115,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:51:06.808222Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC155_AoA_14/boundary_geo_LHC155_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC155_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624394000000000,
+    "extracted_vtu_size_bytes": 23298244029,
+    "geometry_sha256": "02d0a748c5885088f993ce903c555d21cd9a77364302a5453cdcf01ec121e884",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4667721,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1465502,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3180001,
+      "13": 874990,
+      "14": 1329725,
+      "15": 451363,
+      "16": 920119,
+      "17": 359171,
+      "18": 746971,
+      "19": 303638,
+      "20": 663273,
+      "21": 219249,
+      "22": 339864,
+      "23": 115588,
+      "24": 191379,
+      "25": 67006,
+      "26": 89364,
+      "27": 50957,
+      "28": 123825,
+      "29": 52518,
+      "3": 60646,
+      "30": 114725,
+      "31": 49131,
+      "32": 108127,
+      "33": 38568,
+      "34": 66228,
+      "35": 27724,
+      "36": 62613,
+      "37": 22946,
+      "38": 39378,
+      "39": 16424,
+      "4": 138540,
+      "40": 30280,
+      "41": 11059,
+      "42": 14442,
+      "43": 5964,
+      "44": 7921,
+      "45": 3743,
+      "46": 4254,
+      "47": 2521,
+      "48": 3586,
+      "49": 2214,
+      "5": 956795,
+      "50": 2911,
+      "51": 1869,
+      "52": 2696,
+      "53": 1763,
+      "54": 2455,
+      "55": 1722,
+      "56": 2552,
+      "57": 1767,
+      "58": 2295,
+      "59": 1700,
+      "6": 5428148,
+      "60": 2473,
+      "61": 1651,
+      "62": 2224,
+      "63": 1601,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2158294,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6882867,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2090735,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60646,
+      "7": 34405806,
+      "9": 138540
+    },
+    "connectivity_max": 151575709,
+    "connectivity_min": 0,
+    "n_cells": 34604992,
+    "n_connectivity_values": 372350272,
+    "n_fan_triangles": 303140288,
+    "n_points": 151575710
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.022449181758186e-11,
+    "float64_area_closure_relative": 7.268485443138014e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 303140288,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947600.1216938882,
+    "surface_area_float64_in2": 1947600.1217722294,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947600.121772371,
+    "zero_area_triangles": 245998,
+    "zero_weight_points": 6344
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC155_AoA_16.json b/surface_dual_areas/cases/geo_LHC155_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..56c8d61d3c57d4d200bfec632a5c11b702183463
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC155_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC155_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC155_AoA_16/boundary_dual_area_geo_LHC155_AoA_16.npy",
+    "sha256": "18dcc1a80b1f11f6a1e325041c238af0f73073ea19d64ece45178e21c650aed5",
+    "shape": [
+      151927066
+    ],
+    "size_bytes": 607708392
+  },
+  "runtime": {
+    "accumulation_seconds": 11.579977330053225,
+    "completed_at_utc": "2026-08-07T08:50:56.012561Z",
+    "elapsed_seconds": 25.59950012108311,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.54982845694758,
+    "geometry_read_seconds": 5.273380500962958,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "10",
+    "slurm_job_id": "5945305",
+    "started_at_utc": "2026-08-07T08:50:30.412976Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC155_AoA_16/boundary_geo_LHC155_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC155_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624719000000000,
+    "extracted_vtu_size_bytes": 23353170142,
+    "geometry_sha256": "89dadb18dff8fb206a34929042b3b26c6ec8438ed3309e6337dc3157fe2792da",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4763945,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1482099,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3193180,
+      "13": 865857,
+      "14": 1280970,
+      "15": 438069,
+      "16": 906962,
+      "17": 355390,
+      "18": 751491,
+      "19": 305655,
+      "20": 667329,
+      "21": 221283,
+      "22": 342275,
+      "23": 116632,
+      "24": 192656,
+      "25": 67553,
+      "26": 89590,
+      "27": 51041,
+      "28": 123835,
+      "29": 52534,
+      "3": 61370,
+      "30": 114716,
+      "31": 49128,
+      "32": 108128,
+      "33": 38569,
+      "34": 66232,
+      "35": 27723,
+      "36": 62616,
+      "37": 22954,
+      "38": 39380,
+      "39": 16426,
+      "4": 139432,
+      "40": 30287,
+      "41": 11058,
+      "42": 14444,
+      "43": 5965,
+      "44": 7921,
+      "45": 3743,
+      "46": 4254,
+      "47": 2521,
+      "48": 3586,
+      "49": 2214,
+      "5": 956710,
+      "50": 2911,
+      "51": 1869,
+      "52": 2696,
+      "53": 1763,
+      "54": 2455,
+      "55": 1722,
+      "56": 2552,
+      "57": 1767,
+      "58": 2295,
+      "59": 1700,
+      "6": 5409089,
+      "60": 2473,
+      "61": 1651,
+      "62": 2224,
+      "63": 1601,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2166944,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6927402,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2115956,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61370,
+      "7": 34521207,
+      "9": 139432
+    },
+    "connectivity_max": 151927065,
+    "connectivity_min": 0,
+    "n_cells": 34722009,
+    "n_connectivity_values": 373287018,
+    "n_fan_triangles": 303843000,
+    "n_points": 151927066
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.943475877675987e-11,
+    "float64_area_closure_relative": 6.850068900218393e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 303843000,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947600.2468260257,
+    "surface_area_float64_in2": 1947600.2469028288,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947600.2469029622,
+    "zero_area_triangles": 246335,
+    "zero_weight_points": 6393
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC155_AoA_20.json b/surface_dual_areas/cases/geo_LHC155_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0ea8d50f04a62730ef27d66db8c27162f0d2861
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC155_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC155_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC155_AoA_20/boundary_dual_area_geo_LHC155_AoA_20.npy",
+    "sha256": "4edccd347cc4d8dbb9ffdaf5cef228c5cdffaa0926606cba98c3e20233432673",
+    "shape": [
+      151351894
+    ],
+    "size_bytes": 605407704
+  },
+  "runtime": {
+    "accumulation_seconds": 11.785278614144772,
+    "completed_at_utc": "2026-08-07T08:08:23.105364Z",
+    "elapsed_seconds": 22.88066391996108,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.416633084183559,
+    "geometry_read_seconds": 2.6099381339736283,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:08:00.224621Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC155_AoA_20/boundary_geo_LHC155_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC155_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624530000000000,
+    "extracted_vtu_size_bytes": 23263699561,
+    "geometry_sha256": "9c120747d1a153029d7ea595a5692f90fe378efeddba3518f312581cef52abc9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4741346,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1471018,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3156019,
+      "13": 855593,
+      "14": 1253289,
+      "15": 434736,
+      "16": 908456,
+      "17": 357760,
+      "18": 757312,
+      "19": 308503,
+      "20": 672179,
+      "21": 223190,
+      "22": 344603,
+      "23": 117513,
+      "24": 193512,
+      "25": 67743,
+      "26": 89684,
+      "27": 51078,
+      "28": 123885,
+      "29": 52540,
+      "3": 62049,
+      "30": 114719,
+      "31": 49131,
+      "32": 108132,
+      "33": 38558,
+      "34": 66228,
+      "35": 27724,
+      "36": 62599,
+      "37": 22946,
+      "38": 39380,
+      "39": 16424,
+      "4": 141127,
+      "40": 30281,
+      "41": 11059,
+      "42": 14444,
+      "43": 5965,
+      "44": 7918,
+      "45": 3744,
+      "46": 4256,
+      "47": 2521,
+      "48": 3585,
+      "49": 2215,
+      "5": 953070,
+      "50": 2911,
+      "51": 1870,
+      "52": 2695,
+      "53": 1762,
+      "54": 2455,
+      "55": 1722,
+      "56": 2552,
+      "57": 1767,
+      "58": 2295,
+      "59": 1700,
+      "6": 5365689,
+      "60": 2473,
+      "61": 1651,
+      "62": 2224,
+      "63": 1601,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2159417,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6899953,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 2110217,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 62049,
+      "7": 34345028,
+      "9": 141127
+    },
+    "connectivity_max": 151351893,
+    "connectivity_min": 0,
+    "n_cells": 34548204,
+    "n_connectivity_values": 371789064,
+    "n_fan_triangles": 302692656,
+    "n_points": 151351894
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.066190961486401e-11,
+    "float64_area_closure_relative": 7.973814199520861e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 302692656,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947600.4259059364,
+    "surface_area_float64_in2": 1947600.4259851296,
+    "weight_max_in2": 1.1007770601127116,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947600.4259852848,
+    "zero_area_triangles": 245883,
+    "zero_weight_points": 6393
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC158_AoA_16.json b/surface_dual_areas/cases/geo_LHC158_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..7e114ca902b1310e279efce61eca7739434d726b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC158_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC158_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC158_AoA_16/boundary_dual_area_geo_LHC158_AoA_16.npy",
+    "sha256": "dae3bad22e65e4c4ea417ac3208c11c852a08f2697b69b4d9972d6cc723b0b1b",
+    "shape": [
+      142531556
+    ],
+    "size_bytes": 570126352
+  },
+  "runtime": {
+    "accumulation_seconds": 10.977300942875445,
+    "completed_at_utc": "2026-08-07T08:10:25.131883Z",
+    "elapsed_seconds": 22.47082807100378,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2624908050056547,
+    "geometry_read_seconds": 2.1066894738469273,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T08:10:02.660971Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC158_AoA_16/boundary_geo_LHC158_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC158_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624675000000000,
+    "extracted_vtu_size_bytes": 21898306999,
+    "geometry_sha256": "32d5d6afc1745c5d8386238ff90b8c4d5089a4322fcbf115ad9d1269a1e101c5",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4108947,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1280575,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2764477,
+      "13": 803921,
+      "14": 1270868,
+      "15": 447633,
+      "16": 888257,
+      "17": 347201,
+      "18": 733597,
+      "19": 297328,
+      "20": 656312,
+      "21": 222629,
+      "22": 361041,
+      "23": 123817,
+      "24": 210791,
+      "25": 70408,
+      "26": 96411,
+      "27": 52241,
+      "28": 124735,
+      "29": 52991,
+      "3": 53246,
+      "30": 114460,
+      "31": 48966,
+      "32": 108378,
+      "33": 38409,
+      "34": 66302,
+      "35": 27639,
+      "36": 63084,
+      "37": 23035,
+      "38": 39662,
+      "39": 16472,
+      "4": 123361,
+      "40": 30183,
+      "41": 10985,
+      "42": 14517,
+      "43": 5932,
+      "44": 7690,
+      "45": 3708,
+      "46": 4249,
+      "47": 2489,
+      "48": 3557,
+      "49": 2130,
+      "5": 946521,
+      "50": 2970,
+      "51": 1864,
+      "52": 2797,
+      "53": 1798,
+      "54": 2428,
+      "55": 1738,
+      "56": 2570,
+      "57": 1751,
+      "58": 2290,
+      "59": 1720,
+      "6": 5258286,
+      "60": 2507,
+      "61": 1656,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 2062258,
+      "70": 1022,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6235618,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1878543,
+      "90": 59,
+      "91": 56,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53246,
+      "7": 31972291,
+      "9": 123361
+    },
+    "connectivity_max": 142531555,
+    "connectivity_min": 0,
+    "n_cells": 32148898,
+    "n_connectivity_values": 349349790,
+    "n_fan_triangles": 285051994,
+    "n_points": 142531556
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.70068265218365e-11,
+    "float64_area_closure_relative": 1.2127126328905018e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285051994,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939115.2009458684,
+    "surface_area_float64_in2": 1939115.201017629,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939115.2010176054,
+    "zero_area_triangles": 240275,
+    "zero_weight_points": 5611
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC158_AoA_8.json b/surface_dual_areas/cases/geo_LHC158_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a15d8f9ed2fcefdfeaab15800c83fc12dbcdb9d
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC158_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC158_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC158_AoA_8/boundary_dual_area_geo_LHC158_AoA_8.npy",
+    "sha256": "b8ead555706cfdb98e02ad2655349886f09f0502664ec71fe0a089285dd80703",
+    "shape": [
+      141349011
+    ],
+    "size_bytes": 565396172
+  },
+  "runtime": {
+    "accumulation_seconds": 10.835744430078194,
+    "completed_at_utc": "2026-08-07T08:09:41.530345Z",
+    "elapsed_seconds": 22.025076476158574,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1948634090367705,
+    "geometry_read_seconds": 3.1507617151364684,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:09:19.505177Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC158_AoA_8/boundary_geo_LHC158_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC158_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624717000000000,
+    "extracted_vtu_size_bytes": 21712869839,
+    "geometry_sha256": "4d41bb738d8f2d41640f8e74e33ed0f6e5136bd9f716c9b5a2af0d91c2c96210",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3805925,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1202645,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2695461,
+      "13": 809537,
+      "14": 1438928,
+      "15": 483943,
+      "16": 957348,
+      "17": 363047,
+      "18": 740902,
+      "19": 298903,
+      "20": 653003,
+      "21": 219117,
+      "22": 344357,
+      "23": 119138,
+      "24": 196182,
+      "25": 67503,
+      "26": 93753,
+      "27": 51467,
+      "28": 124411,
+      "29": 52916,
+      "3": 52686,
+      "30": 114433,
+      "31": 48957,
+      "32": 108383,
+      "33": 38409,
+      "34": 66299,
+      "35": 27641,
+      "36": 63085,
+      "37": 23035,
+      "38": 39661,
+      "39": 16471,
+      "4": 120738,
+      "40": 30185,
+      "41": 10983,
+      "42": 14514,
+      "43": 5933,
+      "44": 7691,
+      "45": 3710,
+      "46": 4252,
+      "47": 2489,
+      "48": 3555,
+      "49": 2129,
+      "5": 946530,
+      "50": 2970,
+      "51": 1864,
+      "52": 2798,
+      "53": 1798,
+      "54": 2426,
+      "55": 1738,
+      "56": 2570,
+      "57": 1751,
+      "58": 2290,
+      "59": 1720,
+      "6": 5274866,
+      "60": 2507,
+      "61": 1656,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 2037552,
+      "70": 1022,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6111624,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1792744,
+      "90": 59,
+      "91": 56,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52686,
+      "7": 31558654,
+      "9": 120738
+    },
+    "connectivity_max": 141349010,
+    "connectivity_min": 0,
+    "n_cells": 31732078,
+    "n_connectivity_values": 346151060,
+    "n_fan_triangles": 282686904,
+    "n_points": 141349011
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.675841422867127e-11,
+    "float64_area_closure_relative": 3.482047470541147e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282686904,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1939114.4787192338,
+    "surface_area_float64_in2": 1939114.4787905125,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1939114.4787905193,
+    "zero_area_triangles": 238780,
+    "zero_weight_points": 5535
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC159_AoA_10.json b/surface_dual_areas/cases/geo_LHC159_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..3df5870e871871924e5773221feca940fbf48182
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC159_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC159_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC159_AoA_10/boundary_dual_area_geo_LHC159_AoA_10.npy",
+    "sha256": "0180467ba636ba737e5b46c3b3bf066ccc38e90f406c1c08dd3e978c793f1e13",
+    "shape": [
+      145386070
+    ],
+    "size_bytes": 581544408
+  },
+  "runtime": {
+    "accumulation_seconds": 11.701593000907451,
+    "completed_at_utc": "2026-08-07T08:55:57.855138Z",
+    "elapsed_seconds": 22.524175650905818,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2711226819083095,
+    "geometry_read_seconds": 2.188229674939066,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:55:35.330856Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC159_AoA_10/boundary_geo_LHC159_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC159_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624472000000000,
+    "extracted_vtu_size_bytes": 22337012298,
+    "geometry_sha256": "befc03272f8e928ca3ac019f68ab3e55febda4db8d1673b07bd5c7fbcc4b65ac",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3941467,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1275609,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2808975,
+      "13": 850707,
+      "14": 1494539,
+      "15": 490137,
+      "16": 967121,
+      "17": 360598,
+      "18": 734904,
+      "19": 294838,
+      "20": 656760,
+      "21": 219525,
+      "22": 354779,
+      "23": 121070,
+      "24": 209000,
+      "25": 72112,
+      "26": 94470,
+      "27": 52654,
+      "28": 124262,
+      "29": 53184,
+      "3": 58400,
+      "30": 114309,
+      "31": 49148,
+      "32": 107785,
+      "33": 38722,
+      "34": 65946,
+      "35": 27944,
+      "36": 62343,
+      "37": 23010,
+      "38": 38872,
+      "39": 16393,
+      "4": 130945,
+      "40": 29618,
+      "41": 10691,
+      "42": 14282,
+      "43": 5854,
+      "44": 7734,
+      "45": 3626,
+      "46": 4280,
+      "47": 2549,
+      "48": 3510,
+      "49": 2144,
+      "5": 960900,
+      "50": 2911,
+      "51": 1873,
+      "52": 2738,
+      "53": 1761,
+      "54": 2487,
+      "55": 1716,
+      "56": 2610,
+      "57": 1730,
+      "58": 2320,
+      "59": 1708,
+      "6": 5360317,
+      "60": 2445,
+      "61": 1667,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2087726,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6465037,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1884865,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58400,
+      "7": 32609044,
+      "9": 130945
+    },
+    "connectivity_max": 145386069,
+    "connectivity_min": 0,
+    "n_cells": 32798389,
+    "n_connectivity_values": 356357794,
+    "n_fan_triangles": 290761016,
+    "n_points": 145386070
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.9196804559750914e-11,
+    "float64_area_closure_relative": 4.749938084810743e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 290761016,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945999.3767807272,
+    "surface_area_float64_in2": 1945999.3768375441,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945999.3768376366,
+    "zero_area_triangles": 236269,
+    "zero_weight_points": 5720
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC159_AoA_20.json b/surface_dual_areas/cases/geo_LHC159_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..a6ab28fb39953652f2ded4fb354856dd68337d74
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC159_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC159_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC159_AoA_20/boundary_dual_area_geo_LHC159_AoA_20.npy",
+    "sha256": "ee3e17cc9309220e275d2f6594a7de8bf5449840cf430b2ca286bd0b04d0d5f4",
+    "shape": [
+      147477327
+    ],
+    "size_bytes": 589909436
+  },
+  "runtime": {
+    "accumulation_seconds": 11.216808581957594,
+    "completed_at_utc": "2026-08-07T08:11:03.350007Z",
+    "elapsed_seconds": 23.847809755941853,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3294263621792197,
+    "geometry_read_seconds": 3.0966224200092256,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T08:10:39.502076Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC159_AoA_20/boundary_geo_LHC159_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC159_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624437000000000,
+    "extracted_vtu_size_bytes": 22663604084,
+    "geometry_sha256": "e793d21b93b2ed97640c32486277fb4a3b4c2b74d671897a399cbf2ef535dcd4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4396704,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1407010,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2896468,
+      "13": 842320,
+      "14": 1231969,
+      "15": 440992,
+      "16": 888238,
+      "17": 348049,
+      "18": 743055,
+      "19": 297661,
+      "20": 670635,
+      "21": 222571,
+      "22": 375587,
+      "23": 123343,
+      "24": 222362,
+      "25": 73478,
+      "26": 96230,
+      "27": 52985,
+      "28": 124313,
+      "29": 53193,
+      "3": 59988,
+      "30": 114317,
+      "31": 49150,
+      "32": 107793,
+      "33": 38723,
+      "34": 65950,
+      "35": 27935,
+      "36": 62341,
+      "37": 23009,
+      "38": 38869,
+      "39": 16393,
+      "4": 135069,
+      "40": 29614,
+      "41": 10687,
+      "42": 14286,
+      "43": 5855,
+      "44": 7732,
+      "45": 3625,
+      "46": 4280,
+      "47": 2552,
+      "48": 3510,
+      "49": 2143,
+      "5": 956095,
+      "50": 2911,
+      "51": 1873,
+      "52": 2738,
+      "53": 1761,
+      "54": 2487,
+      "55": 1716,
+      "56": 2610,
+      "57": 1730,
+      "58": 2320,
+      "59": 1708,
+      "6": 5301904,
+      "60": 2445,
+      "61": 1667,
+      "62": 2198,
+      "63": 1587,
+      "64": 2148,
+      "65": 1369,
+      "66": 1770,
+      "67": 1095,
+      "68": 1505,
+      "69": 880,
+      "7": 2133043,
+      "70": 1008,
+      "71": 541,
+      "72": 692,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6679291,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2035774,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59988,
+      "7": 33286762,
+      "9": 135069
+    },
+    "connectivity_max": 147477326,
+    "connectivity_min": 0,
+    "n_cells": 33481819,
+    "n_connectivity_values": 361907168,
+    "n_fan_triangles": 294943530,
+    "n_points": 147477327
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.960874269442567e-11,
+    "float64_area_closure_relative": 2.668101030774205e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294943530,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945999.5305428738,
+    "surface_area_float64_in2": 1945999.5306004924,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945999.5306005443,
+    "zero_area_triangles": 240425,
+    "zero_weight_points": 5968
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC160_AoA_4.json b/surface_dual_areas/cases/geo_LHC160_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..1ec019e69e91191003dbcd06aceef5ef9b0b0f13
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC160_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC160_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC160_AoA_4/boundary_dual_area_geo_LHC160_AoA_4.npy",
+    "sha256": "bbdb5cf7aef20457ab6466ac5eca739a3a71bad514d5cfe064455b74c0176308",
+    "shape": [
+      135256029
+    ],
+    "size_bytes": 541024244
+  },
+  "runtime": {
+    "accumulation_seconds": 10.538103739963844,
+    "completed_at_utc": "2026-08-07T08:52:15.240951Z",
+    "elapsed_seconds": 21.209956214996055,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3004616380203515,
+    "geometry_read_seconds": 2.2319358189124614,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:51:54.030855Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC160_AoA_4/boundary_geo_LHC160_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC160_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624468000000000,
+    "extracted_vtu_size_bytes": 20759829802,
+    "geometry_sha256": "231bf03c4d7d54294e58e03a7e5079dbce399730eb8c61e066f57ab1d7903d56",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2776144,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 927884,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2182799,
+      "13": 779852,
+      "14": 1758779,
+      "15": 566584,
+      "16": 1070997,
+      "17": 389196,
+      "18": 765962,
+      "19": 308936,
+      "20": 685793,
+      "21": 230281,
+      "22": 375657,
+      "23": 126493,
+      "24": 209552,
+      "25": 70770,
+      "26": 91546,
+      "27": 51890,
+      "28": 123956,
+      "29": 53095,
+      "3": 56795,
+      "30": 115514,
+      "31": 49515,
+      "32": 109131,
+      "33": 38780,
+      "34": 66505,
+      "35": 28025,
+      "36": 62014,
+      "37": 22803,
+      "38": 37830,
+      "39": 16125,
+      "4": 129255,
+      "40": 28928,
+      "41": 10523,
+      "42": 14227,
+      "43": 5805,
+      "44": 7690,
+      "45": 3634,
+      "46": 4193,
+      "47": 2489,
+      "48": 3521,
+      "49": 2105,
+      "5": 937611,
+      "50": 2817,
+      "51": 1813,
+      "52": 2661,
+      "53": 1691,
+      "54": 2326,
+      "55": 1674,
+      "56": 2466,
+      "57": 1724,
+      "58": 2279,
+      "59": 1735,
+      "6": 5171120,
+      "60": 2509,
+      "61": 1626,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1403,
+      "66": 1790,
+      "67": 1101,
+      "68": 1467,
+      "69": 907,
+      "7": 1945795,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5682207,
+      "80": 183,
+      "81": 120,
+      "82": 143,
+      "83": 117,
+      "84": 116,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 71,
+      "89": 59,
+      "9": 1538376,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 56795,
+      "7": 29494880,
+      "9": 129255
+    },
+    "connectivity_max": 135256028,
+    "connectivity_min": 0,
+    "n_cells": 29680930,
+    "n_connectivity_values": 329862800,
+    "n_fan_triangles": 270500940,
+    "n_points": 135256029
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.6885932173869753e-11,
+    "float64_area_closure_relative": 4.0804613038323263e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 270500940,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1945742.002485546,
+    "surface_area_float64_in2": 1945742.0025378591,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1945742.0025377797,
+    "zero_area_triangles": 225439,
+    "zero_weight_points": 4937
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC161_AoA_12.json b/surface_dual_areas/cases/geo_LHC161_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..18fa2b9c13ddb50b6e14343fb9415b7acb9be81f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC161_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC161_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC161_AoA_12/boundary_dual_area_geo_LHC161_AoA_12.npy",
+    "sha256": "8c02c543d79782042f76f248ae4c6dcb18298b1dcbe1c214ce311bce61cd24a9",
+    "shape": [
+      142525951
+    ],
+    "size_bytes": 570103932
+  },
+  "runtime": {
+    "accumulation_seconds": 11.086496111005545,
+    "completed_at_utc": "2026-08-07T08:52:16.621071Z",
+    "elapsed_seconds": 23.382835223106667,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.409208331955597,
+    "geometry_read_seconds": 2.5473799100145698,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:51:53.238146Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC161_AoA_12/boundary_geo_LHC161_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC161_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624455000000000,
+    "extracted_vtu_size_bytes": 21888926258,
+    "geometry_sha256": "1e73bebf8c1755234988c4b3f248b77961fd74131555b657911c494d4909d281",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3664348,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1194884,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2638380,
+      "13": 849513,
+      "14": 1547015,
+      "15": 532142,
+      "16": 967582,
+      "17": 376246,
+      "18": 748853,
+      "19": 301889,
+      "20": 674798,
+      "21": 223486,
+      "22": 369272,
+      "23": 122840,
+      "24": 206923,
+      "25": 70354,
+      "26": 91623,
+      "27": 51953,
+      "28": 123907,
+      "29": 53145,
+      "3": 57994,
+      "30": 115311,
+      "31": 49664,
+      "32": 108889,
+      "33": 39189,
+      "34": 67875,
+      "35": 28288,
+      "36": 63061,
+      "37": 22820,
+      "38": 37930,
+      "39": 15995,
+      "4": 133386,
+      "40": 28960,
+      "41": 10559,
+      "42": 14183,
+      "43": 5869,
+      "44": 7754,
+      "45": 3617,
+      "46": 4254,
+      "47": 2552,
+      "48": 3458,
+      "49": 2064,
+      "5": 936534,
+      "50": 2731,
+      "51": 1707,
+      "52": 2474,
+      "53": 1615,
+      "54": 2156,
+      "55": 1601,
+      "56": 2462,
+      "57": 1673,
+      "58": 2280,
+      "59": 1681,
+      "6": 5189907,
+      "60": 2442,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2011714,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6212765,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1779856,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57994,
+      "7": 31615469,
+      "9": 133386
+    },
+    "connectivity_max": 142525950,
+    "connectivity_min": 0,
+    "n_cells": 31806849,
+    "n_connectivity_values": 348654485,
+    "n_fan_triangles": 285040787,
+    "n_points": 142525951
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.62733634829019e-11,
+    "float64_area_closure_relative": 4.06716772937498e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 285040787,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946377.0394052034,
+    "surface_area_float64_in2": 1946377.0394952688,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946377.0394952768,
+    "zero_area_triangles": 248147,
+    "zero_weight_points": 5728
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC161_AoA_20.json b/surface_dual_areas/cases/geo_LHC161_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f8b1e87ad3b191fe0d47becab455c130773535f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC161_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC161_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC161_AoA_20/boundary_dual_area_geo_LHC161_AoA_20.npy",
+    "sha256": "0d9855938e1cbca580c3bbd468dd8300786310190711369afc72e064a357fc80",
+    "shape": [
+      148603209
+    ],
+    "size_bytes": 594412964
+  },
+  "runtime": {
+    "accumulation_seconds": 11.3293915130198,
+    "completed_at_utc": "2026-08-07T08:11:04.946350Z",
+    "elapsed_seconds": 25.44423194997944,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.396430282155052,
+    "geometry_read_seconds": 3.650046753929928,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:10:39.502038Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC161_AoA_20/boundary_geo_LHC161_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC161_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624647000000000,
+    "extracted_vtu_size_bytes": 22833297167,
+    "geometry_sha256": "e1bd299199a1d43cfc7495745ff58c6d6f9e71d74187abdc7e9b85cbae4614e7",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4463902,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1445454,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2950196,
+      "13": 885511,
+      "14": 1366309,
+      "15": 475511,
+      "16": 903490,
+      "17": 356120,
+      "18": 741717,
+      "19": 298533,
+      "20": 670017,
+      "21": 221441,
+      "22": 363572,
+      "23": 121330,
+      "24": 203774,
+      "25": 69712,
+      "26": 91070,
+      "27": 51831,
+      "28": 123856,
+      "29": 53129,
+      "3": 60736,
+      "30": 115282,
+      "31": 49675,
+      "32": 108901,
+      "33": 39180,
+      "34": 67887,
+      "35": 28286,
+      "36": 63049,
+      "37": 22825,
+      "38": 37925,
+      "39": 15999,
+      "4": 136095,
+      "40": 28968,
+      "41": 10555,
+      "42": 14181,
+      "43": 5866,
+      "44": 7752,
+      "45": 3615,
+      "46": 4254,
+      "47": 2553,
+      "48": 3459,
+      "49": 2061,
+      "5": 937302,
+      "50": 2731,
+      "51": 1708,
+      "52": 2473,
+      "53": 1613,
+      "54": 2156,
+      "55": 1603,
+      "56": 2462,
+      "57": 1673,
+      "58": 2280,
+      "59": 1681,
+      "6": 5194964,
+      "60": 2442,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2103760,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6594320,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2045145,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60736,
+      "7": 33407487,
+      "9": 136095
+    },
+    "connectivity_max": 148603208,
+    "connectivity_min": 0,
+    "n_cells": 33604318,
+    "n_connectivity_values": 364403939,
+    "n_fan_triangles": 297195303,
+    "n_points": 148603209
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.6826167251161566e-11,
+    "float64_area_closure_relative": 5.119849478092204e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 297195303,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946375.8828379225,
+    "surface_area_float64_in2": 1946375.8829290639,
+    "weight_max_in2": 1.1001539559263787,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946375.8829289642,
+    "zero_area_triangles": 254901,
+    "zero_weight_points": 6157
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC162_AoA_16.json b/surface_dual_areas/cases/geo_LHC162_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..faaae7bf7d32e4cbf25276cfec3d2c8da01d6a49
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC162_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC162_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC162_AoA_16/boundary_dual_area_geo_LHC162_AoA_16.npy",
+    "sha256": "1b50709af8490a24f661860c0c175fbcd52cc98aaeab89d38ceb743da6962a9e",
+    "shape": [
+      139799714
+    ],
+    "size_bytes": 559198984
+  },
+  "runtime": {
+    "accumulation_seconds": 11.344993208069354,
+    "completed_at_utc": "2026-08-07T08:52:51.687916Z",
+    "elapsed_seconds": 22.50170977297239,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.6044387770816684,
+    "geometry_read_seconds": 2.6909121519420296,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:52:29.186069Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC162_AoA_16/boundary_geo_LHC162_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC162_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624564000000000,
+    "extracted_vtu_size_bytes": 21472617643,
+    "geometry_sha256": "24f2de0e58da1dbad568c5e43f7223b2a6673494fc1fc695941d4d9331fb46e4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3994546,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1178467,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2612509,
+      "13": 768641,
+      "14": 1308481,
+      "15": 459289,
+      "16": 907036,
+      "17": 357581,
+      "18": 759858,
+      "19": 309545,
+      "20": 680244,
+      "21": 227574,
+      "22": 356355,
+      "23": 122083,
+      "24": 194964,
+      "25": 67685,
+      "26": 92384,
+      "27": 51642,
+      "28": 124153,
+      "29": 53350,
+      "3": 52621,
+      "30": 115701,
+      "31": 49647,
+      "32": 108868,
+      "33": 39069,
+      "34": 66712,
+      "35": 28206,
+      "36": 62925,
+      "37": 22861,
+      "38": 38094,
+      "39": 15859,
+      "4": 118328,
+      "40": 28989,
+      "41": 10521,
+      "42": 13985,
+      "43": 5766,
+      "44": 7835,
+      "45": 3708,
+      "46": 4310,
+      "47": 2515,
+      "48": 3571,
+      "49": 2181,
+      "5": 924654,
+      "50": 2794,
+      "51": 1733,
+      "52": 2464,
+      "53": 1618,
+      "54": 2168,
+      "55": 1610,
+      "56": 2418,
+      "57": 1715,
+      "58": 2245,
+      "59": 1681,
+      "6": 5147026,
+      "60": 2464,
+      "61": 1650,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1992701,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5985368,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1771823,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52621,
+      "7": 31122881,
+      "9": 118328
+    },
+    "connectivity_max": 139799713,
+    "connectivity_min": 0,
+    "n_cells": 31293830,
+    "n_connectivity_values": 342175965,
+    "n_fan_triangles": 279588305,
+    "n_points": 139799714
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1178202794906925e-11,
+    "float64_area_closure_relative": 3.8508693650231456e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 279588305,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1934778.8487358233,
+    "surface_area_float64_in2": 1934778.8487961462,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1934778.8487962207,
+    "zero_area_triangles": 239991,
+    "zero_weight_points": 5588
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC163_AoA_16.json b/surface_dual_areas/cases/geo_LHC163_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..7d8da5fc7f0a5d2a28c19137b0f17b38564c1b27
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC163_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC163_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC163_AoA_16/boundary_dual_area_geo_LHC163_AoA_16.npy",
+    "sha256": "59fc015f4dfb762464bf3123f657012342e7079a9f271a5faa8998f384f678be",
+    "shape": [
+      142146332
+    ],
+    "size_bytes": 568585456
+  },
+  "runtime": {
+    "accumulation_seconds": 11.430600818945095,
+    "completed_at_utc": "2026-08-07T08:54:57.332038Z",
+    "elapsed_seconds": 22.901156093925238,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.409069702960551,
+    "geometry_read_seconds": 2.7511638989672065,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:54:34.430765Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC163_AoA_16/boundary_geo_LHC163_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC163_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624502000000000,
+    "extracted_vtu_size_bytes": 21837605066,
+    "geometry_sha256": "b306aa26862c3cb183d1c3e8dd044a74482bcb366759968e49c1218aa18956af",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4090645,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1228366,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2744570,
+      "13": 771688,
+      "14": 1295152,
+      "15": 445349,
+      "16": 896238,
+      "17": 350456,
+      "18": 741440,
+      "19": 298111,
+      "20": 665512,
+      "21": 223934,
+      "22": 364331,
+      "23": 123844,
+      "24": 210716,
+      "25": 71571,
+      "26": 95296,
+      "27": 52663,
+      "28": 124557,
+      "29": 53136,
+      "3": 54800,
+      "30": 115166,
+      "31": 49447,
+      "32": 108835,
+      "33": 38755,
+      "34": 65657,
+      "35": 27826,
+      "36": 62205,
+      "37": 23052,
+      "38": 39353,
+      "39": 16499,
+      "4": 120914,
+      "40": 29739,
+      "41": 10876,
+      "42": 14470,
+      "43": 5904,
+      "44": 7679,
+      "45": 3570,
+      "46": 4143,
+      "47": 2482,
+      "48": 3511,
+      "49": 2103,
+      "5": 926864,
+      "50": 2917,
+      "51": 1835,
+      "52": 2801,
+      "53": 1770,
+      "54": 2526,
+      "55": 1718,
+      "56": 2570,
+      "57": 1767,
+      "58": 2290,
+      "59": 1750,
+      "6": 5242113,
+      "60": 2510,
+      "61": 1626,
+      "62": 2259,
+      "63": 1602,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2041158,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6235863,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1855782,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 54800,
+      "7": 31825635,
+      "9": 120914
+    },
+    "connectivity_max": 142146331,
+    "connectivity_min": 0,
+    "n_cells": 32001349,
+    "n_connectivity_values": 348284237,
+    "n_fan_triangles": 284281539,
+    "n_points": 142146332
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.763150405513164e-11,
+    "float64_area_closure_relative": 4.5597799633782054e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284281539,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940348.9926209513,
+    "surface_area_float64_in2": 1940348.9926939695,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940348.992694058,
+    "zero_area_triangles": 238040,
+    "zero_weight_points": 5821
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC163_AoA_18.json b/surface_dual_areas/cases/geo_LHC163_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..7cb88bb9366f90828fa6994e14d68d07090b87da
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC163_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC163_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC163_AoA_18/boundary_dual_area_geo_LHC163_AoA_18.npy",
+    "sha256": "5aa7f5c014ca4e198a553ce21bf6b7edde7ce04cea277e89160df00c057505d5",
+    "shape": [
+      142106691
+    ],
+    "size_bytes": 568426892
+  },
+  "runtime": {
+    "accumulation_seconds": 12.906493915012106,
+    "completed_at_utc": "2026-08-07T08:59:31.604475Z",
+    "elapsed_seconds": 22.85660462686792,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.15084594883956,
+    "geometry_read_seconds": 2.0169315019156784,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T08:59:08.747784Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC163_AoA_18/boundary_geo_LHC163_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC163_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624610000000000,
+    "extracted_vtu_size_bytes": 21831648048,
+    "geometry_sha256": "ab234a3af9550c09feeda5d603fbf45360147754bc9f62f837a02c00b505a425",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4142317,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1247619,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2743259,
+      "13": 775227,
+      "14": 1228998,
+      "15": 436361,
+      "16": 882370,
+      "17": 347330,
+      "18": 748547,
+      "19": 299170,
+      "20": 673946,
+      "21": 225049,
+      "22": 370413,
+      "23": 124131,
+      "24": 212339,
+      "25": 71751,
+      "26": 95199,
+      "27": 52667,
+      "28": 124488,
+      "29": 53119,
+      "3": 55228,
+      "30": 115159,
+      "31": 49453,
+      "32": 108837,
+      "33": 38754,
+      "34": 65654,
+      "35": 27827,
+      "36": 62205,
+      "37": 23052,
+      "38": 39354,
+      "39": 16500,
+      "4": 121751,
+      "40": 29738,
+      "41": 10877,
+      "42": 14470,
+      "43": 5904,
+      "44": 7679,
+      "45": 3570,
+      "46": 4143,
+      "47": 2482,
+      "48": 3511,
+      "49": 2103,
+      "5": 926426,
+      "50": 2917,
+      "51": 1835,
+      "52": 2801,
+      "53": 1770,
+      "54": 2526,
+      "55": 1718,
+      "56": 2570,
+      "57": 1767,
+      "58": 2290,
+      "59": 1750,
+      "6": 5220009,
+      "60": 2510,
+      "61": 1626,
+      "62": 2258,
+      "63": 1602,
+      "64": 2166,
+      "65": 1403,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2042725,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 303,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6229447,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 55,
+      "88": 72,
+      "89": 59,
+      "9": 1871578,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 52,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 55228,
+      "7": 31820764,
+      "9": 121751
+    },
+    "connectivity_max": 142106690,
+    "connectivity_min": 0,
+    "n_cells": 31997743,
+    "n_connectivity_values": 348197743,
+    "n_fan_triangles": 284202257,
+    "n_points": 142106691
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.739198948260284e-11,
+    "float64_area_closure_relative": 4.871764109537973e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284202257,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940349.3107325628,
+    "surface_area_float64_in2": 1940349.3108051163,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940349.3108052108,
+    "zero_area_triangles": 238079,
+    "zero_weight_points": 5855
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC163_AoA_4.json b/surface_dual_areas/cases/geo_LHC163_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..80cc30196288523857ce9f1137292a35690fb635
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC163_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC163_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC163_AoA_4/boundary_dual_area_geo_LHC163_AoA_4.npy",
+    "sha256": "ef136a4aeb1ad938dcea7d49918ed95ef338dccbd932d97851c34d21f0b48658",
+    "shape": [
+      132342614
+    ],
+    "size_bytes": 529370584
+  },
+  "runtime": {
+    "accumulation_seconds": 10.154369219904765,
+    "completed_at_utc": "2026-08-07T08:11:44.511699Z",
+    "elapsed_seconds": 37.76434952695854,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1263963459059596,
+    "geometry_read_seconds": 19.649292648071423,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:11:06.747269Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC163_AoA_4/boundary_geo_LHC163_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC163_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624550000000000,
+    "extracted_vtu_size_bytes": 20313414334,
+    "geometry_sha256": "2a6d12b8110f3438a4216bc31c6dc51d151844daaa73c9a3921b482af7144b63",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2622670,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 862378,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1980248,
+      "13": 729967,
+      "14": 1815016,
+      "15": 555328,
+      "16": 1098607,
+      "17": 384380,
+      "18": 753061,
+      "19": 300561,
+      "20": 662410,
+      "21": 223153,
+      "22": 352034,
+      "23": 122617,
+      "24": 201285,
+      "25": 70918,
+      "26": 94532,
+      "27": 52626,
+      "28": 124681,
+      "29": 53188,
+      "3": 49245,
+      "30": 115170,
+      "31": 49448,
+      "32": 108839,
+      "33": 38755,
+      "34": 65654,
+      "35": 27828,
+      "36": 62204,
+      "37": 23051,
+      "38": 39354,
+      "39": 16498,
+      "4": 113839,
+      "40": 29739,
+      "41": 10878,
+      "42": 14470,
+      "43": 5903,
+      "44": 7679,
+      "45": 3569,
+      "46": 4144,
+      "47": 2482,
+      "48": 3511,
+      "49": 2103,
+      "5": 925369,
+      "50": 2917,
+      "51": 1835,
+      "52": 2801,
+      "53": 1770,
+      "54": 2526,
+      "55": 1718,
+      "56": 2570,
+      "57": 1767,
+      "58": 2290,
+      "59": 1750,
+      "6": 5285073,
+      "60": 2510,
+      "61": 1626,
+      "62": 2259,
+      "63": 1602,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1916545,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5564899,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1480813,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 49245,
+      "7": 28908646,
+      "9": 113839
+    },
+    "connectivity_max": 132342613,
+    "connectivity_min": 0,
+    "n_cells": 29071730,
+    "n_connectivity_values": 322817564,
+    "n_fan_triangles": 264674104,
+    "n_points": 132342614
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.762653963126073e-11,
+    "float64_area_closure_relative": 5.159744886769178e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 264674104,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940351.2957417972,
+    "surface_area_float64_in2": 1940351.295814806,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940351.295814796,
+    "zero_area_triangles": 218149,
+    "zero_weight_points": 4628
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC164_AoA_18.json b/surface_dual_areas/cases/geo_LHC164_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..473b13ce9f50005c3d2134992999e35a16fd7dd4
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC164_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC164_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC164_AoA_18/boundary_dual_area_geo_LHC164_AoA_18.npy",
+    "sha256": "73c9d27ea2cf4ceb569d4e757b6f111aade0b752ab903909266afdbd9b928b90",
+    "shape": [
+      150618523
+    ],
+    "size_bytes": 602474220
+  },
+  "runtime": {
+    "accumulation_seconds": 11.537923641037196,
+    "completed_at_utc": "2026-08-07T08:56:00.043573Z",
+    "elapsed_seconds": 62.15222092601471,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4349478220101446,
+    "geometry_read_seconds": 41.99897996685468,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:54:57.891244Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC164_AoA_18/boundary_geo_LHC164_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC164_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624723000000000,
+    "extracted_vtu_size_bytes": 23150368129,
+    "geometry_sha256": "b50d78f1d7a91cffe0ea0aa47c7056ae241fbb5efe70130b401d54b288aef7b8",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4653379,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1516852,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2996605,
+      "13": 881183,
+      "14": 1281772,
+      "15": 445724,
+      "16": 891973,
+      "17": 350338,
+      "18": 739280,
+      "19": 299638,
+      "20": 666324,
+      "21": 220772,
+      "22": 355158,
+      "23": 119951,
+      "24": 205825,
+      "25": 70661,
+      "26": 92883,
+      "27": 52092,
+      "28": 123895,
+      "29": 52898,
+      "3": 61093,
+      "30": 114658,
+      "31": 49272,
+      "32": 108305,
+      "33": 38685,
+      "34": 66280,
+      "35": 27957,
+      "36": 62095,
+      "37": 23028,
+      "38": 39059,
+      "39": 16510,
+      "4": 138275,
+      "40": 30017,
+      "41": 10945,
+      "42": 14421,
+      "43": 5935,
+      "44": 7761,
+      "45": 3649,
+      "46": 4192,
+      "47": 2508,
+      "48": 3507,
+      "49": 2123,
+      "5": 959369,
+      "50": 2922,
+      "51": 1845,
+      "52": 2784,
+      "53": 1782,
+      "54": 2507,
+      "55": 1723,
+      "56": 2523,
+      "57": 1752,
+      "58": 2295,
+      "59": 1752,
+      "6": 5335739,
+      "60": 2510,
+      "61": 1625,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2180198,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6834166,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2154607,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 61093,
+      "7": 34157136,
+      "9": 138275
+    },
+    "connectivity_max": 150618522,
+    "connectivity_min": 0,
+    "n_cells": 34356504,
+    "n_connectivity_values": 369938919,
+    "n_fan_triangles": 301225911,
+    "n_points": 150618523
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.901902068262138e-11,
+    "float64_area_closure_relative": 1.4107697051602882e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 301225911,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1947448.6763920889,
+    "surface_area_float64_in2": 1947448.6764680764,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1947448.676468104,
+    "zero_area_triangles": 242133,
+    "zero_weight_points": 6166
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC165_AoA_16.json b/surface_dual_areas/cases/geo_LHC165_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..95f8404c9e985b62694aaceff08fb0e14d7c7742
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC165_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC165_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC165_AoA_16/boundary_dual_area_geo_LHC165_AoA_16.npy",
+    "sha256": "d3b55b4f9fd36ac8cdb491186e98c263f46774b7600cb819f6b99697bdb9da9b",
+    "shape": [
+      141204597
+    ],
+    "size_bytes": 564818516
+  },
+  "runtime": {
+    "accumulation_seconds": 10.885959248058498,
+    "completed_at_utc": "2026-08-07T08:09:54.885863Z",
+    "elapsed_seconds": 21.741545329103246,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0688857298810035,
+    "geometry_read_seconds": 3.150585015071556,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T08:09:33.144228Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC165_AoA_16/boundary_geo_LHC165_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC165_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624589000000000,
+    "extracted_vtu_size_bytes": 21693247327,
+    "geometry_sha256": "6ba1c6936c1ae5b82e2463fbea91f8e2bf1af0a7345284f06b8e60d9c96de273",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4064985,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1216041,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2679857,
+      "13": 765535,
+      "14": 1274607,
+      "15": 447795,
+      "16": 903674,
+      "17": 358581,
+      "18": 747298,
+      "19": 305376,
+      "20": 661425,
+      "21": 225230,
+      "22": 348365,
+      "23": 123312,
+      "24": 203855,
+      "25": 71437,
+      "26": 94905,
+      "27": 52573,
+      "28": 124776,
+      "29": 53138,
+      "3": 53445,
+      "30": 114022,
+      "31": 48996,
+      "32": 106664,
+      "33": 38504,
+      "34": 66519,
+      "35": 27667,
+      "36": 63275,
+      "37": 22868,
+      "38": 39527,
+      "39": 16444,
+      "4": 116174,
+      "40": 30298,
+      "41": 11059,
+      "42": 14490,
+      "43": 5885,
+      "44": 7639,
+      "45": 3706,
+      "46": 4242,
+      "47": 2521,
+      "48": 3516,
+      "49": 2104,
+      "5": 931426,
+      "50": 2927,
+      "51": 1851,
+      "52": 2738,
+      "53": 1796,
+      "54": 2408,
+      "55": 1721,
+      "56": 2564,
+      "57": 1749,
+      "58": 2303,
+      "59": 1723,
+      "6": 5275441,
+      "60": 2507,
+      "61": 1658,
+      "62": 2230,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2024465,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6185313,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1818242,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 53445,
+      "7": 31632491,
+      "9": 116174
+    },
+    "connectivity_max": 141204596,
+    "connectivity_min": 0,
+    "n_cells": 31802110,
+    "n_connectivity_values": 346002291,
+    "n_fan_triangles": 282398071,
+    "n_points": 141204597
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4353149178272297e-11,
+    "float64_area_closure_relative": 1.790396836425716e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282398071,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937657.9089858201,
+    "surface_area_float64_in2": 1937657.9090523848,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937657.90905235,
+    "zero_area_triangles": 238447,
+    "zero_weight_points": 5603
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC166_AoA_10.json b/surface_dual_areas/cases/geo_LHC166_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..ab446198b7633d4d1b234e13d2e078bde574885b
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC166_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC166_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC166_AoA_10/boundary_dual_area_geo_LHC166_AoA_10.npy",
+    "sha256": "d0999e9cf135dcb5876b0e6dafa7c622430a2f1438fa0e6bd8176120da929981",
+    "shape": [
+      141874640
+    ],
+    "size_bytes": 567498688
+  },
+  "runtime": {
+    "accumulation_seconds": 10.9888124759309,
+    "completed_at_utc": "2026-08-07T08:57:31.787041Z",
+    "elapsed_seconds": 58.59651936101727,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.329897107789293,
+    "geometry_read_seconds": 37.99548072600737,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "9",
+    "slurm_job_id": "5945304",
+    "started_at_utc": "2026-08-07T08:56:33.190415Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC166_AoA_10/boundary_geo_LHC166_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC166_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624380000000000,
+    "extracted_vtu_size_bytes": 21796030368,
+    "geometry_sha256": "1b4e52d22441a1b10d5ee4cdf061225b8ab6c174869f96c92207321a276d2597",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4175179,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1202966,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2733143,
+      "13": 768403,
+      "14": 1314135,
+      "15": 445430,
+      "16": 910393,
+      "17": 348752,
+      "18": 745288,
+      "19": 301768,
+      "20": 664227,
+      "21": 224294,
+      "22": 351352,
+      "23": 121966,
+      "24": 197681,
+      "25": 68405,
+      "26": 93236,
+      "27": 51493,
+      "28": 124399,
+      "29": 53203,
+      "3": 51738,
+      "30": 115917,
+      "31": 49328,
+      "32": 108172,
+      "33": 38676,
+      "34": 65771,
+      "35": 27935,
+      "36": 62943,
+      "37": 23106,
+      "38": 39030,
+      "39": 16271,
+      "4": 115673,
+      "40": 29532,
+      "41": 10752,
+      "42": 14141,
+      "43": 5860,
+      "44": 7777,
+      "45": 3690,
+      "46": 4260,
+      "47": 2515,
+      "48": 3578,
+      "49": 2191,
+      "5": 927168,
+      "50": 2933,
+      "51": 1856,
+      "52": 2757,
+      "53": 1757,
+      "54": 2397,
+      "55": 1702,
+      "56": 2495,
+      "57": 1744,
+      "58": 2266,
+      "59": 1682,
+      "6": 5243495,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2015171,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6210967,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1810665,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51738,
+      "7": 31779368,
+      "9": 115673
+    },
+    "connectivity_max": 141874639,
+    "connectivity_min": 0,
+    "n_cells": 31946779,
+    "n_connectivity_values": 347631709,
+    "n_fan_triangles": 283738151,
+    "n_points": 141874640
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.458319813144528e-11,
+    "float64_area_closure_relative": 2.9936257903068225e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 283738151,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936609.1265016254,
+    "surface_area_float64_in2": 1936609.1265492334,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936609.1265492914,
+    "zero_area_triangles": 239584,
+    "zero_weight_points": 5689
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC166_AoA_14.json b/surface_dual_areas/cases/geo_LHC166_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..3316446b7f5b8b3a004ca87170433ef8232f8691
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC166_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC166_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC166_AoA_14/boundary_dual_area_geo_LHC166_AoA_14.npy",
+    "sha256": "d5b4d5adda7d907be3ff2da288cdac76552fc074033095c9f67fdc755fa9a475",
+    "shape": [
+      141093317
+    ],
+    "size_bytes": 564373396
+  },
+  "runtime": {
+    "accumulation_seconds": 10.973675512010232,
+    "completed_at_utc": "2026-08-07T08:58:43.435688Z",
+    "elapsed_seconds": 35.147107823053375,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5541759959887713,
+    "geometry_read_seconds": 15.767414731206372,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T08:58:08.288498Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC166_AoA_14/boundary_geo_LHC166_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC166_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624538000000000,
+    "extracted_vtu_size_bytes": 21675156539,
+    "geometry_sha256": "a1ab3164b19369ab7a84200ebced77b4bd08fd051e93b61f6e799eb650209ab9",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4174183,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1193880,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2701835,
+      "13": 752824,
+      "14": 1252792,
+      "15": 431349,
+      "16": 888562,
+      "17": 345335,
+      "18": 748023,
+      "19": 303670,
+      "20": 670636,
+      "21": 227966,
+      "22": 363535,
+      "23": 125388,
+      "24": 204027,
+      "25": 69636,
+      "26": 93734,
+      "27": 51584,
+      "28": 124421,
+      "29": 53199,
+      "3": 52728,
+      "30": 115919,
+      "31": 49321,
+      "32": 108171,
+      "33": 38683,
+      "34": 65778,
+      "35": 27936,
+      "36": 62945,
+      "37": 23099,
+      "38": 39031,
+      "39": 16272,
+      "4": 118390,
+      "40": 29531,
+      "41": 10752,
+      "42": 14144,
+      "43": 5861,
+      "44": 7769,
+      "45": 3691,
+      "46": 4260,
+      "47": 2515,
+      "48": 3579,
+      "49": 2192,
+      "5": 923617,
+      "50": 2934,
+      "51": 1855,
+      "52": 2756,
+      "53": 1757,
+      "54": 2399,
+      "55": 1702,
+      "56": 2495,
+      "57": 1745,
+      "58": 2266,
+      "59": 1682,
+      "6": 5208548,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1113,
+      "68": 1527,
+      "69": 920,
+      "7": 2001631,
+      "70": 991,
+      "71": 568,
+      "72": 674,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6176743,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1802828,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52728,
+      "7": 31566140,
+      "9": 118390
+    },
+    "connectivity_max": 141093316,
+    "connectivity_min": 0,
+    "n_cells": 31737258,
+    "n_connectivity_values": 345650021,
+    "n_fan_triangles": 282175505,
+    "n_points": 141093317
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.4577180131855654e-11,
+    "float64_area_closure_relative": 1.719230406679887e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282175505,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936609.6546641877,
+    "surface_area_float64_in2": 1936609.654711784,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936609.6547118174,
+    "zero_area_triangles": 239196,
+    "zero_weight_points": 5636
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC166_AoA_22.json b/surface_dual_areas/cases/geo_LHC166_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..d33a474089302882b805e7bc9b80d821b0f6848e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC166_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC166_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC166_AoA_22/boundary_dual_area_geo_LHC166_AoA_22.npy",
+    "sha256": "bf6ce6609a5356282ed46a14bb14c839890efcf46e31da634314cc3fbe70f3ee",
+    "shape": [
+      137696386
+    ],
+    "size_bytes": 550785672
+  },
+  "runtime": {
+    "accumulation_seconds": 10.51673680706881,
+    "completed_at_utc": "2026-08-07T08:14:00.935199Z",
+    "elapsed_seconds": 21.217478772858158,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1577104639727622,
+    "geometry_read_seconds": 2.4313068869523704,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T08:13:39.717624Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC166_AoA_22/boundary_geo_LHC166_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC166_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624457000000000,
+    "extracted_vtu_size_bytes": 21149099901,
+    "geometry_sha256": "4129d7eeae4666e40a44ddb7f3d7de5bf5795aa6d7d2a2fc82c42d07a84d4415",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3793489,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1126212,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2488348,
+      "13": 705643,
+      "14": 1213374,
+      "15": 420968,
+      "16": 902615,
+      "17": 348604,
+      "18": 757468,
+      "19": 308136,
+      "20": 685104,
+      "21": 233412,
+      "22": 384415,
+      "23": 129916,
+      "24": 215455,
+      "25": 71910,
+      "26": 95423,
+      "27": 52052,
+      "28": 124633,
+      "29": 53268,
+      "3": 49722,
+      "30": 115945,
+      "31": 49321,
+      "32": 108166,
+      "33": 38684,
+      "34": 65769,
+      "35": 27940,
+      "36": 62948,
+      "37": 23098,
+      "38": 39028,
+      "39": 16273,
+      "4": 115253,
+      "40": 29533,
+      "41": 10754,
+      "42": 14145,
+      "43": 5858,
+      "44": 7771,
+      "45": 3693,
+      "46": 4260,
+      "47": 2514,
+      "48": 3579,
+      "49": 2192,
+      "5": 923896,
+      "50": 2932,
+      "51": 1856,
+      "52": 2756,
+      "53": 1757,
+      "54": 2399,
+      "55": 1702,
+      "56": 2495,
+      "57": 1744,
+      "58": 2266,
+      "59": 1682,
+      "6": 5196762,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1985842,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6002845,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1743844,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49722,
+      "7": 30639849,
+      "9": 115253
+    },
+    "connectivity_max": 137696385,
+    "connectivity_min": 0,
+    "n_cells": 30804824,
+    "n_connectivity_values": 336991291,
+    "n_fan_triangles": 275381643,
+    "n_points": 137696386
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.4720475130745433e-11,
+    "float64_area_closure_relative": 4.3882429092546255e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275381643,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936610.7731259707,
+    "surface_area_float64_in2": 1936610.7731738447,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936610.7731739297,
+    "zero_area_triangles": 234410,
+    "zero_weight_points": 5382
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC166_AoA_4.json b/surface_dual_areas/cases/geo_LHC166_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..fcac95e1af8b6368e1b385373617d4b35e328b88
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC166_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC166_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC166_AoA_4/boundary_dual_area_geo_LHC166_AoA_4.npy",
+    "sha256": "606b672caa3ed85674c34b45ee6d1bb9067cb6c30830aa286585684bb258e57f",
+    "shape": [
+      136860111
+    ],
+    "size_bytes": 547440572
+  },
+  "runtime": {
+    "accumulation_seconds": 10.482768673915416,
+    "completed_at_utc": "2026-08-07T08:56:20.155945Z",
+    "elapsed_seconds": 20.942911349004135,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0940968089271337,
+    "geometry_read_seconds": 2.469175553880632,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:55:59.212838Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC166_AoA_4/boundary_geo_LHC166_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC166_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624714000000000,
+    "extracted_vtu_size_bytes": 21015930276,
+    "geometry_sha256": "7533aad3b77e8647e3c7ab882e8f1610f186e16886eb687c0544544661ad697d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3356648,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1023591,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2403078,
+      "13": 758707,
+      "14": 1577005,
+      "15": 508295,
+      "16": 1004475,
+      "17": 369334,
+      "18": 748311,
+      "19": 301896,
+      "20": 661406,
+      "21": 222369,
+      "22": 344986,
+      "23": 119644,
+      "24": 194037,
+      "25": 67516,
+      "26": 93075,
+      "27": 51447,
+      "28": 124433,
+      "29": 53203,
+      "3": 49505,
+      "30": 115923,
+      "31": 49318,
+      "32": 108176,
+      "33": 38681,
+      "34": 65773,
+      "35": 27942,
+      "36": 62945,
+      "37": 23097,
+      "38": 39030,
+      "39": 16274,
+      "4": 112250,
+      "40": 29536,
+      "41": 10754,
+      "42": 14140,
+      "43": 5858,
+      "44": 7773,
+      "45": 3690,
+      "46": 4261,
+      "47": 2516,
+      "48": 3579,
+      "49": 2191,
+      "5": 923389,
+      "50": 2932,
+      "51": 1856,
+      "52": 2757,
+      "53": 1757,
+      "54": 2397,
+      "55": 1702,
+      "56": 2495,
+      "57": 1744,
+      "58": 2266,
+      "59": 1682,
+      "6": 5249864,
+      "60": 2465,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1953830,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5859344,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1620949,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49505,
+      "7": 30267032,
+      "9": 112250
+    },
+    "connectivity_max": 136860110,
+    "connectivity_min": 0,
+    "n_cells": 30428787,
+    "n_connectivity_values": 334566667,
+    "n_fan_triangles": 273709093,
+    "n_points": 136860111
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.5648867918505616e-11,
+    "float64_area_closure_relative": 4.676786532372742e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273709093,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1936610.1008052954,
+    "surface_area_float64_in2": 1936610.1008549673,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1936610.1008550578,
+    "zero_area_triangles": 230130,
+    "zero_weight_points": 5161
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC168_AoA_10.json b/surface_dual_areas/cases/geo_LHC168_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..7bfbdb68373af8b0a2615f33d7c1274cdfdf13b8
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC168_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC168_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC168_AoA_10/boundary_dual_area_geo_LHC168_AoA_10.npy",
+    "sha256": "a45463a037fc8aea0cc188c55364a8a58a922ca378fa211545b996952a598e34",
+    "shape": [
+      136653153
+    ],
+    "size_bytes": 546612740
+  },
+  "runtime": {
+    "accumulation_seconds": 10.53810117393732,
+    "completed_at_utc": "2026-08-07T08:57:06.825664Z",
+    "elapsed_seconds": 21.271964316954836,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.19275397202,
+    "geometry_read_seconds": 2.887835210887715,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:56:45.553603Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC168_AoA_10/boundary_geo_LHC168_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC168_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624548000000000,
+    "extracted_vtu_size_bytes": 20978757797,
+    "geometry_sha256": "a74a9885737f9cdf2d560900989de07919a7e71f5e648aab6c21833a13645515",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2929226,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 971827,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2203519,
+      "13": 799083,
+      "14": 1744717,
+      "15": 573702,
+      "16": 1023229,
+      "17": 384501,
+      "18": 755252,
+      "19": 303618,
+      "20": 678368,
+      "21": 227805,
+      "22": 378442,
+      "23": 126789,
+      "24": 213384,
+      "25": 72500,
+      "26": 92917,
+      "27": 52462,
+      "28": 124019,
+      "29": 53316,
+      "3": 56075,
+      "30": 115144,
+      "31": 49690,
+      "32": 109045,
+      "33": 38899,
+      "34": 66192,
+      "35": 28042,
+      "36": 62583,
+      "37": 22732,
+      "38": 38111,
+      "39": 15942,
+      "4": 131381,
+      "40": 28857,
+      "41": 10477,
+      "42": 13941,
+      "43": 5684,
+      "44": 7527,
+      "45": 3627,
+      "46": 4215,
+      "47": 2521,
+      "48": 3511,
+      "49": 2083,
+      "5": 951788,
+      "50": 2983,
+      "51": 1825,
+      "52": 2720,
+      "53": 1740,
+      "54": 2331,
+      "55": 1678,
+      "56": 2485,
+      "57": 1719,
+      "58": 2274,
+      "59": 1717,
+      "6": 5243093,
+      "60": 2508,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1968043,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5849575,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1585040,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56075,
+      "7": 29979620,
+      "9": 131381
+    },
+    "connectivity_max": 136653152,
+    "connectivity_min": 0,
+    "n_cells": 30167076,
+    "n_connectivity_values": 333629339,
+    "n_fan_triangles": 273295187,
+    "n_points": 136653153
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.6905865543168212e-11,
+    "float64_area_closure_relative": 6.3395730102869024e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273295187,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946507.137515341,
+    "surface_area_float64_in2": 1946507.1375677134,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946507.1375677257,
+    "zero_area_triangles": 223335,
+    "zero_weight_points": 4846
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC169_AoA_14.json b/surface_dual_areas/cases/geo_LHC169_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..a30e8e8762da4890738ba1f02c5764e86f0b130e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC169_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC169_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC169_AoA_14/boundary_dual_area_geo_LHC169_AoA_14.npy",
+    "sha256": "4207385d2f8d35d6bc65de2ecbb142e8dbec39a58ac2540ce5b0caadc780d8f9",
+    "shape": [
+      147061700
+    ],
+    "size_bytes": 588246928
+  },
+  "runtime": {
+    "accumulation_seconds": 11.477327008964494,
+    "completed_at_utc": "2026-08-07T08:58:03.232204Z",
+    "elapsed_seconds": 55.246776490006596,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3676508381031454,
+    "geometry_read_seconds": 35.284081948921084,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T08:57:07.985340Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC169_AoA_14/boundary_geo_LHC169_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC169_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624688000000000,
+    "extracted_vtu_size_bytes": 22594296804,
+    "geometry_sha256": "d471a4db920adac6e6808b2a6ecfed96fc885b3a7bb10a1a638227535f409cd6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4169463,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1342067,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2860188,
+      "13": 892530,
+      "14": 1531293,
+      "15": 514793,
+      "16": 937119,
+      "17": 357077,
+      "18": 722661,
+      "19": 289905,
+      "20": 653957,
+      "21": 217700,
+      "22": 360567,
+      "23": 119128,
+      "24": 200440,
+      "25": 68881,
+      "26": 91094,
+      "27": 51392,
+      "28": 123878,
+      "29": 52600,
+      "3": 59969,
+      "30": 115162,
+      "31": 49294,
+      "32": 108861,
+      "33": 38676,
+      "34": 66362,
+      "35": 28019,
+      "36": 63378,
+      "37": 22990,
+      "38": 39331,
+      "39": 16479,
+      "4": 135746,
+      "40": 29767,
+      "41": 10828,
+      "42": 14328,
+      "43": 5818,
+      "44": 7641,
+      "45": 3655,
+      "46": 4222,
+      "47": 2506,
+      "48": 3529,
+      "49": 2129,
+      "5": 943679,
+      "50": 2971,
+      "51": 1842,
+      "52": 2778,
+      "53": 1787,
+      "54": 2458,
+      "55": 1732,
+      "56": 2537,
+      "57": 1748,
+      "58": 2290,
+      "59": 1734,
+      "6": 5259122,
+      "60": 2501,
+      "61": 1658,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 2088387,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6502404,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1946042,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59969,
+      "7": 32974324,
+      "9": 135746
+    },
+    "connectivity_max": 147061699,
+    "connectivity_min": 0,
+    "n_cells": 33170039,
+    "n_connectivity_values": 360452356,
+    "n_fan_triangles": 294112278,
+    "n_points": 147061700
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.071962789481429e-11,
+    "float64_area_closure_relative": 1.2069500744457666e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 294112278,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948373.4668243811,
+    "surface_area_float64_in2": 1948373.4668842345,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948373.466884258,
+    "zero_area_triangles": 236891,
+    "zero_weight_points": 5888
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC169_AoA_16.json b/surface_dual_areas/cases/geo_LHC169_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..21944dc14ee6463e98c088f843f5323d3c080b92
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC169_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC169_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC169_AoA_16/boundary_dual_area_geo_LHC169_AoA_16.npy",
+    "sha256": "e0122cd421dcb989ded819e595e551f6413ec39611b9e60eec94c9519e439a33",
+    "shape": [
+      148240122
+    ],
+    "size_bytes": 592960616
+  },
+  "runtime": {
+    "accumulation_seconds": 11.5374884060584,
+    "completed_at_utc": "2026-08-07T08:57:28.323997Z",
+    "elapsed_seconds": 22.636963777942583,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.472528629936278,
+    "geometry_read_seconds": 2.2623847951181233,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T08:57:05.686959Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC169_AoA_16/boundary_geo_LHC169_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC169_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624381000000000,
+    "extracted_vtu_size_bytes": 22777606810,
+    "geometry_sha256": "6f1c982cf6d01089e3b839f1a3cd254d6a7398b65f82863d0c226adca648214f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4323990,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1410259,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2906605,
+      "13": 898586,
+      "14": 1471394,
+      "15": 495031,
+      "16": 924130,
+      "17": 351639,
+      "18": 726718,
+      "19": 290017,
+      "20": 655931,
+      "21": 217699,
+      "22": 360780,
+      "23": 119038,
+      "24": 201048,
+      "25": 68940,
+      "26": 91169,
+      "27": 51386,
+      "28": 123879,
+      "29": 52607,
+      "3": 59951,
+      "30": 115162,
+      "31": 49296,
+      "32": 108862,
+      "33": 38676,
+      "34": 66358,
+      "35": 28020,
+      "36": 63380,
+      "37": 22992,
+      "38": 39326,
+      "39": 16480,
+      "4": 135881,
+      "40": 29769,
+      "41": 10826,
+      "42": 14329,
+      "43": 5816,
+      "44": 7640,
+      "45": 3657,
+      "46": 4222,
+      "47": 2505,
+      "48": 3529,
+      "49": 2130,
+      "5": 942262,
+      "50": 2972,
+      "51": 1842,
+      "52": 2777,
+      "53": 1787,
+      "54": 2458,
+      "55": 1732,
+      "56": 2537,
+      "57": 1748,
+      "58": 2290,
+      "59": 1734,
+      "6": 5253915,
+      "60": 2501,
+      "61": 1658,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 2113026,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6584112,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2018231,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59951,
+      "7": 33330349,
+      "9": 135881
+    },
+    "connectivity_max": 148240121,
+    "connectivity_min": 0,
+    "n_cells": 33526181,
+    "n_connectivity_values": 363521484,
+    "n_fan_triangles": 296469122,
+    "n_points": 148240122
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.090318115388362e-11,
+    "float64_area_closure_relative": 2.5334002585510386e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 296469122,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948373.3881564438,
+    "surface_area_float64_in2": 1948373.3882166548,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948373.3882166054,
+    "zero_area_triangles": 238327,
+    "zero_weight_points": 5946
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC169_AoA_18.json b/surface_dual_areas/cases/geo_LHC169_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..15064d26708908c037166d6a4bb3b06c7af1e545
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC169_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC169_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC169_AoA_18/boundary_dual_area_geo_LHC169_AoA_18.npy",
+    "sha256": "106de3e192b59b01e1a3821eec6f54c1ca59c5f686cef43ce9009d5615272cda",
+    "shape": [
+      147884940
+    ],
+    "size_bytes": 591539888
+  },
+  "runtime": {
+    "accumulation_seconds": 13.974581436952576,
+    "completed_at_utc": "2026-08-07T09:02:05.201712Z",
+    "elapsed_seconds": 25.24754525604658,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.4857052678707987,
+    "geometry_read_seconds": 2.6991805389989167,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T09:01:39.954085Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC169_AoA_18/boundary_geo_LHC169_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC169_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624588000000000,
+    "extracted_vtu_size_bytes": 22723835974,
+    "geometry_sha256": "26efbab67354d0bc63aa1fa5a1bc3f3a2718cafb340e4716d6e5d5c113654450",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4372468,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1437953,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2847982,
+      "13": 880469,
+      "14": 1351115,
+      "15": 467470,
+      "16": 903456,
+      "17": 347553,
+      "18": 741337,
+      "19": 293917,
+      "20": 671756,
+      "21": 221753,
+      "22": 373691,
+      "23": 122030,
+      "24": 206976,
+      "25": 70093,
+      "26": 91665,
+      "27": 51491,
+      "28": 123883,
+      "29": 52609,
+      "3": 60324,
+      "30": 115166,
+      "31": 49297,
+      "32": 108865,
+      "33": 38674,
+      "34": 66355,
+      "35": 28022,
+      "36": 63381,
+      "37": 22994,
+      "38": 39325,
+      "39": 16480,
+      "4": 136876,
+      "40": 29771,
+      "41": 10826,
+      "42": 14328,
+      "43": 5816,
+      "44": 7640,
+      "45": 3657,
+      "46": 4222,
+      "47": 2505,
+      "48": 3529,
+      "49": 2130,
+      "5": 940265,
+      "50": 2972,
+      "51": 1842,
+      "52": 2777,
+      "53": 1787,
+      "54": 2458,
+      "55": 1732,
+      "56": 2537,
+      "57": 1748,
+      "58": 2290,
+      "59": 1734,
+      "6": 5239511,
+      "60": 2501,
+      "61": 1658,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 2123560,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6612683,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2057174,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60324,
+      "7": 33280825,
+      "9": 136876
+    },
+    "connectivity_max": 147884939,
+    "connectivity_min": 0,
+    "n_cells": 33478025,
+    "n_connectivity_values": 362714808,
+    "n_fan_triangles": 295758758,
+    "n_points": 147884940
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.08559733501699e-11,
+    "float64_area_closure_relative": 3.4296497610458045e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 295758758,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948373.7227507024,
+    "surface_area_float64_in2": 1948373.7228108214,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948373.7228107546,
+    "zero_area_triangles": 238815,
+    "zero_weight_points": 5972
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC169_AoA_4.json b/surface_dual_areas/cases/geo_LHC169_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..f3a765da7af559afabc2589133c22272e88c9468
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC169_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC169_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC169_AoA_4/boundary_dual_area_geo_LHC169_AoA_4.npy",
+    "sha256": "427f160b5f912ffee6b27a389b09e4976204e1c88e9216f7ffed47a658c636b7",
+    "shape": [
+      136344540
+    ],
+    "size_bytes": 545378288
+  },
+  "runtime": {
+    "accumulation_seconds": 10.425325792981312,
+    "completed_at_utc": "2026-08-07T08:15:13.817276Z",
+    "elapsed_seconds": 54.29528401885182,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0897783441469073,
+    "geometry_read_seconds": 36.15710667986423,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:14:19.521901Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC169_AoA_4/boundary_geo_LHC169_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC169_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624594000000000,
+    "extracted_vtu_size_bytes": 20927970749,
+    "geometry_sha256": "8fd3d1944c5f830c4d9dc506a24c62c97caa09eb30f5500668b759827c808596",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2866506,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 952794,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2260808,
+      "13": 830481,
+      "14": 1865751,
+      "15": 608697,
+      "16": 1037912,
+      "17": 387808,
+      "18": 735676,
+      "19": 295664,
+      "20": 663067,
+      "21": 221706,
+      "22": 370415,
+      "23": 121903,
+      "24": 204890,
+      "25": 69921,
+      "26": 91586,
+      "27": 51541,
+      "28": 123919,
+      "29": 52609,
+      "3": 56245,
+      "30": 115162,
+      "31": 49295,
+      "32": 108867,
+      "33": 38675,
+      "34": 66362,
+      "35": 28015,
+      "36": 63378,
+      "37": 22989,
+      "38": 39335,
+      "39": 16480,
+      "4": 128043,
+      "40": 29765,
+      "41": 10827,
+      "42": 14328,
+      "43": 5818,
+      "44": 7641,
+      "45": 3656,
+      "46": 4223,
+      "47": 2506,
+      "48": 3529,
+      "49": 2129,
+      "5": 933950,
+      "50": 2972,
+      "51": 1842,
+      "52": 2778,
+      "53": 1787,
+      "54": 2456,
+      "55": 1732,
+      "56": 2537,
+      "57": 1748,
+      "58": 2290,
+      "59": 1734,
+      "6": 5218016,
+      "60": 2501,
+      "61": 1658,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 1927343,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5674350,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1533022,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56245,
+      "7": 29778296,
+      "9": 128043
+    },
+    "connectivity_max": 136344539,
+    "connectivity_min": 0,
+    "n_cells": 29962584,
+    "n_connectivity_values": 332603126,
+    "n_fan_triangles": 272677958,
+    "n_points": 136344540
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.07810145606317e-11,
+    "float64_area_closure_relative": 1.2666985827530497e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272677958,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948375.7669413942,
+    "surface_area_float64_in2": 1948375.7670013672,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948375.7670013919,
+    "zero_area_triangles": 221708,
+    "zero_weight_points": 4949
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC169_AoA_8.json b/surface_dual_areas/cases/geo_LHC169_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..b8a76d7aae3753ca9ae86bddac0c4ebf16a476cc
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC169_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC169_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC169_AoA_8/boundary_dual_area_geo_LHC169_AoA_8.npy",
+    "sha256": "c9a09b2618605c99db95f2192f543e29be391f9b8311eebcb455a399544bdb8f",
+    "shape": [
+      137629027
+    ],
+    "size_bytes": 550516236
+  },
+  "runtime": {
+    "accumulation_seconds": 13.100939041934907,
+    "completed_at_utc": "2026-08-07T08:11:25.135892Z",
+    "elapsed_seconds": 24.731150390114635,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9601275459863245,
+    "geometry_read_seconds": 4.080631781136617,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T08:11:00.404653Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC169_AoA_8/boundary_geo_LHC169_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC169_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624482000000000,
+    "extracted_vtu_size_bytes": 21127824950,
+    "geometry_sha256": "1c564be38dae9d46ce0c4455ec99658da28b7e9fd4eb531c18e7fb33be331e94",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2941580,
+      "100": 45,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 969630,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2296853,
+      "13": 845292,
+      "14": 1889139,
+      "15": 615365,
+      "16": 1039937,
+      "17": 386136,
+      "18": 731132,
+      "19": 293770,
+      "20": 658686,
+      "21": 219587,
+      "22": 364959,
+      "23": 120288,
+      "24": 202829,
+      "25": 69349,
+      "26": 91387,
+      "27": 51432,
+      "28": 123907,
+      "29": 52599,
+      "3": 57088,
+      "30": 115168,
+      "31": 49289,
+      "32": 108869,
+      "33": 38675,
+      "34": 66361,
+      "35": 28020,
+      "36": 63375,
+      "37": 22991,
+      "38": 39334,
+      "39": 16482,
+      "4": 131915,
+      "40": 29764,
+      "41": 10828,
+      "42": 14328,
+      "43": 5818,
+      "44": 7641,
+      "45": 3655,
+      "46": 4222,
+      "47": 2505,
+      "48": 3529,
+      "49": 2130,
+      "5": 938817,
+      "50": 2972,
+      "51": 1842,
+      "52": 2777,
+      "53": 1787,
+      "54": 2458,
+      "55": 1732,
+      "56": 2537,
+      "57": 1748,
+      "58": 2290,
+      "59": 1734,
+      "6": 5245419,
+      "60": 2501,
+      "61": 1658,
+      "62": 2229,
+      "63": 1635,
+      "64": 2178,
+      "65": 1375,
+      "66": 1818,
+      "67": 1098,
+      "68": 1464,
+      "69": 904,
+      "7": 1938603,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5847963,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1550961,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57088,
+      "7": 30163586,
+      "9": 131915
+    },
+    "connectivity_max": 137629026,
+    "connectivity_min": 0,
+    "n_cells": 30352589,
+    "n_connectivity_values": 335952110,
+    "n_fan_triangles": 275246932,
+    "n_points": 137629027
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.04713868365598e-11,
+    "float64_area_closure_relative": 4.7680441065713535e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275246932,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948375.9952435954,
+    "surface_area_float64_in2": 1948375.9953029652,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948375.995303058,
+    "zero_area_triangles": 221420,
+    "zero_weight_points": 4961
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC170_AoA_22.json b/surface_dual_areas/cases/geo_LHC170_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..79ede99815c393c83d3dd8b817c7a6a360875951
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC170_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC170_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC170_AoA_22/boundary_dual_area_geo_LHC170_AoA_22.npy",
+    "sha256": "107467c7a9c89df7650b62b83cc6525ce9c58bdf687c2b81798e252294bf2fee",
+    "shape": [
+      140657509
+    ],
+    "size_bytes": 562630164
+  },
+  "runtime": {
+    "accumulation_seconds": 10.762012599036098,
+    "completed_at_utc": "2026-08-07T09:02:28.193219Z",
+    "elapsed_seconds": 21.107806943822652,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.258079912979156,
+    "geometry_read_seconds": 2.3721912188921124,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T09:02:07.085325Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC170_AoA_22/boundary_geo_LHC170_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC170_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624707000000000,
+    "extracted_vtu_size_bytes": 21608701332,
+    "geometry_sha256": "fae9e1613a1e79b2d733f73b97ec956d008d37fbdab9611cfc041728bcdeb381",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4012584,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1258515,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2603523,
+      "13": 780669,
+      "14": 1181201,
+      "15": 446237,
+      "16": 889213,
+      "17": 359066,
+      "18": 758707,
+      "19": 307000,
+      "20": 678423,
+      "21": 227574,
+      "22": 368223,
+      "23": 122883,
+      "24": 204858,
+      "25": 68603,
+      "26": 93796,
+      "27": 51995,
+      "28": 124909,
+      "29": 53420,
+      "3": 52983,
+      "30": 114062,
+      "31": 49031,
+      "32": 107081,
+      "33": 38414,
+      "34": 65856,
+      "35": 27806,
+      "36": 62451,
+      "37": 22792,
+      "38": 39253,
+      "39": 16409,
+      "4": 123201,
+      "40": 30121,
+      "41": 10903,
+      "42": 14596,
+      "43": 5911,
+      "44": 7691,
+      "45": 3678,
+      "46": 4288,
+      "47": 2510,
+      "48": 3517,
+      "49": 2132,
+      "5": 933664,
+      "50": 2979,
+      "51": 1859,
+      "52": 2752,
+      "53": 1770,
+      "54": 2456,
+      "55": 1753,
+      "56": 2540,
+      "57": 1732,
+      "58": 2287,
+      "59": 1738,
+      "6": 5219731,
+      "60": 2510,
+      "61": 1656,
+      "62": 2230,
+      "63": 1637,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 2037435,
+      "70": 1022,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6166377,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1860746,
+      "90": 59,
+      "91": 56,
+      "92": 55,
+      "93": 50,
+      "94": 50,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52983,
+      "7": 31482835,
+      "9": 123201
+    },
+    "connectivity_max": 140657508,
+    "connectivity_min": 0,
+    "n_cells": 31659019,
+    "n_connectivity_values": 344621971,
+    "n_fan_triangles": 281303933,
+    "n_points": 140657509
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 2.7475317515100237e-11,
+    "float64_area_closure_relative": 1.129474878387936e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 281303933,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937721.7609390067,
+    "surface_area_float64_in2": 1937721.7609922462,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937721.760992268,
+    "zero_area_triangles": 236270,
+    "zero_weight_points": 5519
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC171_AoA_10.json b/surface_dual_areas/cases/geo_LHC171_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..97a64fb9525235aa18138b257f4f846cd7de8f02
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC171_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC171_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC171_AoA_10/boundary_dual_area_geo_LHC171_AoA_10.npy",
+    "sha256": "ea6697e45d2f004a04f572a36bd3e538fbcc486b2b33f60c9a687de3d47705fb",
+    "shape": [
+      141123874
+    ],
+    "size_bytes": 564495624
+  },
+  "runtime": {
+    "accumulation_seconds": 11.239153753966093,
+    "completed_at_utc": "2026-08-07T09:01:29.240827Z",
+    "elapsed_seconds": 21.370024103904143,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.364378185942769,
+    "geometry_read_seconds": 1.9635808728635311,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T09:01:07.870714Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC171_AoA_10/boundary_geo_LHC171_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC171_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624485000000000,
+    "extracted_vtu_size_bytes": 21679178806,
+    "geometry_sha256": "06755ae75867b6a598fabb9a63e9a7524ca7e87ab69f7d11409e23fdf52bb3b0",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3960432,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1188410,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2650009,
+      "13": 791859,
+      "14": 1362669,
+      "15": 476015,
+      "16": 946706,
+      "17": 364076,
+      "18": 754444,
+      "19": 302758,
+      "20": 660212,
+      "21": 220951,
+      "22": 339970,
+      "23": 118663,
+      "24": 193958,
+      "25": 66830,
+      "26": 93715,
+      "27": 51440,
+      "28": 124528,
+      "29": 52846,
+      "3": 52032,
+      "30": 114957,
+      "31": 49161,
+      "32": 108275,
+      "33": 38876,
+      "34": 66651,
+      "35": 27942,
+      "36": 63277,
+      "37": 23205,
+      "38": 39279,
+      "39": 16309,
+      "4": 114540,
+      "40": 29703,
+      "41": 10806,
+      "42": 14171,
+      "43": 5838,
+      "44": 7735,
+      "45": 3711,
+      "46": 4238,
+      "47": 2501,
+      "48": 3598,
+      "49": 2225,
+      "5": 942871,
+      "50": 2899,
+      "51": 1842,
+      "52": 2710,
+      "53": 1745,
+      "54": 2393,
+      "55": 1704,
+      "56": 2495,
+      "57": 1753,
+      "58": 2277,
+      "59": 1685,
+      "6": 5262687,
+      "60": 2468,
+      "61": 1650,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2042434,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6103240,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1801835,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52032,
+      "7": 31550677,
+      "9": 114540
+    },
+    "connectivity_max": 141123873,
+    "connectivity_min": 0,
+    "n_cells": 31717249,
+    "n_connectivity_values": 345671124,
+    "n_fan_triangles": 282236626,
+    "n_points": 141123874
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.1063352984218464e-11,
+    "float64_area_closure_relative": 2.2614712804356773e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 282236626,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935561.2155788678,
+    "surface_area_float64_in2": 1935561.2156389928,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935561.2156390366,
+    "zero_area_triangles": 240066,
+    "zero_weight_points": 5713
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC171_AoA_18.json b/surface_dual_areas/cases/geo_LHC171_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b4fb53174ad835ce689d99cdf62f9e3b27ad37e
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC171_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC171_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC171_AoA_18/boundary_dual_area_geo_LHC171_AoA_18.npy",
+    "sha256": "ad9ee515251761294d5565db9251055b4d662115ae13cbc7469eda5af4169660",
+    "shape": [
+      139487040
+    ],
+    "size_bytes": 557948288
+  },
+  "runtime": {
+    "accumulation_seconds": 10.573215794982389,
+    "completed_at_utc": "2026-08-07T08:15:32.595581Z",
+    "elapsed_seconds": 21.01591946487315,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0581965181045234,
+    "geometry_read_seconds": 2.433870597044006,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T08:15:11.579541Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC171_AoA_18/boundary_geo_LHC171_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC171_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624601000000000,
+    "extracted_vtu_size_bytes": 21427125624,
+    "geometry_sha256": "c0f6facd7f8ee4e4fdd7331afe834f12f6b4de0d6f93ff156c3476d5b2b6a66b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3909700,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1201128,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2544132,
+      "13": 765719,
+      "14": 1211236,
+      "15": 448142,
+      "16": 895782,
+      "17": 354401,
+      "18": 752133,
+      "19": 302950,
+      "20": 674121,
+      "21": 225893,
+      "22": 374327,
+      "23": 123608,
+      "24": 214111,
+      "25": 69556,
+      "26": 96233,
+      "27": 51980,
+      "28": 124757,
+      "29": 52922,
+      "3": 50965,
+      "30": 114975,
+      "31": 49186,
+      "32": 108282,
+      "33": 38884,
+      "34": 66652,
+      "35": 27941,
+      "36": 63274,
+      "37": 23202,
+      "38": 39275,
+      "39": 16307,
+      "4": 115371,
+      "40": 29702,
+      "41": 10808,
+      "42": 14172,
+      "43": 5837,
+      "44": 7732,
+      "45": 3710,
+      "46": 4238,
+      "47": 2498,
+      "48": 3599,
+      "49": 2225,
+      "5": 938820,
+      "50": 2899,
+      "51": 1842,
+      "52": 2708,
+      "53": 1746,
+      "54": 2393,
+      "55": 1703,
+      "56": 2496,
+      "57": 1753,
+      "58": 2277,
+      "59": 1685,
+      "6": 5230630,
+      "60": 2468,
+      "61": 1650,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2040533,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6059401,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1819469,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50965,
+      "7": 31158843,
+      "9": 115371
+    },
+    "connectivity_max": 139487039,
+    "connectivity_min": 0,
+    "n_cells": 31325179,
+    "n_connectivity_values": 341613316,
+    "n_fan_triangles": 278962958,
+    "n_points": 139487040
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.0683102678160973e-11,
+    "float64_area_closure_relative": 9.86386076044285e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 278962958,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935561.87001309,
+    "surface_area_float64_in2": 1935561.8700724791,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935561.87007246,
+    "zero_area_triangles": 237055,
+    "zero_weight_points": 5605
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC171_AoA_4.json b/surface_dual_areas/cases/geo_LHC171_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..0b26a275b722b71630e69f270369b3d9515598f1
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC171_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC171_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC171_AoA_4/boundary_dual_area_geo_LHC171_AoA_4.npy",
+    "sha256": "d3c0be09696a9e6856d4896489c0189dc5ca9a0f935188090c6d13b099045109",
+    "shape": [
+      133691162
+    ],
+    "size_bytes": 534764776
+  },
+  "runtime": {
+    "accumulation_seconds": 10.549785184906796,
+    "completed_at_utc": "2026-08-07T08:56:57.327437Z",
+    "elapsed_seconds": 19.819855416892096,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 2.9535510269925,
+    "geometry_read_seconds": 1.9211864238604903,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:56:37.507499Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC171_AoA_4/boundary_geo_LHC171_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC171_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624673000000000,
+    "extracted_vtu_size_bytes": 20523889654,
+    "geometry_sha256": "165a4c1e9252676c8c3c8194a8c2b50390bcc7f804f0ad689491d351262b517b",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2869122,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 941753,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2121299,
+      "13": 757832,
+      "14": 1680612,
+      "15": 546970,
+      "16": 1066348,
+      "17": 388737,
+      "18": 763097,
+      "19": 304883,
+      "20": 661177,
+      "21": 221470,
+      "22": 340721,
+      "23": 118904,
+      "24": 193889,
+      "25": 66916,
+      "26": 93518,
+      "27": 51415,
+      "28": 124578,
+      "29": 52853,
+      "3": 49060,
+      "30": 114954,
+      "31": 49180,
+      "32": 108286,
+      "33": 38882,
+      "34": 66645,
+      "35": 27945,
+      "36": 63277,
+      "37": 23206,
+      "38": 39269,
+      "39": 16308,
+      "4": 110718,
+      "40": 29703,
+      "41": 10809,
+      "42": 14171,
+      "43": 5837,
+      "44": 7735,
+      "45": 3711,
+      "46": 4239,
+      "47": 2498,
+      "48": 3598,
+      "49": 2224,
+      "5": 939561,
+      "50": 2900,
+      "51": 1842,
+      "52": 2708,
+      "53": 1745,
+      "54": 2393,
+      "55": 1704,
+      "56": 2496,
+      "57": 1753,
+      "58": 2277,
+      "59": 1685,
+      "6": 5260854,
+      "60": 2468,
+      "61": 1650,
+      "62": 2224,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1957087,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5596101,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1550725,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 49060,
+      "7": 29347560,
+      "9": 110718
+    },
+    "connectivity_max": 133691161,
+    "connectivity_min": 0,
+    "n_cells": 29507338,
+    "n_connectivity_values": 326385878,
+    "n_fan_triangles": 267371202,
+    "n_points": 133691162
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.0806503766056e-11,
+    "float64_area_closure_relative": 1.8163928421220057e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 267371202,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1935562.9671816193,
+    "surface_area_float64_in2": 1935562.9672412472,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1935562.9672412823,
+    "zero_area_triangles": 225844,
+    "zero_weight_points": 4799
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC172_AoA_14.json b/surface_dual_areas/cases/geo_LHC172_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe17db636414056868abcdcd8a17d7cc9d4ad018
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC172_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC172_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC172_AoA_14/boundary_dual_area_geo_LHC172_AoA_14.npy",
+    "sha256": "2bf91b8c3148ef19dcb8716b78a9e68dc30968e385f2b3e0b6116fb64726562c",
+    "shape": [
+      142252778
+    ],
+    "size_bytes": 569011240
+  },
+  "runtime": {
+    "accumulation_seconds": 11.112576822051778,
+    "completed_at_utc": "2026-08-07T09:01:52.162891Z",
+    "elapsed_seconds": 22.03265164210461,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.606172251049429,
+    "geometry_read_seconds": 2.087773918174207,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T09:01:30.130144Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC172_AoA_14/boundary_geo_LHC172_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC172_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624686000000000,
+    "extracted_vtu_size_bytes": 21855668851,
+    "geometry_sha256": "74a8528754c7ccdab9b7d94e055a68c1ddf1cad063c943bb0b05f7f8f9f029ea",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4196936,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1236937,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2756639,
+      "13": 787803,
+      "14": 1266067,
+      "15": 451459,
+      "16": 889309,
+      "17": 352469,
+      "18": 740467,
+      "19": 299952,
+      "20": 656579,
+      "21": 222148,
+      "22": 355096,
+      "23": 121142,
+      "24": 202297,
+      "25": 68490,
+      "26": 94496,
+      "27": 52046,
+      "28": 124562,
+      "29": 53275,
+      "3": 52233,
+      "30": 115550,
+      "31": 49177,
+      "32": 108020,
+      "33": 38385,
+      "34": 65452,
+      "35": 27741,
+      "36": 62687,
+      "37": 22945,
+      "38": 39668,
+      "39": 16580,
+      "4": 117562,
+      "40": 30027,
+      "41": 10944,
+      "42": 14328,
+      "43": 5974,
+      "44": 7971,
+      "45": 3756,
+      "46": 4287,
+      "47": 2506,
+      "48": 3603,
+      "49": 2221,
+      "5": 931632,
+      "50": 2944,
+      "51": 1861,
+      "52": 2738,
+      "53": 1771,
+      "54": 2416,
+      "55": 1737,
+      "56": 2515,
+      "57": 1764,
+      "58": 2283,
+      "59": 1691,
+      "6": 5276073,
+      "60": 2463,
+      "61": 1651,
+      "62": 2223,
+      "63": 1600,
+      "64": 2206,
+      "65": 1377,
+      "66": 1811,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 2021868,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 6261386,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1828124,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52233,
+      "7": 31923947,
+      "9": 117562
+    },
+    "connectivity_max": 142252777,
+    "connectivity_min": 0,
+    "n_cells": 32093742,
+    "n_connectivity_values": 348681909,
+    "n_fan_triangles": 284494425,
+    "n_points": 142252778
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.022677153090453e-11,
+    "float64_area_closure_relative": 5.528049025114219e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284494425,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937430.2867051498,
+    "surface_area_float64_in2": 1937430.2867830864,
+    "weight_max_in2": 1.1013640053961358,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937430.2867831935,
+    "zero_area_triangles": 239598,
+    "zero_weight_points": 5812
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC173_AoA_10.json b/surface_dual_areas/cases/geo_LHC173_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..29054f69a020390dd34456f200ae092986caecf1
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC173_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC173_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC173_AoA_10/boundary_dual_area_geo_LHC173_AoA_10.npy",
+    "sha256": "9c98c0a9aacee3dc0f6aada74574787b2a22004f6672c09e2308c32c0e89cc21",
+    "shape": [
+      136111042
+    ],
+    "size_bytes": 544444296
+  },
+  "runtime": {
+    "accumulation_seconds": 13.090856987982988,
+    "completed_at_utc": "2026-08-07T09:03:40.439383Z",
+    "elapsed_seconds": 39.814104072982445,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.686531193787232,
+    "geometry_read_seconds": 18.16294110682793,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T09:03:00.625193Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC173_AoA_10/boundary_geo_LHC173_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC173_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624428000000000,
+    "extracted_vtu_size_bytes": 20899232170,
+    "geometry_sha256": "feee46df0eb7956d1b8909f480db657240f2edf75abf6ca2145bda94bf7ede2a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3379357,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1053656,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2384244,
+      "13": 749971,
+      "14": 1466806,
+      "15": 481173,
+      "16": 984961,
+      "17": 363857,
+      "18": 756448,
+      "19": 304584,
+      "20": 667775,
+      "21": 227521,
+      "22": 358295,
+      "23": 125893,
+      "24": 204324,
+      "25": 72097,
+      "26": 94104,
+      "27": 52697,
+      "28": 124282,
+      "29": 53269,
+      "3": 50141,
+      "30": 114460,
+      "31": 49271,
+      "32": 107981,
+      "33": 38653,
+      "34": 66115,
+      "35": 28094,
+      "36": 63092,
+      "37": 23193,
+      "38": 38964,
+      "39": 16195,
+      "4": 109874,
+      "40": 29320,
+      "41": 10739,
+      "42": 14136,
+      "43": 5828,
+      "44": 7770,
+      "45": 3706,
+      "46": 4194,
+      "47": 2536,
+      "48": 3610,
+      "49": 2184,
+      "5": 926286,
+      "50": 2926,
+      "51": 1856,
+      "52": 2722,
+      "53": 1756,
+      "54": 2379,
+      "55": 1720,
+      "56": 2525,
+      "57": 1758,
+      "58": 2272,
+      "59": 1684,
+      "6": 5180906,
+      "60": 2471,
+      "61": 1651,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1378,
+      "66": 1810,
+      "67": 1114,
+      "68": 1527,
+      "69": 920,
+      "7": 1958427,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5743673,
+      "80": 176,
+      "81": 123,
+      "82": 143,
+      "83": 112,
+      "84": 123,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1645928,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50141,
+      "7": 30035334,
+      "9": 109874
+    },
+    "connectivity_max": 136111041,
+    "connectivity_min": 0,
+    "n_cells": 30195349,
+    "n_connectivity_values": 332601660,
+    "n_fan_triangles": 272210962,
+    "n_points": 136111042
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.253228346940945e-11,
+    "float64_area_closure_relative": 3.641579348557952e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 272210962,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937282.6532741615,
+    "surface_area_float64_in2": 1937282.6533371857,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937282.6533372563,
+    "zero_area_triangles": 231695,
+    "zero_weight_points": 5237
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC173_AoA_22.json b/surface_dual_areas/cases/geo_LHC173_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..47b265b916a2877040a56b4888b6325dacf40938
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC173_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC173_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC173_AoA_22/boundary_dual_area_geo_LHC173_AoA_22.npy",
+    "sha256": "08c45bca20c20e4b9ac4178d8787e9ff6393c84423f3d494e29fe48f117ac768",
+    "shape": [
+      138356112
+    ],
+    "size_bytes": 553424576
+  },
+  "runtime": {
+    "accumulation_seconds": 10.653170855017379,
+    "completed_at_utc": "2026-08-07T08:16:17.578640Z",
+    "elapsed_seconds": 20.494772701058537,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2078195160720497,
+    "geometry_read_seconds": 2.0098940341267735,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T08:15:57.083780Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC173_AoA_22/boundary_geo_LHC173_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC173_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624550000000000,
+    "extracted_vtu_size_bytes": 21250486505,
+    "geometry_sha256": "baf08354952f464b59169b39c259384734af7770e2cc3d09e118fa6b155105f3",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3757463,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1173359,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2568503,
+      "13": 746879,
+      "14": 1239800,
+      "15": 424069,
+      "16": 890126,
+      "17": 341594,
+      "18": 749210,
+      "19": 303390,
+      "20": 674317,
+      "21": 232475,
+      "22": 381770,
+      "23": 132056,
+      "24": 218453,
+      "25": 75438,
+      "26": 96225,
+      "27": 53299,
+      "28": 124492,
+      "29": 53351,
+      "3": 51163,
+      "30": 114468,
+      "31": 49270,
+      "32": 107987,
+      "33": 38657,
+      "34": 66111,
+      "35": 28098,
+      "36": 63093,
+      "37": 23190,
+      "38": 38964,
+      "39": 16196,
+      "4": 114143,
+      "40": 29318,
+      "41": 10738,
+      "42": 14136,
+      "43": 5829,
+      "44": 7768,
+      "45": 3705,
+      "46": 4194,
+      "47": 2537,
+      "48": 3610,
+      "49": 2184,
+      "5": 933452,
+      "50": 2926,
+      "51": 1856,
+      "52": 2722,
+      "53": 1756,
+      "54": 2379,
+      "55": 1720,
+      "56": 2525,
+      "57": 1758,
+      "58": 2272,
+      "59": 1685,
+      "6": 5199821,
+      "60": 2471,
+      "61": 1651,
+      "62": 2223,
+      "63": 1599,
+      "64": 2207,
+      "65": 1377,
+      "66": 1811,
+      "67": 1113,
+      "68": 1527,
+      "69": 920,
+      "7": 2008732,
+      "70": 992,
+      "71": 568,
+      "72": 673,
+      "73": 453,
+      "74": 425,
+      "75": 308,
+      "76": 305,
+      "77": 229,
+      "78": 234,
+      "79": 148,
+      "8": 5957794,
+      "80": 176,
+      "81": 122,
+      "82": 144,
+      "83": 112,
+      "84": 122,
+      "85": 79,
+      "86": 99,
+      "87": 59,
+      "88": 71,
+      "89": 59,
+      "9": 1778522,
+      "90": 58,
+      "91": 57,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 51,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 51163,
+      "7": 30789402,
+      "9": 114143
+    },
+    "connectivity_max": 138356111,
+    "connectivity_min": 0,
+    "n_cells": 30954708,
+    "n_connectivity_values": 338610518,
+    "n_fan_triangles": 276701102,
+    "n_points": 138356112
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.2962542010807266e-11,
+    "float64_area_closure_relative": 1.6104674020017623e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 276701102,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1937282.692577964,
+    "surface_area_float64_in2": 1937282.6926418217,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1937282.692641853,
+    "zero_area_triangles": 235160,
+    "zero_weight_points": 5515
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC174_AoA_16.json b/surface_dual_areas/cases/geo_LHC174_AoA_16.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8f612d7dd3d276ff3c748549ff49c4fcc7c4ff5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC174_AoA_16.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC174_AoA_16",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC174_AoA_16/boundary_dual_area_geo_LHC174_AoA_16.npy",
+    "sha256": "d93ae17adaef62abca4a5a7eb19ccf51865e8c9dfcbb02c8d19de04722039c8b",
+    "shape": [
+      150609926
+    ],
+    "size_bytes": 602439832
+  },
+  "runtime": {
+    "accumulation_seconds": 11.465071167098358,
+    "completed_at_utc": "2026-08-07T08:59:12.974032Z",
+    "elapsed_seconds": 54.484409146010876,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.401302464073524,
+    "geometry_read_seconds": 34.06828491715714,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:58:18.489545Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC174_AoA_16/boundary_geo_LHC174_AoA_16.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC174_AoA_16.vtu",
+    "extracted_vtu_mtime_ns": 1783624655000000000,
+    "extracted_vtu_size_bytes": 23146283501,
+    "geometry_sha256": "4968eef62f14a402972f52ebc6a6e4f890aec0eeb2c3ba9063642e56075d828f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4687995,
+      "100": 44,
+      "101": 32,
+      "102": 40,
+      "103": 31,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1373194,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 3209679,
+      "13": 829425,
+      "14": 1337224,
+      "15": 447326,
+      "16": 913431,
+      "17": 350841,
+      "18": 744361,
+      "19": 302830,
+      "20": 675331,
+      "21": 224224,
+      "22": 354395,
+      "23": 120457,
+      "24": 197783,
+      "25": 68386,
+      "26": 88520,
+      "27": 51097,
+      "28": 123661,
+      "29": 52987,
+      "3": 60728,
+      "30": 115299,
+      "31": 49413,
+      "32": 108620,
+      "33": 38921,
+      "34": 66556,
+      "35": 28071,
+      "36": 61768,
+      "37": 22725,
+      "38": 38213,
+      "39": 16167,
+      "4": 135624,
+      "40": 29049,
+      "41": 10627,
+      "42": 14127,
+      "43": 5846,
+      "44": 7582,
+      "45": 3564,
+      "46": 4125,
+      "47": 2482,
+      "48": 3492,
+      "49": 2105,
+      "5": 957431,
+      "50": 2934,
+      "51": 1814,
+      "52": 2753,
+      "53": 1769,
+      "54": 2451,
+      "55": 1680,
+      "56": 2503,
+      "57": 1727,
+      "58": 2274,
+      "59": 1739,
+      "6": 5281210,
+      "60": 2510,
+      "61": 1625,
+      "62": 2258,
+      "63": 1600,
+      "64": 2167,
+      "65": 1402,
+      "66": 1791,
+      "67": 1099,
+      "68": 1467,
+      "69": 907,
+      "7": 2152904,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6798420,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 2031088,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 60728,
+      "7": 34047656,
+      "9": 135624
+    },
+    "connectivity_max": 150609925,
+    "connectivity_min": 0,
+    "n_cells": 34244008,
+    "n_connectivity_values": 369696749,
+    "n_fan_triangles": 301208733,
+    "n_points": 150609926
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.007360157058141e-11,
+    "float64_area_closure_relative": 1.4711922209365842e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 301208733,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1946596.0165318723,
+    "surface_area_float64_in2": 1946596.0166098794,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1946596.0166098508,
+    "zero_area_triangles": 246626,
+    "zero_weight_points": 6429
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC175_AoA_10.json b/surface_dual_areas/cases/geo_LHC175_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..82638ccfcfb4cfbee3e1d88853b5cd970e71da17
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC175_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC175_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC175_AoA_10/boundary_dual_area_geo_LHC175_AoA_10.npy",
+    "sha256": "e38335360a3d82278dcc30db9e0ee2b06fcd579a7d36bfca1dd9c5a370218553",
+    "shape": [
+      146981494
+    ],
+    "size_bytes": 587926104
+  },
+  "runtime": {
+    "accumulation_seconds": 11.17479875893332,
+    "completed_at_utc": "2026-08-07T08:16:40.552993Z",
+    "elapsed_seconds": 22.477476910920814,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2904073568060994,
+    "geometry_read_seconds": 2.491836756002158,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T08:16:18.075426Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC175_AoA_10/boundary_geo_LHC175_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC175_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624710000000000,
+    "extracted_vtu_size_bytes": 22583930085,
+    "geometry_sha256": "676dd46a01c9df50ef5c6e9ca74a96bd461fcc6aa0e2c7c7ab80568cbe62883a",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4049412,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1311306,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2869213,
+      "13": 867809,
+      "14": 1530198,
+      "15": 501245,
+      "16": 963856,
+      "17": 362097,
+      "18": 731197,
+      "19": 294120,
+      "20": 658692,
+      "21": 216851,
+      "22": 348034,
+      "23": 118587,
+      "24": 204024,
+      "25": 69671,
+      "26": 91919,
+      "27": 51605,
+      "28": 124412,
+      "29": 52925,
+      "3": 60345,
+      "30": 115571,
+      "31": 49538,
+      "32": 109279,
+      "33": 38833,
+      "34": 66418,
+      "35": 27635,
+      "36": 62180,
+      "37": 22805,
+      "38": 38827,
+      "39": 16398,
+      "4": 136660,
+      "40": 29647,
+      "41": 10862,
+      "42": 14515,
+      "43": 5931,
+      "44": 7826,
+      "45": 3663,
+      "46": 4334,
+      "47": 2542,
+      "48": 3540,
+      "49": 2152,
+      "5": 971185,
+      "50": 2888,
+      "51": 1851,
+      "52": 2731,
+      "53": 1776,
+      "54": 2474,
+      "55": 1721,
+      "56": 2591,
+      "57": 1730,
+      "58": 2313,
+      "59": 1689,
+      "6": 5356489,
+      "60": 2445,
+      "61": 1665,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2125214,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6547261,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1938733,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60345,
+      "7": 33033187,
+      "9": 136660
+    },
+    "connectivity_max": 146981493,
+    "connectivity_min": 0,
+    "n_cells": 33230192,
+    "n_connectivity_values": 360412243,
+    "n_fan_triangles": 293951859,
+    "n_points": 146981494
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.2970159284552384e-11,
+    "float64_area_closure_relative": 1.936123958870872e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293951859,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948148.2111651765,
+    "surface_area_float64_in2": 1948148.2112294072,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948148.2112293695,
+    "zero_area_triangles": 237562,
+    "zero_weight_points": 5823
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC175_AoA_8.json b/surface_dual_areas/cases/geo_LHC175_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..195a473f8244ae0139d68fbed9c65aed9c293cc7
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC175_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC175_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC175_AoA_8/boundary_dual_area_geo_LHC175_AoA_8.npy",
+    "sha256": "266885e7af2df0c39a770f849dfb92335cabf9caef970186e3853c3985107d84",
+    "shape": [
+      142231991
+    ],
+    "size_bytes": 568928092
+  },
+  "runtime": {
+    "accumulation_seconds": 10.863659851020202,
+    "completed_at_utc": "2026-08-07T08:14:19.531882Z",
+    "elapsed_seconds": 21.17000519996509,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1920503999572247,
+    "geometry_read_seconds": 2.2444463139399886,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "2",
+    "slurm_job_id": "5945297",
+    "started_at_utc": "2026-08-07T08:13:58.361777Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC175_AoA_8/boundary_geo_LHC175_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC175_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624578000000000,
+    "extracted_vtu_size_bytes": 21845486383,
+    "geometry_sha256": "3aff147c9998d593fc5be7ce094c5b400aa0425c5e16af1b5d494cddf0785c4f",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3462262,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1117277,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2572348,
+      "13": 839398,
+      "14": 1691486,
+      "15": 552988,
+      "16": 1021583,
+      "17": 380021,
+      "18": 739165,
+      "19": 297019,
+      "20": 661696,
+      "21": 218110,
+      "22": 349342,
+      "23": 119266,
+      "24": 204774,
+      "25": 69883,
+      "26": 92017,
+      "27": 51628,
+      "28": 124393,
+      "29": 52925,
+      "3": 57377,
+      "30": 115579,
+      "31": 49533,
+      "32": 109277,
+      "33": 38834,
+      "34": 66421,
+      "35": 27636,
+      "36": 62180,
+      "37": 22802,
+      "38": 38829,
+      "39": 16401,
+      "4": 134149,
+      "40": 29647,
+      "41": 10861,
+      "42": 14510,
+      "43": 5933,
+      "44": 7828,
+      "45": 3663,
+      "46": 4333,
+      "47": 2543,
+      "48": 3541,
+      "49": 2152,
+      "5": 967373,
+      "50": 2887,
+      "51": 1850,
+      "52": 2730,
+      "53": 1776,
+      "54": 2475,
+      "55": 1721,
+      "56": 2591,
+      "57": 1730,
+      "58": 2313,
+      "59": 1689,
+      "6": 5337732,
+      "60": 2445,
+      "61": 1665,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2049856,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6230794,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1737503,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 57377,
+      "7": 31617976,
+      "9": 134149
+    },
+    "connectivity_max": 142231990,
+    "connectivity_min": 0,
+    "n_cells": 31809502,
+    "n_connectivity_values": 348071856,
+    "n_fan_triangles": 284452852,
+    "n_points": 142231991
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.384342193098335e-11,
+    "float64_area_closure_relative": 2.450031604320842e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284452852,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948149.6427740543,
+    "surface_area_float64_in2": 1948149.6428399864,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948149.642840034,
+    "zero_area_triangles": 229149,
+    "zero_weight_points": 5297
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC176_AoA_10.json b/surface_dual_areas/cases/geo_LHC176_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..a8acbdd62e5076307efa962d512fc63751912b07
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC176_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC176_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC176_AoA_10/boundary_dual_area_geo_LHC176_AoA_10.npy",
+    "sha256": "9f353280b7d2e6e86c60d07907beaf11e6fcffee46077b19b2024886534dc10b",
+    "shape": [
+      136959080
+    ],
+    "size_bytes": 547836448
+  },
+  "runtime": {
+    "accumulation_seconds": 10.381776680005714,
+    "completed_at_utc": "2026-08-07T08:17:00.808573Z",
+    "elapsed_seconds": 20.214403359917924,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1013384500984102,
+    "geometry_read_seconds": 1.9705363670364022,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "1",
+    "slurm_job_id": "5945296",
+    "started_at_utc": "2026-08-07T08:16:40.594057Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC176_AoA_10/boundary_geo_LHC176_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC176_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624507000000000,
+    "extracted_vtu_size_bytes": 21028133910,
+    "geometry_sha256": "28629f475479a33256c7aa59bb6c852ecf6ea07d9caa2251fc133385b7f9c9c6",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3251246,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1070266,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2450489,
+      "13": 796585,
+      "14": 1581635,
+      "15": 523667,
+      "16": 1016203,
+      "17": 376640,
+      "18": 748079,
+      "19": 300047,
+      "20": 661815,
+      "21": 220313,
+      "22": 342830,
+      "23": 119175,
+      "24": 197229,
+      "25": 67578,
+      "26": 93203,
+      "27": 51337,
+      "28": 124507,
+      "29": 52838,
+      "3": 50963,
+      "30": 115104,
+      "31": 49466,
+      "32": 109471,
+      "33": 39039,
+      "34": 67701,
+      "35": 28085,
+      "36": 63023,
+      "37": 22724,
+      "38": 38590,
+      "39": 16155,
+      "4": 114395,
+      "40": 29415,
+      "41": 10671,
+      "42": 14174,
+      "43": 5700,
+      "44": 7639,
+      "45": 3659,
+      "46": 4280,
+      "47": 2510,
+      "48": 3501,
+      "49": 2112,
+      "5": 930251,
+      "50": 2887,
+      "51": 1803,
+      "52": 2632,
+      "53": 1704,
+      "54": 2319,
+      "55": 1686,
+      "56": 2522,
+      "57": 1731,
+      "58": 2274,
+      "59": 1719,
+      "6": 5136518,
+      "60": 2503,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1975138,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5745771,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1654914,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50963,
+      "7": 30165675,
+      "9": 114395
+    },
+    "connectivity_max": 136959079,
+    "connectivity_min": 0,
+    "n_cells": 30331033,
+    "n_connectivity_values": 334569106,
+    "n_fan_triangles": 273907040,
+    "n_points": 136959080
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.068120469566299e-11,
+    "float64_area_closure_relative": 2.330440082753004e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 273907040,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938223.8231203733,
+    "surface_area_float64_in2": 1938223.8231798403,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938223.8231798855,
+    "zero_area_triangles": 234211,
+    "zero_weight_points": 5340
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC176_AoA_14.json b/surface_dual_areas/cases/geo_LHC176_AoA_14.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e4bc549a10bddb42c128b923a99ff93fbb7c8e5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC176_AoA_14.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC176_AoA_14",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC176_AoA_14/boundary_dual_area_geo_LHC176_AoA_14.npy",
+    "sha256": "b13bdcd34015bf9830435e76f9468759f2714fa31a111614b62e49fb4262d78e",
+    "shape": [
+      138733677
+    ],
+    "size_bytes": 554934836
+  },
+  "runtime": {
+    "accumulation_seconds": 10.50910521298647,
+    "completed_at_utc": "2026-08-07T08:17:03.275545Z",
+    "elapsed_seconds": 21.651033028028905,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1205520641524345,
+    "geometry_read_seconds": 3.2721312399953604,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "3",
+    "slurm_job_id": "5945298",
+    "started_at_utc": "2026-08-07T08:16:41.624396Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC176_AoA_14/boundary_geo_LHC176_AoA_14.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC176_AoA_14.vtu",
+    "extracted_vtu_mtime_ns": 1783624409000000000,
+    "extracted_vtu_size_bytes": 21304930391,
+    "geometry_sha256": "0dc295ee2f74f8bfab27a157d352cfbfc842c28790550580827cbe3117a45a93",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3598832,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1154693,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2584563,
+      "13": 796001,
+      "14": 1415560,
+      "15": 486936,
+      "16": 949015,
+      "17": 363321,
+      "18": 746866,
+      "19": 299759,
+      "20": 667242,
+      "21": 222485,
+      "22": 355723,
+      "23": 121791,
+      "24": 206349,
+      "25": 68807,
+      "26": 94541,
+      "27": 51552,
+      "28": 124681,
+      "29": 52877,
+      "3": 52349,
+      "30": 115100,
+      "31": 49479,
+      "32": 109479,
+      "33": 39035,
+      "34": 67708,
+      "35": 28091,
+      "36": 63021,
+      "37": 22728,
+      "38": 38590,
+      "39": 16155,
+      "4": 116459,
+      "40": 29417,
+      "41": 10669,
+      "42": 14174,
+      "43": 5700,
+      "44": 7639,
+      "45": 3658,
+      "46": 4279,
+      "47": 2509,
+      "48": 3501,
+      "49": 2113,
+      "5": 926567,
+      "50": 2887,
+      "51": 1803,
+      "52": 2631,
+      "53": 1704,
+      "54": 2321,
+      "55": 1686,
+      "56": 2522,
+      "57": 1731,
+      "58": 2274,
+      "59": 1719,
+      "6": 5124909,
+      "60": 2503,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1996281,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5901646,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1740045,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 52349,
+      "7": 30728470,
+      "9": 116459
+    },
+    "connectivity_max": 138733676,
+    "connectivity_min": 0,
+    "n_cells": 30897278,
+    "n_connectivity_values": 339250790,
+    "n_fan_triangles": 277456234,
+    "n_points": 138733677
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.044275565996283e-11,
+    "float64_area_closure_relative": 4.252452610497364e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 277456234,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938223.782847063,
+    "surface_area_float64_in2": 1938223.7829060678,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938223.7829059854,
+    "zero_area_triangles": 237553,
+    "zero_weight_points": 5562
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC176_AoA_6.json b/surface_dual_areas/cases/geo_LHC176_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..38959067cb4d2efcbb07fa759ce6759327e6a548
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC176_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC176_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC176_AoA_6/boundary_dual_area_geo_LHC176_AoA_6.npy",
+    "sha256": "fe1dd837e8ffd0af37580060d878a78f7f3a1e845e528de884b5267e01e25d63",
+    "shape": [
+      130669600
+    ],
+    "size_bytes": 522678528
+  },
+  "runtime": {
+    "accumulation_seconds": 10.654340491862968,
+    "completed_at_utc": "2026-08-07T09:04:16.019611Z",
+    "elapsed_seconds": 21.84148357785307,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2422494750935584,
+    "geometry_read_seconds": 3.045311528025195,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T09:03:54.178041Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC176_AoA_6/boundary_geo_LHC176_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC176_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624646000000000,
+    "extracted_vtu_size_bytes": 20050490844,
+    "geometry_sha256": "6e47480cab4abda80bfbc3b8f4156f4a3adbf76748a1d16770c23427b34fa39c",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2437108,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 874182,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1981990,
+      "13": 760697,
+      "14": 1810294,
+      "15": 575090,
+      "16": 1103573,
+      "17": 394249,
+      "18": 758762,
+      "19": 303421,
+      "20": 664645,
+      "21": 222483,
+      "22": 345349,
+      "23": 120725,
+      "24": 199854,
+      "25": 68132,
+      "26": 93980,
+      "27": 51480,
+      "28": 124753,
+      "29": 52866,
+      "3": 46890,
+      "30": 115115,
+      "31": 49471,
+      "32": 109469,
+      "33": 39042,
+      "34": 67700,
+      "35": 28083,
+      "36": 63023,
+      "37": 22724,
+      "38": 38589,
+      "39": 16159,
+      "4": 109105,
+      "40": 29415,
+      "41": 10669,
+      "42": 14174,
+      "43": 5700,
+      "44": 7640,
+      "45": 3658,
+      "46": 4279,
+      "47": 2509,
+      "48": 3501,
+      "49": 2113,
+      "5": 923091,
+      "50": 2887,
+      "51": 1803,
+      "52": 2631,
+      "53": 1704,
+      "54": 2321,
+      "55": 1686,
+      "56": 2522,
+      "57": 1731,
+      "58": 2274,
+      "59": 1719,
+      "6": 5109062,
+      "60": 2503,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1900890,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5291144,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1457801,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 46890,
+      "7": 28303037,
+      "9": 109105
+    },
+    "connectivity_max": 130669599,
+    "connectivity_min": 0,
+    "n_cells": 28459032,
+    "n_connectivity_values": 318246144,
+    "n_fan_triangles": 261328080,
+    "n_points": 130669600
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.114582456932081e-11,
+    "float64_area_closure_relative": 1.9099982283511493e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 261328080,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938225.4805424975,
+    "surface_area_float64_in2": 1938225.480602865,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938225.4806029021,
+    "zero_area_triangles": 222034,
+    "zero_weight_points": 4625
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC176_AoA_8.json b/surface_dual_areas/cases/geo_LHC176_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..6767ef246ad8a8367a00a09f48c5c8d542c581f2
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC176_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC176_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC176_AoA_8/boundary_dual_area_geo_LHC176_AoA_8.npy",
+    "sha256": "19d97e8a35c22003d6f1fd0991800f434484823a23e44720822f6596e6c3b16c",
+    "shape": [
+      135053663
+    ],
+    "size_bytes": 540214780
+  },
+  "runtime": {
+    "accumulation_seconds": 10.219750165008008,
+    "completed_at_utc": "2026-08-07T08:17:24.602099Z",
+    "elapsed_seconds": 19.89518715790473,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0603526271879673,
+    "geometry_read_seconds": 2.092103993985802,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:17:04.706821Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC176_AoA_8/boundary_geo_LHC176_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC176_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624482000000000,
+    "extracted_vtu_size_bytes": 20732106618,
+    "geometry_sha256": "05342af984af643db7628fb87e300b7a8b8444f5bd2992ded0965b0fe4365314",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3011514,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1013689,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2303594,
+      "13": 784223,
+      "14": 1638842,
+      "15": 536427,
+      "16": 1042196,
+      "17": 382213,
+      "18": 752756,
+      "19": 301905,
+      "20": 663472,
+      "21": 221708,
+      "22": 344268,
+      "23": 120086,
+      "24": 198177,
+      "25": 67891,
+      "26": 93404,
+      "27": 51417,
+      "28": 124598,
+      "29": 52843,
+      "3": 50605,
+      "30": 115112,
+      "31": 49471,
+      "32": 109472,
+      "33": 39036,
+      "34": 67703,
+      "35": 28085,
+      "36": 63018,
+      "37": 22726,
+      "38": 38589,
+      "39": 16155,
+      "4": 113582,
+      "40": 29417,
+      "41": 10669,
+      "42": 14174,
+      "43": 5700,
+      "44": 7639,
+      "45": 3659,
+      "46": 4280,
+      "47": 2510,
+      "48": 3501,
+      "49": 2112,
+      "5": 928356,
+      "50": 2887,
+      "51": 1803,
+      "52": 2632,
+      "53": 1704,
+      "54": 2319,
+      "55": 1686,
+      "56": 2522,
+      "57": 1731,
+      "58": 2274,
+      "59": 1719,
+      "6": 5125849,
+      "60": 2503,
+      "61": 1655,
+      "62": 2229,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1954357,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5616088,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1598540,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 50605,
+      "7": 29605823,
+      "9": 113582
+    },
+    "connectivity_max": 135053662,
+    "connectivity_min": 0,
+    "n_cells": 29770010,
+    "n_connectivity_values": 329636226,
+    "n_fan_triangles": 270096206,
+    "n_points": 135053663
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.115737676815867e-11,
+    "float64_area_closure_relative": 2.967106083414693e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 270096206,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938224.2280508408,
+    "surface_area_float64_in2": 1938224.2281112308,
+    "weight_max_in2": 1.1008657656151284,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938224.2281112883,
+    "zero_area_triangles": 230952,
+    "zero_weight_points": 5185
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC177_AoA_20.json b/surface_dual_areas/cases/geo_LHC177_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d874ea0cb97f7a237245c471a6613effd5937cb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC177_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC177_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC177_AoA_20/boundary_dual_area_geo_LHC177_AoA_20.npy",
+    "sha256": "4969ff6dcce8a39a1b04c9fac346e998da29710cfbf34d15da26b8da96969ec4",
+    "shape": [
+      142429410
+    ],
+    "size_bytes": 569717768
+  },
+  "runtime": {
+    "accumulation_seconds": 10.796035700011998,
+    "completed_at_utc": "2026-08-07T08:17:26.145775Z",
+    "elapsed_seconds": 21.972421027021483,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3219176190905273,
+    "geometry_read_seconds": 3.0704276629257947,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T08:17:04.173260Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC177_AoA_20/boundary_geo_LHC177_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC177_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624415000000000,
+    "extracted_vtu_size_bytes": 21881331385,
+    "geometry_sha256": "4cddee178e7ddecb9061bbc9492ad7bfe85c8716d45418845c1ea727d63f4a6e",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4092685,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1246604,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2724649,
+      "13": 789154,
+      "14": 1345956,
+      "15": 459414,
+      "16": 914147,
+      "17": 351369,
+      "18": 741510,
+      "19": 299347,
+      "20": 669607,
+      "21": 223344,
+      "22": 356332,
+      "23": 120529,
+      "24": 197506,
+      "25": 67052,
+      "26": 92329,
+      "27": 51281,
+      "28": 124421,
+      "29": 52935,
+      "3": 50279,
+      "30": 115142,
+      "31": 49345,
+      "32": 110639,
+      "33": 39177,
+      "34": 67895,
+      "35": 28205,
+      "36": 62173,
+      "37": 22881,
+      "38": 37968,
+      "39": 16190,
+      "4": 122138,
+      "40": 28983,
+      "41": 10612,
+      "42": 14222,
+      "43": 5810,
+      "44": 7673,
+      "45": 3634,
+      "46": 4189,
+      "47": 2542,
+      "48": 3554,
+      "49": 2098,
+      "5": 923479,
+      "50": 2846,
+      "51": 1788,
+      "52": 2560,
+      "53": 1688,
+      "54": 2310,
+      "55": 1623,
+      "56": 2444,
+      "57": 1715,
+      "58": 2263,
+      "59": 1734,
+      "6": 5255549,
+      "60": 2505,
+      "61": 1625,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2025258,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6256271,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1844475,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 50279,
+      "7": 31902163,
+      "9": 122138
+    },
+    "connectivity_max": 142429409,
+    "connectivity_min": 0,
+    "n_cells": 32074580,
+    "n_connectivity_values": 348996855,
+    "n_fan_triangles": 284847695,
+    "n_points": 142429410
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.5288371177238786e-11,
+    "float64_area_closure_relative": 6.91971246811472e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 284847695,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938092.8233342452,
+    "surface_area_float64_in2": 1938092.8234026374,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938092.8234027715,
+    "zero_area_triangles": 241431,
+    "zero_weight_points": 5640
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC177_AoA_22.json b/surface_dual_areas/cases/geo_LHC177_AoA_22.json
new file mode 100644
index 0000000000000000000000000000000000000000..b5d51672eecea454ffd1a2c6b243bf9ba16cd743
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC177_AoA_22.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC177_AoA_22",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC177_AoA_22/boundary_dual_area_geo_LHC177_AoA_22.npy",
+    "sha256": "796029269c2e0591245ac91eaa68f7604f74b386a7f7f64167c56843291f6553",
+    "shape": [
+      143773377
+    ],
+    "size_bytes": 575093636
+  },
+  "runtime": {
+    "accumulation_seconds": 11.135044073918834,
+    "completed_at_utc": "2026-08-07T09:02:39.158913Z",
+    "elapsed_seconds": 50.72078872914426,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2621818559709936,
+    "geometry_read_seconds": 31.6794912670739,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T09:01:48.438003Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC177_AoA_22/boundary_geo_LHC177_AoA_22.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC177_AoA_22.vtu",
+    "extracted_vtu_mtime_ns": 1783624553000000000,
+    "extracted_vtu_size_bytes": 22090209618,
+    "geometry_sha256": "41e90a6712e74e3e23457e02dcbc9d38059fd14f0649a94532b207e352d799bd",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4238254,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1267453,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2799608,
+      "13": 792052,
+      "14": 1341272,
+      "15": 457399,
+      "16": 913266,
+      "17": 351516,
+      "18": 738921,
+      "19": 299320,
+      "20": 665923,
+      "21": 221870,
+      "22": 349104,
+      "23": 118585,
+      "24": 194516,
+      "25": 66589,
+      "26": 92345,
+      "27": 51317,
+      "28": 124472,
+      "29": 52942,
+      "3": 51085,
+      "30": 115165,
+      "31": 49332,
+      "32": 110624,
+      "33": 39171,
+      "34": 67895,
+      "35": 28201,
+      "36": 62161,
+      "37": 22877,
+      "38": 37963,
+      "39": 16185,
+      "4": 123678,
+      "40": 28989,
+      "41": 10601,
+      "42": 14221,
+      "43": 5805,
+      "44": 7671,
+      "45": 3632,
+      "46": 4188,
+      "47": 2541,
+      "48": 3555,
+      "49": 2099,
+      "5": 928338,
+      "50": 2846,
+      "51": 1790,
+      "52": 2558,
+      "53": 1687,
+      "54": 2312,
+      "55": 1623,
+      "56": 2444,
+      "57": 1715,
+      "58": 2263,
+      "59": 1734,
+      "6": 5275160,
+      "60": 2505,
+      "61": 1625,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2044260,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 6359897,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1877378,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 51085,
+      "7": 32298662,
+      "9": 123678
+    },
+    "connectivity_max": 143773376,
+    "connectivity_min": 0,
+    "n_cells": 32473425,
+    "n_connectivity_values": 352482478,
+    "n_fan_triangles": 287535628,
+    "n_points": 143773377
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.49475525227399e-11,
+    "float64_area_closure_relative": 1.9341558089964503e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 287535628,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938092.7561576697,
+    "surface_area_float64_in2": 1938092.7562254013,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938092.7562254388,
+    "zero_area_triangles": 243520,
+    "zero_weight_points": 5743
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC177_AoA_4.json b/surface_dual_areas/cases/geo_LHC177_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..964a7d3bdb44a0e3058fae49e00c90d821a72e91
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC177_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC177_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC177_AoA_4/boundary_dual_area_geo_LHC177_AoA_4.npy",
+    "sha256": "38f872fc1c5d83c760be82d2dc0ab7871bc91285ba7beb56d970d06efcea0167",
+    "shape": [
+      132099293
+    ],
+    "size_bytes": 528397300
+  },
+  "runtime": {
+    "accumulation_seconds": 10.740974281914532,
+    "completed_at_utc": "2026-08-07T09:00:01.617309Z",
+    "elapsed_seconds": 21.99884976586327,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.1652683198917657,
+    "geometry_read_seconds": 2.473077269969508,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "8",
+    "slurm_job_id": "5945303",
+    "started_at_utc": "2026-08-07T08:59:39.618381Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC177_AoA_4/boundary_geo_LHC177_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC177_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624637000000000,
+    "extracted_vtu_size_bytes": 20275557193,
+    "geometry_sha256": "0bd7c642fee7c1552e4c55bf8bb10e7d87d9000b5015b01e81a398c6a98b2b88",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2687084,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 888074,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2011154,
+      "13": 739973,
+      "14": 1735370,
+      "15": 552575,
+      "16": 1054349,
+      "17": 383696,
+      "18": 763603,
+      "19": 306279,
+      "20": 681682,
+      "21": 226432,
+      "22": 357928,
+      "23": 121652,
+      "24": 196694,
+      "25": 66880,
+      "26": 92166,
+      "27": 51163,
+      "28": 124365,
+      "29": 52944,
+      "3": 45979,
+      "30": 115174,
+      "31": 49325,
+      "32": 110646,
+      "33": 39198,
+      "34": 67924,
+      "35": 28221,
+      "36": 62201,
+      "37": 22897,
+      "38": 37974,
+      "39": 16196,
+      "4": 112515,
+      "40": 29011,
+      "41": 10611,
+      "42": 14225,
+      "43": 5816,
+      "44": 7677,
+      "45": 3633,
+      "46": 4192,
+      "47": 2546,
+      "48": 3553,
+      "49": 2099,
+      "5": 910598,
+      "50": 2846,
+      "51": 1787,
+      "52": 2560,
+      "53": 1687,
+      "54": 2312,
+      "55": 1624,
+      "56": 2446,
+      "57": 1716,
+      "58": 2263,
+      "59": 1734,
+      "6": 5247745,
+      "60": 2505,
+      "61": 1625,
+      "62": 2259,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1888974,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5546487,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1474393,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 45979,
+      "7": 28839411,
+      "9": 112515
+    },
+    "connectivity_max": 132099292,
+    "connectivity_min": 0,
+    "n_cells": 28997905,
+    "n_connectivity_values": 322183271,
+    "n_fan_triangles": 264187461,
+    "n_points": 132099293
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.542624269141556e-11,
+    "float64_area_closure_relative": 1.6458324286086105e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 264187461,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1938095.1319823351,
+    "surface_area_float64_in2": 1938095.1320509946,
+    "weight_max_in2": 1.1003274795205478,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1938095.1320510264,
+    "zero_area_triangles": 223704,
+    "zero_weight_points": 4540
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC178_AoA_4.json b/surface_dual_areas/cases/geo_LHC178_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..18e2601fd4ba4d8752828794bf23fc4956210b02
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC178_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC178_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC178_AoA_4/boundary_dual_area_geo_LHC178_AoA_4.npy",
+    "sha256": "fe145c740d860bed23b1aef739acbecd36a31af0593527906497734b27c2fdef",
+    "shape": [
+      131788593
+    ],
+    "size_bytes": 527154500
+  },
+  "runtime": {
+    "accumulation_seconds": 10.14032869017683,
+    "completed_at_utc": "2026-08-07T09:02:27.157106Z",
+    "elapsed_seconds": 47.202891040826216,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0308013199828565,
+    "geometry_read_seconds": 29.62368764099665,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T09:01:39.954125Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC178_AoA_4/boundary_geo_LHC178_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC178_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624513000000000,
+    "extracted_vtu_size_bytes": 20227001996,
+    "geometry_sha256": "c5814d7dbb9f5b031d3178a38ea05a076cbda5d6301bfc14f49cbc1b50ee7909",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2563610,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 870011,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 1988565,
+      "13": 747284,
+      "14": 1812689,
+      "15": 568106,
+      "16": 1098177,
+      "17": 386463,
+      "18": 748354,
+      "19": 300574,
+      "20": 663178,
+      "21": 222005,
+      "22": 348546,
+      "23": 121851,
+      "24": 200550,
+      "25": 69783,
+      "26": 93900,
+      "27": 52140,
+      "28": 124128,
+      "29": 53250,
+      "3": 49017,
+      "30": 115746,
+      "31": 49511,
+      "32": 108290,
+      "33": 38495,
+      "34": 65735,
+      "35": 27918,
+      "36": 61797,
+      "37": 22972,
+      "38": 38945,
+      "39": 16431,
+      "4": 112589,
+      "40": 29713,
+      "41": 10860,
+      "42": 14442,
+      "43": 5903,
+      "44": 7692,
+      "45": 3607,
+      "46": 4151,
+      "47": 2486,
+      "48": 3498,
+      "49": 2125,
+      "5": 937801,
+      "50": 2958,
+      "51": 1884,
+      "52": 2804,
+      "53": 1785,
+      "54": 2461,
+      "55": 1717,
+      "56": 2537,
+      "57": 1752,
+      "58": 2289,
+      "59": 1740,
+      "6": 5241429,
+      "60": 2511,
+      "61": 1628,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 1924072,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5448450,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1473213,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 49017,
+      "7": 28733438,
+      "9": 112589
+    },
+    "connectivity_max": 131788592,
+    "connectivity_min": 0,
+    "n_cells": 28895044,
+    "n_connectivity_values": 321356140,
+    "n_fan_triangles": 263566052,
+    "n_points": 131788593
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.6430068937492325e-11,
+    "float64_area_closure_relative": 2.4482331252156722e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 263566052,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940070.6090632146,
+    "surface_area_float64_in2": 1940070.6091338915,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940070.609133939,
+    "zero_area_triangles": 218475,
+    "zero_weight_points": 4550
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC178_AoA_6.json b/surface_dual_areas/cases/geo_LHC178_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..17abe0c3b1a783bd77e613c598f566e1df865b86
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC178_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC178_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC178_AoA_6/boundary_dual_area_geo_LHC178_AoA_6.npy",
+    "sha256": "6e9b09a46e0e35617fb86370d29fee7c776a5d75cd0568cc726bbe11e3768684",
+    "shape": [
+      138002199
+    ],
+    "size_bytes": 552008924
+  },
+  "runtime": {
+    "accumulation_seconds": 10.769096434116364,
+    "completed_at_utc": "2026-08-07T09:06:12.896824Z",
+    "elapsed_seconds": 34.71720373001881,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.3980453819967806,
+    "geometry_read_seconds": 15.77834260603413,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "7",
+    "slurm_job_id": "5945302",
+    "started_at_utc": "2026-08-07T09:05:38.179540Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC178_AoA_6/boundary_geo_LHC178_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC178_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624387000000000,
+    "extracted_vtu_size_bytes": 21192454985,
+    "geometry_sha256": "299a49a582f0f04b3d07f8fb50ad73b59aff08db6fca2aaede8672e0bc0fcd24",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3352464,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1086717,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2478718,
+      "13": 788606,
+      "14": 1564120,
+      "15": 510076,
+      "16": 1010646,
+      "17": 369122,
+      "18": 739857,
+      "19": 298461,
+      "20": 661781,
+      "21": 220846,
+      "22": 345473,
+      "23": 120481,
+      "24": 197525,
+      "25": 69149,
+      "26": 92974,
+      "27": 51958,
+      "28": 123929,
+      "29": 53202,
+      "3": 52189,
+      "30": 115741,
+      "31": 49510,
+      "32": 108287,
+      "33": 38490,
+      "34": 65742,
+      "35": 27917,
+      "36": 61791,
+      "37": 22974,
+      "38": 38944,
+      "39": 16439,
+      "4": 116430,
+      "40": 29707,
+      "41": 10860,
+      "42": 14444,
+      "43": 5900,
+      "44": 7693,
+      "45": 3607,
+      "46": 4151,
+      "47": 2487,
+      "48": 3498,
+      "49": 2124,
+      "5": 940544,
+      "50": 2958,
+      "51": 1884,
+      "52": 2804,
+      "53": 1785,
+      "54": 2461,
+      "55": 1717,
+      "56": 2537,
+      "57": 1752,
+      "58": 2289,
+      "59": 1740,
+      "6": 5251259,
+      "60": 2511,
+      "61": 1628,
+      "62": 2258,
+      "63": 1601,
+      "64": 2166,
+      "65": 1402,
+      "66": 1791,
+      "67": 1100,
+      "68": 1467,
+      "69": 907,
+      "7": 2000603,
+      "70": 1014,
+      "71": 565,
+      "72": 669,
+      "73": 437,
+      "74": 408,
+      "75": 306,
+      "76": 304,
+      "77": 226,
+      "78": 230,
+      "79": 150,
+      "8": 5874488,
+      "80": 183,
+      "81": 119,
+      "82": 144,
+      "83": 117,
+      "84": 115,
+      "85": 81,
+      "86": 96,
+      "87": 56,
+      "88": 72,
+      "89": 59,
+      "9": 1681700,
+      "90": 57,
+      "91": 56,
+      "92": 54,
+      "93": 51,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 43
+    },
+    "cell_type_histogram": {
+      "5": 52189,
+      "7": 30559997,
+      "9": 116430
+    },
+    "connectivity_max": 138002198,
+    "connectivity_min": 0,
+    "n_cells": 30728616,
+    "n_connectivity_values": 337450496,
+    "n_fan_triangles": 275993264,
+    "n_points": 138002199
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.695599905829371e-11,
+    "float64_area_closure_relative": 7.644736228557494e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 275993264,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1940068.5068504906,
+    "surface_area_float64_in2": 1940068.5069221877,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1940068.506922336,
+    "zero_area_triangles": 230940,
+    "zero_weight_points": 5366
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC179_AoA_18.json b/surface_dual_areas/cases/geo_LHC179_AoA_18.json
new file mode 100644
index 0000000000000000000000000000000000000000..b74ac7500058b6c8ef8e58708804d4d7786037cb
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC179_AoA_18.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC179_AoA_18",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC179_AoA_18/boundary_dual_area_geo_LHC179_AoA_18.npy",
+    "sha256": "15871602f21d6eae4db85f35d940230a89ed63c7296f4eb7285f676b7b79c936",
+    "shape": [
+      146226535
+    ],
+    "size_bytes": 584906268
+  },
+  "runtime": {
+    "accumulation_seconds": 11.6119117080234,
+    "completed_at_utc": "2026-08-07T09:06:16.611166Z",
+    "elapsed_seconds": 55.3413628290873,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.5855033211410046,
+    "geometry_read_seconds": 35.1116857919842,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "11",
+    "slurm_job_id": "5945281",
+    "started_at_utc": "2026-08-07T09:05:21.269728Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC179_AoA_18/boundary_geo_LHC179_AoA_18.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC179_AoA_18.vtu",
+    "extracted_vtu_mtime_ns": 1783624505000000000,
+    "extracted_vtu_size_bytes": 22468328731,
+    "geometry_sha256": "71502e49574c1cbf833f1b899ee03cdccab6451b9ec1eccf6f704096dda53d98",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4316101,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1345604,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2838042,
+      "13": 800519,
+      "14": 1283152,
+      "15": 429546,
+      "16": 906716,
+      "17": 350336,
+      "18": 763489,
+      "19": 309786,
+      "20": 687175,
+      "21": 229921,
+      "22": 368459,
+      "23": 125680,
+      "24": 209177,
+      "25": 71586,
+      "26": 91022,
+      "27": 51437,
+      "28": 123304,
+      "29": 52685,
+      "3": 59758,
+      "30": 115210,
+      "31": 49419,
+      "32": 109223,
+      "33": 39048,
+      "34": 67048,
+      "35": 28272,
+      "36": 63168,
+      "37": 22884,
+      "38": 38515,
+      "39": 16108,
+      "4": 131802,
+      "40": 29165,
+      "41": 10651,
+      "42": 14051,
+      "43": 5706,
+      "44": 7551,
+      "45": 3647,
+      "46": 4212,
+      "47": 2513,
+      "48": 3528,
+      "49": 2126,
+      "5": 955168,
+      "50": 2953,
+      "51": 1853,
+      "52": 2716,
+      "53": 1724,
+      "54": 2335,
+      "55": 1690,
+      "56": 2525,
+      "57": 1721,
+      "58": 2280,
+      "59": 1717,
+      "6": 5250391,
+      "60": 2506,
+      "61": 1654,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 905,
+      "7": 2146842,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 440,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6476999,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2024125,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 59758,
+      "7": 32883930,
+      "9": 131802
+    },
+    "connectivity_max": 146226534,
+    "connectivity_min": 0,
+    "n_cells": 33075490,
+    "n_connectivity_values": 358592937,
+    "n_fan_triangles": 292441957,
+    "n_points": 146226535
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.399740602205826e-11,
+    "float64_area_closure_relative": 3.137551472655027e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 292441957,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944243.119735013,
+    "surface_area_float64_in2": 1944243.1198011122,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944243.1198011732,
+    "zero_area_triangles": 243390,
+    "zero_weight_points": 6037
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC179_AoA_20.json b/surface_dual_areas/cases/geo_LHC179_AoA_20.json
new file mode 100644
index 0000000000000000000000000000000000000000..bdf5bb3519ddbe7f9383028a36897c3dc3237f9f
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC179_AoA_20.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC179_AoA_20",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC179_AoA_20/boundary_dual_area_geo_LHC179_AoA_20.npy",
+    "sha256": "d83c56ec16ba422a7a467d485277577ac89ad005bb912aa4bbabe163833753f6",
+    "shape": [
+      146592900
+    ],
+    "size_bytes": 586371728
+  },
+  "runtime": {
+    "accumulation_seconds": 11.437685047043487,
+    "completed_at_utc": "2026-08-07T08:18:32.554298Z",
+    "elapsed_seconds": 21.96791249513626,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.461482440121472,
+    "geometry_read_seconds": 2.343963966006413,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "0",
+    "slurm_job_id": "5945295",
+    "started_at_utc": "2026-08-07T08:18:10.586301Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC179_AoA_20/boundary_geo_LHC179_AoA_20.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC179_AoA_20.vtu",
+    "extracted_vtu_mtime_ns": 1783624612000000000,
+    "extracted_vtu_size_bytes": 22525261951,
+    "geometry_sha256": "848800c318789c85f212e82772c44e8c2c160b3820e1fafdb0d239670e5dcc77",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4363971,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1355983,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2856630,
+      "13": 802899,
+      "14": 1275895,
+      "15": 429621,
+      "16": 905354,
+      "17": 350379,
+      "18": 762815,
+      "19": 309309,
+      "20": 685746,
+      "21": 229477,
+      "22": 367591,
+      "23": 125313,
+      "24": 208665,
+      "25": 71453,
+      "26": 90951,
+      "27": 51398,
+      "28": 123317,
+      "29": 52691,
+      "3": 60517,
+      "30": 115196,
+      "31": 49428,
+      "32": 109210,
+      "33": 39060,
+      "34": 67056,
+      "35": 28269,
+      "36": 63155,
+      "37": 22886,
+      "38": 38511,
+      "39": 16098,
+      "4": 133436,
+      "40": 29172,
+      "41": 10649,
+      "42": 14054,
+      "43": 5702,
+      "44": 7557,
+      "45": 3646,
+      "46": 4205,
+      "47": 2513,
+      "48": 3531,
+      "49": 2126,
+      "5": 956712,
+      "50": 2953,
+      "51": 1855,
+      "52": 2715,
+      "53": 1723,
+      "54": 2337,
+      "55": 1690,
+      "56": 2525,
+      "57": 1721,
+      "58": 2280,
+      "59": 1717,
+      "6": 5252742,
+      "60": 2506,
+      "61": 1654,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 2151170,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 6497571,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 2035683,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 60517,
+      "7": 32989985,
+      "9": 133436
+    },
+    "connectivity_max": 146592899,
+    "connectivity_min": 0,
+    "n_cells": 33183938,
+    "n_connectivity_values": 359542563,
+    "n_fan_triangles": 293174687,
+    "n_points": 146592900
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.438193779132467e-11,
+    "float64_area_closure_relative": 2.7303884698706135e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 293174687,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944243.001940771,
+    "surface_area_float64_in2": 1944243.0020076178,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944243.002007671,
+    "zero_area_triangles": 243814,
+    "zero_weight_points": 6079
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC179_AoA_4.json b/surface_dual_areas/cases/geo_LHC179_AoA_4.json
new file mode 100644
index 0000000000000000000000000000000000000000..ee6303835085874229721f481ae37c14114429aa
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC179_AoA_4.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC179_AoA_4",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC179_AoA_4/boundary_dual_area_geo_LHC179_AoA_4.npy",
+    "sha256": "fa9c474538534510dd1341b176c7d284ee829664105677b3dbbc72b6348261fc",
+    "shape": [
+      134693904
+    ],
+    "size_bytes": 538775744
+  },
+  "runtime": {
+    "accumulation_seconds": 10.211990298936144,
+    "completed_at_utc": "2026-08-07T08:17:48.136252Z",
+    "elapsed_seconds": 20.465436339844018,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0557112370152026,
+    "geometry_read_seconds": 2.03144663781859,
+    "hostname": "cpu-0003",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "4",
+    "slurm_job_id": "5945299",
+    "started_at_utc": "2026-08-07T08:17:27.670721Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC179_AoA_4/boundary_geo_LHC179_AoA_4.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC179_AoA_4.vtu",
+    "extracted_vtu_mtime_ns": 1783624539000000000,
+    "extracted_vtu_size_bytes": 20674901817,
+    "geometry_sha256": "ae22546e2ca81d7513779236f585d42a197b4caa8609a3c71595213dfa4b6bb2",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2730736,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 887499,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2113569,
+      "13": 755172,
+      "14": 1759076,
+      "15": 564343,
+      "16": 1077016,
+      "17": 393462,
+      "18": 779733,
+      "19": 313982,
+      "20": 687760,
+      "21": 229730,
+      "22": 363336,
+      "23": 124171,
+      "24": 206109,
+      "25": 71012,
+      "26": 90954,
+      "27": 51403,
+      "28": 123345,
+      "29": 52681,
+      "3": 56906,
+      "30": 115201,
+      "31": 49443,
+      "32": 109206,
+      "33": 39070,
+      "34": 67050,
+      "35": 28268,
+      "36": 63164,
+      "37": 22891,
+      "38": 38520,
+      "39": 16105,
+      "4": 126818,
+      "40": 29164,
+      "41": 10655,
+      "42": 14053,
+      "43": 5706,
+      "44": 7553,
+      "45": 3645,
+      "46": 4207,
+      "47": 2513,
+      "48": 3530,
+      "49": 2127,
+      "5": 947454,
+      "50": 2951,
+      "51": 1855,
+      "52": 2715,
+      "53": 1724,
+      "54": 2337,
+      "55": 1690,
+      "56": 2525,
+      "57": 1721,
+      "58": 2280,
+      "59": 1717,
+      "6": 5233614,
+      "60": 2506,
+      "61": 1654,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1971103,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5687792,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1536118,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56906,
+      "7": 29427865,
+      "9": 126818
+    },
+    "connectivity_max": 134693903,
+    "connectivity_min": 0,
+    "n_cells": 29611589,
+    "n_connectivity_values": 328599873,
+    "n_fan_triangles": 269376695,
+    "n_points": 134693904
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.377629120900835e-11,
+    "float64_area_closure_relative": 2.6345813712495167e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 269376695,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944245.9497019646,
+    "surface_area_float64_in2": 1944245.949767634,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944245.9497676392,
+    "zero_area_triangles": 224946,
+    "zero_weight_points": 4873
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC179_AoA_6.json b/surface_dual_areas/cases/geo_LHC179_AoA_6.json
new file mode 100644
index 0000000000000000000000000000000000000000..2232e683772d15f2a2a14c2f8a2ec3cd69dafa31
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC179_AoA_6.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC179_AoA_6",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC179_AoA_6/boundary_dual_area_geo_LHC179_AoA_6.npy",
+    "sha256": "73ccd9a4a9e4fe175aaea7d54b196fc3195e10cc304a95044837c75c66dd69dc",
+    "shape": [
+      134636337
+    ],
+    "size_bytes": 538545476
+  },
+  "runtime": {
+    "accumulation_seconds": 10.900275132153183,
+    "completed_at_utc": "2026-08-07T09:03:01.374707Z",
+    "elapsed_seconds": 20.25675481115468,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.058719002176076,
+    "geometry_read_seconds": 1.7467776860576123,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T09:02:41.117858Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC179_AoA_6/boundary_geo_LHC179_AoA_6.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC179_AoA_6.vtu",
+    "extracted_vtu_mtime_ns": 1783624569000000000,
+    "extracted_vtu_size_bytes": 20665979951,
+    "geometry_sha256": "30b04ae28199fe2ca0e501ab872f2a2c2271ae2dd7337c83d623baa64fbbed42",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2703707,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 874395,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2096720,
+      "13": 755535,
+      "14": 1792594,
+      "15": 570963,
+      "16": 1082504,
+      "17": 393554,
+      "18": 775780,
+      "19": 312040,
+      "20": 683854,
+      "21": 228645,
+      "22": 363538,
+      "23": 124179,
+      "24": 206330,
+      "25": 71067,
+      "26": 90955,
+      "27": 51422,
+      "28": 123319,
+      "29": 52671,
+      "3": 56433,
+      "30": 115209,
+      "31": 49437,
+      "32": 109218,
+      "33": 39065,
+      "34": 67049,
+      "35": 28269,
+      "36": 63162,
+      "37": 22895,
+      "38": 38516,
+      "39": 16108,
+      "4": 127996,
+      "40": 29167,
+      "41": 10651,
+      "42": 14054,
+      "43": 5705,
+      "44": 7551,
+      "45": 3646,
+      "46": 4207,
+      "47": 2514,
+      "48": 3531,
+      "49": 2127,
+      "5": 949569,
+      "50": 2950,
+      "51": 1855,
+      "52": 2715,
+      "53": 1724,
+      "54": 2337,
+      "55": 1690,
+      "56": 2525,
+      "57": 1721,
+      "58": 2280,
+      "59": 1717,
+      "6": 5243568,
+      "60": 2506,
+      "61": 1654,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1968914,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5693320,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1525235,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 56433,
+      "7": 29411082,
+      "9": 127996
+    },
+    "connectivity_max": 134636336,
+    "connectivity_min": 0,
+    "n_cells": 29595511,
+    "n_connectivity_values": 328452583,
+    "n_fan_triangles": 269261561,
+    "n_points": 134636337
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4769167925605616e-11,
+    "float64_area_closure_relative": 5.748177339003956e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 269261561,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944246.0167615013,
+    "surface_area_float64_in2": 1944246.0168291011,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944246.01682909,
+    "zero_area_triangles": 224210,
+    "zero_weight_points": 4758
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC179_AoA_8.json b/surface_dual_areas/cases/geo_LHC179_AoA_8.json
new file mode 100644
index 0000000000000000000000000000000000000000..be42a04b781253dde2e020f4b1cfd591d47746f5
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC179_AoA_8.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC179_AoA_8",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC179_AoA_8/boundary_dual_area_geo_LHC179_AoA_8.npy",
+    "sha256": "3a3124dc7826952e03aefc476bc62faa7fbbaaed9d374c69499d883fa435929b",
+    "shape": [
+      135335921
+    ],
+    "size_bytes": 541343812
+  },
+  "runtime": {
+    "accumulation_seconds": 10.437174519058317,
+    "completed_at_utc": "2026-08-07T09:02:49.997356Z",
+    "elapsed_seconds": 21.649769559968263,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.0808546610642225,
+    "geometry_read_seconds": 2.604703556979075,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T09:02:28.347497Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC179_AoA_8/boundary_geo_LHC179_AoA_8.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC179_AoA_8.vtu",
+    "extracted_vtu_mtime_ns": 1783624721000000000,
+    "extracted_vtu_size_bytes": 20774503858,
+    "geometry_sha256": "bc5d0599be7e08079251146fa2cd30f927f995b0505ccd7997279a63667800f4",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 2768121,
+      "100": 45,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 890970,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2153329,
+      "13": 760044,
+      "14": 1787471,
+      "15": 567033,
+      "16": 1077396,
+      "17": 391450,
+      "18": 773948,
+      "19": 311193,
+      "20": 682894,
+      "21": 227966,
+      "22": 360908,
+      "23": 123649,
+      "24": 205305,
+      "25": 70862,
+      "26": 90931,
+      "27": 51401,
+      "28": 123311,
+      "29": 52680,
+      "3": 54345,
+      "30": 115200,
+      "31": 49438,
+      "32": 109219,
+      "33": 39067,
+      "34": 67048,
+      "35": 28269,
+      "36": 63161,
+      "37": 22895,
+      "38": 38516,
+      "39": 16107,
+      "4": 125978,
+      "40": 29167,
+      "41": 10652,
+      "42": 14054,
+      "43": 5705,
+      "44": 7551,
+      "45": 3646,
+      "46": 4207,
+      "47": 2514,
+      "48": 3530,
+      "49": 2127,
+      "5": 949558,
+      "50": 2951,
+      "51": 1855,
+      "52": 2715,
+      "53": 1724,
+      "54": 2337,
+      "55": 1690,
+      "56": 2525,
+      "57": 1721,
+      "58": 2280,
+      "59": 1717,
+      "6": 5252784,
+      "60": 2506,
+      "61": 1654,
+      "62": 2231,
+      "63": 1636,
+      "64": 2177,
+      "65": 1375,
+      "66": 1818,
+      "67": 1099,
+      "68": 1464,
+      "69": 904,
+      "7": 1977733,
+      "70": 1023,
+      "71": 572,
+      "72": 657,
+      "73": 441,
+      "74": 421,
+      "75": 303,
+      "76": 302,
+      "77": 219,
+      "78": 225,
+      "79": 150,
+      "8": 5746272,
+      "80": 192,
+      "81": 121,
+      "82": 141,
+      "83": 116,
+      "84": 116,
+      "85": 79,
+      "86": 96,
+      "87": 59,
+      "88": 70,
+      "89": 59,
+      "9": 1540701,
+      "90": 59,
+      "91": 56,
+      "92": 54,
+      "93": 50,
+      "94": 51,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 54345,
+      "7": 29614607,
+      "9": 125978
+    },
+    "connectivity_max": 135335920,
+    "connectivity_min": 0,
+    "n_cells": 29794930,
+    "n_connectivity_values": 330250589,
+    "n_fan_triangles": 270660729,
+    "n_points": 135335921
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 3.4061904851103726e-11,
+    "float64_area_closure_relative": 4.790148098301354e-15,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 270660729,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1944245.8885853956,
+    "surface_area_float64_in2": 1944245.8886516204,
+    "weight_max_in2": 1.1017823754058682,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1944245.888651611,
+    "zero_area_triangles": 224239,
+    "zero_weight_points": 4801
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC180_AoA_10.json b/surface_dual_areas/cases/geo_LHC180_AoA_10.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d5212e27ccf546b9035b254c192715686b4ced6
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC180_AoA_10.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC180_AoA_10",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC180_AoA_10/boundary_dual_area_geo_LHC180_AoA_10.npy",
+    "sha256": "3b56fa610c5572c17bfea0d5c5eab04fcd60fde67565006b2321169b4e30aae1",
+    "shape": [
+      145831964
+    ],
+    "size_bytes": 583327984
+  },
+  "runtime": {
+    "accumulation_seconds": 11.29363631689921,
+    "completed_at_utc": "2026-08-07T09:03:58.934366Z",
+    "elapsed_seconds": 21.582711842143908,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 3.2297734247986227,
+    "geometry_read_seconds": 1.979293341981247,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "5",
+    "slurm_job_id": "5945300",
+    "started_at_utc": "2026-08-07T09:03:37.351570Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC180_AoA_10/boundary_geo_LHC180_AoA_10.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC180_AoA_10.vtu",
+    "extracted_vtu_mtime_ns": 1783624659000000000,
+    "extracted_vtu_size_bytes": 22405116138,
+    "geometry_sha256": "26e14c32010f385b87fc6b944f05827d3246293bddc114a3988667c448dc84ed",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 3952579,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1302913,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2754385,
+      "13": 887254,
+      "14": 1520889,
+      "15": 525461,
+      "16": 967409,
+      "17": 368667,
+      "18": 728777,
+      "19": 293947,
+      "20": 658523,
+      "21": 218044,
+      "22": 356836,
+      "23": 119842,
+      "24": 199863,
+      "25": 69220,
+      "26": 91362,
+      "27": 51788,
+      "28": 123887,
+      "29": 53060,
+      "3": 58078,
+      "30": 114536,
+      "31": 49248,
+      "32": 107885,
+      "33": 38431,
+      "34": 66115,
+      "35": 27739,
+      "36": 62159,
+      "37": 22882,
+      "38": 38925,
+      "39": 16547,
+      "4": 134573,
+      "40": 30216,
+      "41": 10933,
+      "42": 14607,
+      "43": 5952,
+      "44": 7911,
+      "45": 3680,
+      "46": 4315,
+      "47": 2536,
+      "48": 3513,
+      "49": 2147,
+      "5": 954648,
+      "50": 2921,
+      "51": 1834,
+      "52": 2783,
+      "53": 1796,
+      "54": 2484,
+      "55": 1729,
+      "56": 2589,
+      "57": 1734,
+      "58": 2294,
+      "59": 1694,
+      "6": 5310118,
+      "60": 2440,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2093304,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6504743,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 1907682,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 58078,
+      "7": 32690202,
+      "9": 134573
+    },
+    "connectivity_max": 145831963,
+    "connectivity_min": 0,
+    "n_cells": 32882853,
+    "n_connectivity_values": 357418501,
+    "n_fan_triangles": 291652795,
+    "n_points": 145831964
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.6309625082267955e-11,
+    "float64_area_closure_relative": 3.9783156452162325e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 291652795,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948880.1605367332,
+    "surface_area_float64_in2": 1948880.1606269851,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948880.1606269076,
+    "zero_area_triangles": 233682,
+    "zero_weight_points": 5613
+  }
+}
diff --git a/surface_dual_areas/cases/geo_LHC180_AoA_12.json b/surface_dual_areas/cases/geo_LHC180_AoA_12.json
new file mode 100644
index 0000000000000000000000000000000000000000..447fef5d15115770f62fa28b406d6d03bf3619f3
--- /dev/null
+++ b/surface_dual_areas/cases/geo_LHC180_AoA_12.json
@@ -0,0 +1,191 @@
+{
+  "algorithm_id": "native-point-fan-barycentric-dual-area-v1",
+  "association": "point",
+  "case_id": "geo_LHC180_AoA_12",
+  "payload": {
+    "dtype": "float32",
+    "format": "npy",
+    "path": "geo_LHC180_AoA_12/boundary_dual_area_geo_LHC180_AoA_12.npy",
+    "sha256": "89feab11ea01ea9a972db58dea97f3649e35affe795fc093e296a4358f78f52b",
+    "shape": [
+      148821955
+    ],
+    "size_bytes": 595287948
+  },
+  "runtime": {
+    "accumulation_seconds": 13.593352776020765,
+    "completed_at_utc": "2026-08-07T09:03:41.916415Z",
+    "elapsed_seconds": 50.910328730009496,
+    "excluded_system_dist_packages": true,
+    "geometry_hash_seconds": 4.011150929844007,
+    "geometry_read_seconds": 27.782201007939875,
+    "hostname": "cpu-0007",
+    "numpy": "2.2.6",
+    "platform": "Linux-6.8.0-1028-nvidia-64k-aarch64-with-glibc2.39",
+    "python": "3.12.3",
+    "slurm_array_job_id": "5945281",
+    "slurm_array_task_id": "6",
+    "slurm_job_id": "5945301",
+    "started_at_utc": "2026-08-07T09:02:51.005993Z"
+  },
+  "schema_version": 1,
+  "source": {
+    "archive_path": "geo_LHC180_AoA_12/boundary_geo_LHC180_AoA_12.vtu.tgz",
+    "archive_sha256": null,
+    "cell_type_dtype": "|u1",
+    "connectivity_dtype": "<i8",
+    "coordinate_dtype": "<f4",
+    "extracted_vtu_filename": "boundary_geo_LHC180_AoA_12.vtu",
+    "extracted_vtu_mtime_ns": 1783624679000000000,
+    "extracted_vtu_size_bytes": 22870245181,
+    "geometry_sha256": "a36ba38fb8aafd1c9c928ba62e4caf77507fd9586d9cef16cb7df6e8829bd01d",
+    "offset_dtype": "<i8"
+  },
+  "status": "complete",
+  "topology": {
+    "cell_arity_histogram": {
+      "10": 4330447,
+      "100": 44,
+      "101": 31,
+      "102": 40,
+      "103": 32,
+      "104": 43,
+      "105": 29,
+      "106": 47,
+      "107": 21,
+      "108": 40,
+      "109": 13,
+      "11": 1415159,
+      "110": 32,
+      "111": 12,
+      "112": 7,
+      "113": 6,
+      "115": 1,
+      "116": 1,
+      "12": 2927091,
+      "13": 900081,
+      "14": 1413172,
+      "15": 494730,
+      "16": 933631,
+      "17": 359864,
+      "18": 725857,
+      "19": 292980,
+      "20": 657355,
+      "21": 217570,
+      "22": 355723,
+      "23": 119633,
+      "24": 199234,
+      "25": 69049,
+      "26": 91318,
+      "27": 51763,
+      "28": 123887,
+      "29": 53056,
+      "3": 61464,
+      "30": 114533,
+      "31": 49252,
+      "32": 107888,
+      "33": 38429,
+      "34": 66113,
+      "35": 27737,
+      "36": 62158,
+      "37": 22883,
+      "38": 38926,
+      "39": 16547,
+      "4": 137130,
+      "40": 30216,
+      "41": 10933,
+      "42": 14607,
+      "43": 5952,
+      "44": 7911,
+      "45": 3680,
+      "46": 4315,
+      "47": 2536,
+      "48": 3513,
+      "49": 2148,
+      "5": 957109,
+      "50": 2921,
+      "51": 1833,
+      "52": 2783,
+      "53": 1796,
+      "54": 2484,
+      "55": 1729,
+      "56": 2589,
+      "57": 1734,
+      "58": 2294,
+      "59": 1694,
+      "6": 5325828,
+      "60": 2440,
+      "61": 1664,
+      "62": 2196,
+      "63": 1587,
+      "64": 2150,
+      "65": 1369,
+      "66": 1771,
+      "67": 1095,
+      "68": 1503,
+      "69": 880,
+      "7": 2142800,
+      "70": 1008,
+      "71": 541,
+      "72": 693,
+      "73": 447,
+      "74": 396,
+      "75": 310,
+      "76": 300,
+      "77": 220,
+      "78": 227,
+      "79": 153,
+      "8": 6723186,
+      "80": 178,
+      "81": 120,
+      "82": 139,
+      "83": 113,
+      "84": 118,
+      "85": 79,
+      "86": 100,
+      "87": 57,
+      "88": 70,
+      "89": 58,
+      "9": 2033151,
+      "90": 58,
+      "91": 56,
+      "92": 56,
+      "93": 50,
+      "94": 52,
+      "95": 30,
+      "96": 64,
+      "97": 27,
+      "98": 50,
+      "99": 42
+    },
+    "cell_type_histogram": {
+      "5": 61464,
+      "7": 33588674,
+      "9": 137130
+    },
+    "connectivity_max": 148821954,
+    "connectivity_min": 0,
+    "n_cells": 33787268,
+    "n_connectivity_values": 365207313,
+    "n_fan_triangles": 297632777,
+    "n_points": 148821955
+  },
+  "units": "in^2",
+  "validation": {
+    "float32_area_closure_relative": 4.6172492087798945e-11,
+    "float64_area_closure_relative": 9.796456620634684e-14,
+    "invalid_connectivity": 0,
+    "lhc006_aoa4_reference_difference_in2": null,
+    "n_fan_triangles": 297632777,
+    "negative_weight_points": 0,
+    "nonfinite_triangles": 0,
+    "nonfinite_weight_points": 0,
+    "stored_weight_sum_float64_in2": 1948879.428355888,
+    "surface_area_float64_in2": 1948879.4284458726,
+    "weight_max_in2": 1.100719469302891,
+    "weight_min_in2": 0.0,
+    "weight_sum_float64_in2": 1948879.4284456817,
+    "zero_area_triangles": 238407,
+    "zero_weight_points": 5820
+  }
+}