diff --git "a/build/webgpu/test.json" "b/build/webgpu/test.json"
--- "a/build/webgpu/test.json"
+++ "b/build/webgpu/test.json"
@@ -1,9 +1,45 @@
 {
-  "op": "ai.onnx.Unique",
   "fixtureArrays": {
+    "axis0_f32_hash_sorted_duplicate_rows_input_x": [27.25, 46, -4.125, -24, 13.5, 27.5, -13.375, -32.125, 61.125, 25, -18.125, 21.625, 62.25, -35.75, -48.375, 47.125, -45, 13.25, 54.125, 37.875, 41.25, 4, -63.5, 50.75, -0.5, 12.125, -27.375, -7.75, -49.75, 20.25, 42.625, -59, 40.125, -40.25, -19.25, 6.25, 48.25, 28.625, 58.875, -61.25, -28.5, 20.5, -52, 15.75, 30.875, -56.5, -15.875, -0.75, -54.25, -31, 19.125, -42.5, -62.375, 44.875, -3, -42.75, -41.375, 6.5, -55.375, 2.875, -57.875, -46.125, -14.5, -6.375, -33.25, 35.625, -21.75, -8.875, -1.875, -36.875, 9.875, 55.25, -20.375, 5.125, 26.125, -25.125, 56.625, 63.625, 57.75, -49.5, -21.5, 11, -38, -60.125, -35.5, 14.625, -50.875, -47.25, -56.75, -14.75, 48.5, -28.75, -43.875, 60, 16.875, -29.875, -10, -34.375, 0.625, -22.875, 53, 49.625, 29.75, 34.25, -17, 39, 55.5, 18, 33.125, 43.75, -11.125, 32, 8.75, 23.875, 41.5, 36.75, 34.5, 7.625, -7.5, -53.125, 22.75, -5.25, -26.25, 1.75, 51.875, -39.125, 62.5, -12.25],
+    "axis_nan_ordered_y_float32_nan_head_later_inner_sorted0_input_x": [5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0, 1, 0, "NaN", 9, 3, 0, 5, 0],
+    "axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted0_input_x": ["NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, "NaN", 1, -1, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5],
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+    "axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted0_input_x": [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5, "NaN", 3, 0, 5],
+    "compact_incomplete_first_chunk33": [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -3],
+    "metadata_scrambled_cycle65": [0, 37, 9, 46, 18, 55, 27, 64, 36, 8, 45, 17, 54, 26, 63, 35, 7, 44, 16, 53, 25, 62, 34, 6, 43, 15, 52, 24, 61, 33, 5, 42, 14, 51, 23, 60, 32, 4, 41, 13, 50, 22, 59, 31, 3, 40, 12, 49, 21, 58, 30, 2, 39, 11, 48, 20, 57, 29, 1, 38, 10, 47, 19, 56, 28],
     "ort_axis1_unsorted_f32_input_x": [1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1],
+    "scalar_hash_bool_finite_mask7_flat_sorted0_input_x": [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1],
+    "scalar_hash_float32_finite_mask0_flat_sorted0_input_x": [5, 0, 1, -3, 5, 0, 2, 5, 0, 1, -3, 5, 0, 2, 5, 0, 1, -3, 5, 0, 2, 5, 0, 1, -3, 5, 0, 2, 5, 0, 1, -3, 5],
+    "scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices": [4, 1, 2, 0, 4, 1, 3, 4, 1, 2, 0, 4, 1, 3, 4, 1, 2, 0, 4, 1, 3, 4, 1, 2, 0, 4, 1, 3, 4, 1, 2, 0, 4],
+    "scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices": [0, 1, 2, 3, 0, 1, 4, 0, 1, 2, 3, 0, 1, 4, 0, 1, 2, 3, 0, 1, 4, 0, 1, 2, 3, 0, 1, 4, 0, 1, 2, 3, 0],
+    "scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x": [5, "NaN", 1, "NaN", 3, -2, "NaN", 5, "NaN", 1, "NaN", 3, -2, "NaN", 5, "NaN", 1, "NaN", 3, -2, "NaN", 5, "NaN", 1, "NaN", 3, -2, "NaN", 5, "NaN", 1, "NaN", 3],
+    "scalar_hash_float32_later_nan_mask7_axis_sorted1_output_inverse_indices": [3, 3, 1, 1, 2, 0, 0, 3, 0, 1, 0, 2, 0, 0, 3, 0, 1, 0, 2, 0, 0, 3, 0, 1, 0, 2, 0, 0, 3, 0, 1, 0, 2],
+    "scalar_hash_float32_later_nan_mask7_flat_sorted0_output_inverse_indices": [0, 0, 1, 1, 2, 3, 3, 0, 3, 1, 3, 2, 3, 3, 0, 3, 1, 3, 2, 3, 3, 0, 3, 1, 3, 2, 3, 3, 0, 3, 1, 3, 2],
+    "scalar_hash_float32_leading_nan_mask7_axis_sorted0_input_x": ["NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN", 5, 1, -2, "NaN"],
+    "scalar_hash_hybrid_tile1_input_x": [7, 2, 7, 5, -1, 0, 9, 7, 2, 7, 5, -1, 0, 9, 7, 2, 7, 5, -1, 0, 9, 7, 2, 7, 5, -1, 0, 9, 7, 2, 7, 5, -1, 0, 9],
+    "scalar_hash_int16_finite_mask7_axis_sorted1_output_inverse_indices": [0, 4, 1, 2, 0, 3, 0, 4, 1, 2, 0, 3, 0, 4, 1, 2, 0, 3, 0, 4, 1, 2, 0, 3, 0, 4, 1, 2, 0, 3, 0, 4, 1],
+    "scalar_hash_int16_finite_mask7_flat_sorted0_input_x": [-32768, 32767, -1, 0, -32768, 7, -32768, 32767, -1, 0, -32768, 7, -32768, 32767, -1, 0, -32768, 7, -32768, 32767, -1, 0, -32768, 7, -32768, 32767, -1, 0, -32768, 7, -32768, 32767, -1],
+    "scalar_hash_int32_finite_mask7_flat_sorted0_input_x": [-1, -2147483648, 2147483647, 0, -1, 7, -1, -2147483648, 2147483647, 0, -1, 7, -1, -2147483648, 2147483647, 0, -1, 7, -1, -2147483648, 2147483647, 0, -1, 7, -1, -2147483648, 2147483647, 0, -1, 7, -1, -2147483648, 2147483647],
+    "scalar_hash_int32_finite_mask7_flat_sorted0_output_inverse_indices": [0, 1, 2, 3, 0, 4, 0, 1, 2, 3, 0, 4, 0, 1, 2, 3, 0, 4, 0, 1, 2, 3, 0, 4, 0, 1, 2, 3, 0, 4, 0, 1, 2],
+    "scalar_hash_int8_finite_mask7_flat_sorted0_input_x": [-128, 127, -1, 0, -128, 7, -128, 127, -1, 0, -128, 7, -128, 127, -1, 0, -128, 7, -128, 127, -1, 0, -128, 7, -128, 127, -1, 0, -128, 7, -128, 127, -1],
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272, 271, 270, 269, 268, 267, 266, 265, 264, 263, 262, 261, 260, 259, 258, 257, 256, 255, 254, 253, 252, 251, 250, 249, 248, 247, 246, 245, 244, 243, 242, 241, 240, 239, 238, 237, 236, 235, 234, 233, 232, 231, 230, 229, 228, 227, 226, 225, 224, 223, 222, 221, 220, 219, 218, 217, 216, 215, 214, 213, 212, 211, 210, 209, 208, 207, 206, 205, 204, 203, 202, 201, 200, 199, 198, 197, 196, 195, 194, 193, 192, 191, 190, 189, 188, 187, 186, 185, 184, 183, 182, 181, 180, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
   },
   "cases": [
     {
@@ -440,7 +476,7 @@
       "provenance": {
         "source": "onnxruntime/test/providers/cpu/tensor/unique_op_test.cc",
         "test": "Unique.Flatten_Unsorted",
-        "notes": "Large-input companion to the scalar subnormal case: the exact serial float comparator keeps finite subnormal values distinct from zero and emits three first-seen buckets."
+        "notes": "A 4,096-element cycle of zero and signed subnormal values verifies that the serial float comparator keeps finite subnormals distinct from zero and emits three first-seen buckets."
       },
       "inputs": {
         "x": { "dtype": "float32", "shape": [4096], "data": { "kind": "cycle", "values": [0.0, 1e-40, 0.0, -1e-40] } }
@@ -473,7 +509,7 @@
       "name": "serial_unsorted_first_seen_f32_32k_subnormal",
       "attrs": { "sorted": 0 },
       "provenance": {
-        "notes": "First-seen-order companion for the exact serial float path: comparator-order buckets are reordered by representative input index for sorted=0."
+        "notes": "A 32,768-element subnormal cycle verifies that the serial float path orders output buckets by representative input index when sorted is disabled."
       },
       "inputs": {
         "x": {
@@ -512,7 +548,7 @@
       "name": "hash_sorted_int32_32k",
       "attrs": { "sorted": 1 },
       "provenance": {
-        "notes": "32768 int32 elements cycling 48 distinct values: exercises the hash-set parallel dedup (numel >= 32768 floor) for the sorted flatten path. Bit-exact vs the CPU reference."
+        "notes": "A 32,768-element int32 input cycling 48 distinct values exercises sorted parallel hash deduplication with an exact integer result."
       },
       "inputs": {
         "x": {
@@ -618,7 +654,7 @@
       "name": "axis0_f32_subnormal_collapse_sorted",
       "attrs": { "axis": 0, "sorted": 1 },
       "provenance": {
-        "notes": "Sorted companion to the subnormal axis case. Raw-bit equality and total-order keys preserve -1e-40 < 0 < 1e-40 on FTZ GPUs; the pinned output is cross-checked with ORT."
+        "notes": "Raw-bit equality and total-order keys preserve -1e-40 < 0 < 1e-40 when arithmetic operations flush subnormals to zero."
       },
       "inputs": {
         "x": {
@@ -640,7 +676,7 @@
       "name": "hash_int8_signed_negatives_32k",
       "attrs": { "sorted": 1 },
       "provenance": {
-        "notes": "Exercises hash deduplication at 32768 elements with 12 signed int8 values, including -128, 127, and other negatives. The TypeScript reference is the oracle because ORT CPU does not implement Unique for int8."
+        "notes": "Hash deduplication over 32,768 int8 elements must sort 12 distinct values, including -128, 127, and other negatives. Expected values follow the operator's sorting rule."
       },
       "inputs": {
         "x": {
@@ -655,7 +691,7 @@
       "name": "parallel_uint32_sentinel_first_seen_4k",
       "attrs": { "sorted": 0 },
       "provenance": {
-        "notes": "Exercises grid-parallel deduplication below the hash threshold with 0xffffffff present in first-seen order. The TypeScript reference is the oracle because ORT CPU does not implement Unique for uint32."
+        "notes": "Parallel deduplication over 4,096 uint32 elements must preserve first-seen order, including 0xffffffff. Expected values follow the operator's ordering rule."
       },
       "inputs": {
         "x": {
@@ -691,7 +727,7 @@
     {
       "name": "serial_f32_32k_signed_zero_single_bucket",
       "provenance": {
-        "notes": "32768 f32 elements containing both +0.0 and -0.0 plus finite values verify that exact serial equality canonicalizes signed zero into one bucket, matching ORT."
+        "notes": "32768 f32 elements containing both +0.0 and -0.0 plus finite values verify that exact serial equality canonicalizes signed zero into one bucket."
       },
       "attrs": { "sorted": 1 },
       "inputs": {
@@ -793,7 +829,7 @@
     {
       "name": "axis0_large_y_int32_unsorted_2100_distinct",
       "provenance": {
-        "notes": "axis=0 output axis dim 2100 > 2048 with sorted=0 selects axis_bounded_large's no-bitonic branch: parallel compaction gathers the first-occurrence slice indices in appearance order and scatters them from GLOBAL slots scratch, skipping the sort network. inner=1 so flat-unique == axis-unique (reference exact). Validates the unsorted large-axis path at multi-chunk scale against the single-lane unique-axis kernel."
+        "notes": "An axis length of 2,100 with sorted=0 requires multi-chunk parallel compaction without a sort network. Because each slice has one element, the distinct values must be emitted in first-occurrence order."
       },
       "attrs": { "axis": 0, "sorted": 0 },
       "inputs": {
@@ -815,7 +851,7 @@
     {
       "name": "axis_hash_split_scatter_unsorted_four_distinct",
       "provenance": {
-        "notes": "Unsorted companion for grid-parallel axis scatter: four distinct scalar rows are emitted in first-occurrence order into an exact four-row output."
+        "notes": "Four distinct scalar rows exercise grid-parallel axis scatter and must be emitted in first-occurrence order into an exact four-row output."
       },
       "attrs": { "axis": 0, "sorted": 0 },
       "inputs": {
@@ -826,7 +862,7 @@
     {
       "name": "axis_hash_int32_inner2_duplicate_rows_sorted",
       "provenance": {
-        "notes": "Routes the >=2048-axis exact hash dedup with vector-valued slices. Repeated rows must share one hash bucket, first-occurrence representatives must survive, and sorted output remains lexicographic over the complete two-element slice. Pinned values avoid relying on the flattened TypeScript Unique reference for axis semantics."
+        "notes": "An axis length of 2,048 exercises exact hash deduplication for two-element rows. Repeated rows must share a bucket, first-occurrence representatives must survive, and sorted output must be lexicographic over complete rows."
       },
       "attrs": { "axis": 0, "sorted": 1 },
       "inputs": {
@@ -896,9 +932,9 @@
       "outputs": { "y": { "dtype": "float32", "shape": [1025, 1], "tolerance": 0 } }
     },
     {
-      "name": "axis0_rows65537_over_hash_ceiling_large_y",
+      "name": "axis0_rows65537_above_old_hash_ceiling",
       "provenance": {
-        "notes": "65537 rows exceed the axis hash-table ceiling, while exactly 2049 distinct rows keep the output above the local crossover; this selects the global axis fallback with an exact result."
+        "notes": "A 65,537-row input cycling 2,049 distinct values exercises large-axis hash deduplication and sorted output."
       },
       "attrs": { "axis": 0, "sorted": 1 },
       "inputs": {
@@ -1548,7 +1584,7 @@
     {
       "name": "axis0_f32_hash_unsorted_first_occurrence",
       "provenance": {
-        "notes": "Unsorted companion on the float axis hash route: the same 64 distinct rows must come back in first-occurrence order from the compaction scan alone."
+        "notes": "A 2,560-row float input cycling 64 distinct two-element rows must emit them in first-occurrence order through the hash compaction scan."
       },
       "attrs": { "axis": 0, "sorted": 0 },
       "inputs": {
@@ -1616,6 +1652,5678 @@
         }
       },
       "outputs": { "y": { "dtype": "float32", "shape": [2, 40], "tolerance": 0 } }
+    },
+    {
+      "name": "parallel_metadata_indices_int32_sorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests first indices from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "parallel_metadata_inverse_int32_unsorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests the inverse map from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [512] }
+      }
+    },
+    {
+      "name": "parallel_metadata_counts_int32_sorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests counts from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "parallel_metadata_indices_inverse_int32_unsorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests first indices and the inverse map from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] },
+        "inverse_indices": { "dtype": "uint32", "shape": [512] }
+      }
+    },
+    {
+      "name": "parallel_metadata_indices_counts_int32_sorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests first indices and counts from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "parallel_metadata_inverse_counts_int32_unsorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests the inverse map and counts from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [512] },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "parallel_metadata_all_int32_sorted",
+      "provenance": {
+        "notes": "A scrambled 65-value cycle over 512 elements gives uneven counts and makes first-occurrence order differ from sorted order. This case requests first indices, the inverse map, and counts from the parallel integer-dedup route."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [512],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] },
+        "inverse_indices": { "dtype": "uint32", "shape": [512] },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "hash_metadata_inverse_int32_unsorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests the inverse map."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [32768] }
+      }
+    },
+    {
+      "name": "hash_metadata_counts_int32_sorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests counts."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "hash_metadata_all_int32_unsorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests first indices, the inverse map, and counts."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] },
+        "inverse_indices": { "dtype": "uint32", "shape": [32768] },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "hash_metadata_indices_int32_sorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests first indices."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "hash_metadata_indices_inverse_int32_unsorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests first indices and the inverse map."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] },
+        "inverse_indices": { "dtype": "uint32", "shape": [32768] }
+      }
+    },
+    {
+      "name": "hash_metadata_indices_counts_int32_sorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests first indices and counts."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "indices": { "dtype": "uint32", "shape": [65] },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "hash_metadata_inverse_counts_int32_unsorted",
+      "provenance": {
+        "notes": "The smallest hash-route input uses a scrambled 65-value cycle, giving uneven counts and distinct first-occurrence and sorted orders. This case requests the inverse map and counts."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [32768],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/metadata_scrambled_cycle65" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "int32", "shape": [65], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [32768] },
+        "counts": { "dtype": "uint32", "shape": [65] }
+      }
+    },
+    {
+      "name": "axis0_f32_rows70000_above_old_hash_ceiling",
+      "provenance": {
+        "notes": "A 70,000-row float input cycling eight one-element rows exercises large-axis hash deduplication and lexicographic sorted output."
+      },
+      "attrs": { "axis": 0, "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [70000, 1],
+          "data": { "kind": "cycle", "values": [-4.0, -2.5, -1.0, 0.0, 1.5, 2.0, 3.25, 8.0] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [8, 1], "tolerance": 0 } }
+    },
+    {
+      "name": "flat_i32_70000_distinct_above_old_ceiling",
+      "provenance": {
+        "notes": "A flat 70,000-element input with every value distinct exercises large-output parallel deduplication and sorted emission."
+      },
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": { "dtype": "int32", "shape": [70000], "data": { "kind": "linspace", "start": -35000, "end": 34999 } }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [70000], "tolerance": 0 } }
+    },
+    {
+      "name": "flat_i32_above_old_input_length_ceiling",
+      "provenance": {
+        "notes": "A 1,049,600-element class-label stream cycling six values exercises large-input parallel deduplication and first-occurrence output."
+      },
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1049600],
+          "data": { "kind": "cycle", "values": [7, -3, 0, 11, -3, 42, 7, 5] }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [6], "tolerance": 0 } }
+    },
+    {
+      "name": "hash_float32_sorted0_leading_nan_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["NaN", 5.0, 1.0, "NaN", "-Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [1], "tolerance": 0, "allowNaN": true } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted0_later_nan_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [5.0, "NaN", 1.0, 3.0, "NaN", 1.0] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [3], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted0_negative_zero_first_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [-0.0, 0.0, 1e-40, -1e-40, "Infinity", "-Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted0_positive_zero_first_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [0.0, -0.0, -1e-40, 1e-40, "-Infinity", "Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted0_infinity_duplicates_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["Infinity", "-Infinity", 2.0, -3.0, "Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [4], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted1_leading_nan_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["NaN", 5.0, 1.0, "NaN", "-Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [1], "tolerance": 0, "allowNaN": true } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted1_later_nan_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [5.0, "NaN", 1.0, 3.0, "NaN", 1.0] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [3], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted1_negative_zero_first_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [-0.0, 0.0, 1e-40, -1e-40, "Infinity", "-Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted1_positive_zero_first_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [0.0, -0.0, -1e-40, 1e-40, "-Infinity", "Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted1_infinity_duplicates_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["Infinity", "-Infinity", 2.0, -3.0, "Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [4], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted0_leading_nan_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["NaN", 5.0, 1.0, "NaN", "-Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [1], "tolerance": 0, "allowNaN": true } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted0_later_nan_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [5.0, "NaN", 1.0, 3.0, "NaN", 1.0] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [3], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted0_negative_zero_first_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "cycle",
+            "values": [-0.0, 0.0, 5.960464477539063e-8, -5.960464477539063e-8, "Infinity", "-Infinity"]
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted0_positive_zero_first_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "cycle",
+            "values": [0.0, -0.0, -5.960464477539063e-8, 5.960464477539063e-8, "-Infinity", "Infinity"]
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted0_infinity_duplicates_tail33",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["Infinity", "-Infinity", 2.0, -3.0, "Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [4], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted1_leading_nan_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["NaN", 5.0, 1.0, "NaN", "-Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [1], "tolerance": 0, "allowNaN": true } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted1_later_nan_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": [5.0, "NaN", 1.0, 3.0, "NaN", 1.0] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [3], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted1_negative_zero_first_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "cycle",
+            "values": [-0.0, 0.0, 5.960464477539063e-8, -5.960464477539063e-8, "Infinity", "-Infinity"]
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted1_positive_zero_first_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "cycle",
+            "values": [0.0, -0.0, -5.960464477539063e-8, 5.960464477539063e-8, "-Infinity", "Infinity"]
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [5], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float16_sorted1_infinity_duplicates_tail33",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "cycle", "values": ["Infinity", "-Infinity", 2.0, -3.0, "Infinity"] }
+        }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [4], "tolerance": 0 } },
+      "tunables": { "HASH_MIN_INPUT": 32 },
+      "provenance": {
+        "notes": "Small forced-hash fixture preserves ordered-map NaN semantics, IEEE subnormal identity, and the earliest signed-zero representative in the Y-only float path."
+      }
+    },
+    {
+      "name": "hash_float32_sorted0_compact_first_chunk_incomplete_tail33",
+      "provenance": {
+        "notes": "With 32 invocations, the first compact chunk contains only the representative 7. The distinct final -3 must be consumed from the second chunk before sorting or preserving appearance order."
+      },
+      "attrs": { "sorted": 0 },
+      "tunables": { "WORKGROUP_SIZE": 32, "HASH_MIN_INPUT": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/compact_incomplete_first_chunk33" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [7.0, -3.0] } }
+      }
+    },
+    {
+      "name": "hash_float32_sorted1_compact_first_chunk_incomplete_tail33",
+      "provenance": {
+        "notes": "With 32 invocations, the first compact chunk contains only the representative 7. The distinct final -3 must be consumed from the second chunk before sorting or preserving appearance order."
+      },
+      "attrs": { "sorted": 1 },
+      "tunables": { "WORKGROUP_SIZE": 32, "HASH_MIN_INPUT": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/compact_incomplete_first_chunk33" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [-3.0, 7.0] } }
+      }
+    },
+    {
+      "name": "hash_float16_sorted0_compact_first_chunk_incomplete_tail33",
+      "provenance": {
+        "notes": "With 32 invocations, the first compact chunk contains only the representative 7. The distinct final -3 must be consumed from the second chunk before sorting or preserving appearance order."
+      },
+      "attrs": { "sorted": 0 },
+      "tunables": { "WORKGROUP_SIZE": 32, "HASH_MIN_INPUT": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/compact_incomplete_first_chunk33" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [7.0, -3.0] } }
+      }
+    },
+    {
+      "name": "hash_float16_sorted1_compact_first_chunk_incomplete_tail33",
+      "provenance": {
+        "notes": "With 32 invocations, the first compact chunk contains only the representative 7. The distinct final -3 must be consumed from the second chunk before sorting or preserving appearance order."
+      },
+      "attrs": { "sorted": 1 },
+      "tunables": { "WORKGROUP_SIZE": 32, "HASH_MIN_INPUT": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/compact_incomplete_first_chunk33" } }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [-3.0, 7.0] } }
+      }
+    },
+    {
+      "name": "hybrid_sort_i32_extremes_sentinel_duplicates",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [8],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, -1, 9, -2147483648] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [5],
+          "data": { "kind": "values", "values": [-2147483648, -1, 0, 9, 2147483647] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior."
+      }
+    },
+    {
+      "name": "hybrid_sort_u32_real_max_before_padding",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "uint32",
+          "shape": [8],
+          "data": { "kind": "values", "values": [4294967295, 0, 2147483648, 4, 1, 4294967295, 0, 4] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "uint32",
+          "shape": [5],
+          "data": { "kind": "values", "values": [0, 1, 4, 2147483648, 4294967295] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior."
+      }
+    },
+    {
+      "name": "hybrid_sort_i32_underfilled_capacity_zero_tail",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [12],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, -1, 9, -2147483648, 9, 9, 0, -1] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [7],
+          "data": { "kind": "values", "values": [-2147483648, -1, 0, 9, 2147483647, 0, 0] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior."
+      }
+    },
+    {
+      "name": "hash_global_nonpower_tile_i32_extremes_sentinel_duplicates",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 3
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [8],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, -1, 9, -2147483648] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [5],
+          "data": { "kind": "values", "values": [-2147483648, -1, 0, 9, 2147483647] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior. Non-power-of-two tile3 rejects hybrid and pins sorted hash-only fallback."
+      }
+    },
+    {
+      "name": "hash_global_nonpower_tile_u32_real_max_before_padding",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 3
+      },
+      "inputs": {
+        "x": {
+          "dtype": "uint32",
+          "shape": [8],
+          "data": { "kind": "values", "values": [4294967295, 0, 2147483648, 4, 1, 4294967295, 0, 4] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "uint32",
+          "shape": [5],
+          "data": { "kind": "values", "values": [0, 1, 4, 2147483648, 4294967295] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior. Non-power-of-two tile3 rejects hybrid and pins sorted hash-only fallback."
+      }
+    },
+    {
+      "name": "hash_global_unsorted_first_seen_sentinel_zero_tail",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [12],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, -1, 9, -2147483648, 9, 9, 0, -1] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [7],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, 0, 0] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior. Unsorted output preserves appearance order, not numeric order, and zero-fills excess capacity."
+      }
+    },
+    {
+      "name": "hybrid_sort_network_tile1",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 1
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [8],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, -1, 9, -2147483648] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [5],
+          "data": { "kind": "values", "values": [-2147483648, -1, 0, 9, 2147483647] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior. Tile1 emits no shared passes; tile2 finishes one pair locally per tile."
+      }
+    },
+    {
+      "name": "hybrid_sort_network_tile2",
+      "attrs": { "sorted": 1 },
+      "tunables": {
+        "HASH_MIN_INPUT": 1,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_SORT_MAX_CAPACITY": 1,
+        "SORT_WORKGROUP": 32,
+        "WORKGROUP_SIZE": 32,
+        "GLOBAL_SORT_TILE": 2
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [8],
+          "data": { "kind": "values", "values": [-1, 2147483647, -2147483648, 9, 0, -1, 9, -2147483648] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [5],
+          "data": { "kind": "values", "values": [-2147483648, -1, 0, 9, 2147483647] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "Low HASH_MIN_INPUT/LOCAL_SORT_CROSSOVER/HASH_SORT_MAX_CAPACITY tunables exercise the large-output integer hash family on a bounded input; GLOBAL_SORT_TILE chooses the documented shared-tile or hash fallback boundary. Exact integer outputs pin sentinel, padding, and first-occurrence behavior. Tile1 emits no shared passes; tile2 finishes one pair locally per tile."
+      }
+    },
+    {
+      "name": "hybrid_sort_default_tile512_sorted513_signed_boundary",
+      "attrs": { "sorted": 1 },
+      "tunables": { "HASH_MIN_INPUT": 32, "LOCAL_SORT_CROSSOVER": 32, "HASH_SORT_MAX_CAPACITY": 32 },
+      "inputs": { "x": { "dtype": "int32", "shape": [513], "data": { "kind": "linspace", "start": 256, "end": -256 } } },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [513],
+          "tolerance": 0,
+          "data": { "kind": "linspace", "start": -256, "end": 256 }
+        }
+      },
+      "provenance": {
+        "notes": "Lower input and collected-key crossover tunables admit the global integer family while retaining the default512-record shared tile and default256-lane WG.513 distinct descending signed values cross two512-record padded sort tiles and exercise the final real/padding boundary."
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_finite_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 7, 1],
+          "data": { "kind": "values", "values": [5.0, 1.0, 5.0, 3.0, -2.0, 1.0, 7.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_finite_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 7, 1],
+          "data": { "kind": "values", "values": [5.0, 1.0, 5.0, 3.0, -2.0, 1.0, 7.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_later_nan_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 8, 1],
+          "data": { "kind": "values", "values": [5.0, "NaN", 1.0, "NaN", 3.0, -2.0, "NaN", 5.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 4, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [8], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_later_nan_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 8, 1],
+          "data": { "kind": "values", "values": [5.0, "NaN", 1.0, "NaN", 3.0, -2.0, "NaN", 5.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 4, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [8], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_leading_nan_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "data": { "kind": "values", "values": ["NaN", 5.0, 1.0, "NaN", -2.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 1, 1], "tolerance": 0, "allowNaN": true },
+        "inverse_indices": { "dtype": "uint32", "shape": [5], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_leading_nan_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "data": { "kind": "values", "values": ["NaN", 5.0, 1.0, "NaN", -2.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 1, 1], "tolerance": 0, "allowNaN": true },
+        "inverse_indices": { "dtype": "uint32", "shape": [5], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_local_sort_below_crossover_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "provenance": {
+        "notes": "A slice count at or below LOCAL_SORT_CROSSOVER keeps the single-workgroup local-sort metadata route while the distinct slices still give every inverse index its own answer."
+      },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 6, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 7, 1],
+          "data": { "kind": "values", "values": [5.0, 1.0, 5.0, 3.0, -2.0, 1.0, 7.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_zero_subnormal_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 9, 1],
+          "data": {
+            "kind": "values",
+            "values": [-0.0, 0.0, 1.401298464324817e-45, -1.401298464324817e-45, 1.401298464324817e-45, "Infinity", "-Infinity", 1.0, -1.0]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 7, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [9], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_zero_subnormal_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 9, 1],
+          "data": {
+            "kind": "values",
+            "values": [-0.0, 0.0, 1.401298464324817e-45, -1.401298464324817e-45, 1.401298464324817e-45, "Infinity", "-Infinity", 1.0, -1.0]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 7, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [9], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_zero_reverse_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 7, 1],
+          "data": {
+            "kind": "values",
+            "values": [0.0, -0.0, -1.401298464324817e-45, 1.401298464324817e-45, 1.0, -1.0, "NaN"]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float32_zero_reverse_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 7, 1],
+          "data": {
+            "kind": "values",
+            "values": [0.0, -0.0, -1.401298464324817e-45, 1.401298464324817e-45, 1.0, -1.0, "NaN"]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_finite_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 7, 1],
+          "data": { "kind": "values", "values": [5.0, 1.0, 5.0, 3.0, -2.0, 1.0, 7.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_finite_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 7, 1],
+          "data": { "kind": "values", "values": [5.0, 1.0, 5.0, 3.0, -2.0, 1.0, 7.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_later_nan_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 8, 1],
+          "data": { "kind": "values", "values": [5.0, "NaN", 1.0, "NaN", 3.0, -2.0, "NaN", 5.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 4, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [8], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_later_nan_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 8, 1],
+          "data": { "kind": "values", "values": [5.0, "NaN", 1.0, "NaN", 3.0, -2.0, "NaN", 5.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 4, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [8], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_leading_nan_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "data": { "kind": "values", "values": ["NaN", 5.0, 1.0, "NaN", -2.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 1, 1], "tolerance": 0, "allowNaN": true },
+        "inverse_indices": { "dtype": "uint32", "shape": [5], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_leading_nan_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "data": { "kind": "values", "values": ["NaN", 5.0, 1.0, "NaN", -2.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 1, 1], "tolerance": 0, "allowNaN": true },
+        "inverse_indices": { "dtype": "uint32", "shape": [5], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_local_sort_below_crossover_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "provenance": {
+        "notes": "A slice count at or below LOCAL_SORT_CROSSOVER keeps the single-workgroup local-sort metadata route while the distinct slices still give every inverse index its own answer."
+      },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 6, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 7, 1],
+          "data": { "kind": "values", "values": [5.0, 1.0, 5.0, 3.0, -2.0, 1.0, 7.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_zero_subnormal_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 9, 1],
+          "data": {
+            "kind": "values",
+            "values": [-0.0, 0.0, 5.960464477539063e-8, -5.960464477539063e-8, 5.960464477539063e-8, "Infinity", "-Infinity", 1.0, -1.0]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 7, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [9], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_zero_subnormal_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 9, 1],
+          "data": {
+            "kind": "values",
+            "values": [-0.0, 0.0, 5.960464477539063e-8, -5.960464477539063e-8, 5.960464477539063e-8, "Infinity", "-Infinity", 1.0, -1.0]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 7, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [9], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_zero_reverse_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 7, 1],
+          "data": {
+            "kind": "values",
+            "values": [0.0, -0.0, -5.960464477539063e-8, 5.960464477539063e-8, 1.0, -1.0, "NaN"]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "axis_scalar_hash_float16_zero_reverse_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 7, 1],
+          "data": {
+            "kind": "values",
+            "values": [0.0, -0.0, -5.960464477539063e-8, 5.960464477539063e-8, 1.0, -1.0, "NaN"]
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float16", "shape": [1, 5, 1], "tolerance": 0 },
+        "inverse_indices": { "dtype": "uint32", "shape": [7], "tolerance": 0 }
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask0_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask0_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask1_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask1_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask2_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask2_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask3_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask3_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask4_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask4_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask5_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask5_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask6_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask6_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask0_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask0_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask1_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask1_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask2_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask2_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask3_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask3_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask4_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask4_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask5_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask5_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask6_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask6_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, -0.0, 1.0, -3.0, 2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 6] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [10, 9, 5, 5, 4] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask0_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-3.0, -0.0, 1.0, 2.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [3, 1, 2, 6, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_finite_mask2_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 9, 5, 4, 10] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_int32_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-1, -2147483648, 2147483647, 0, 7] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 6, 5, 5] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_int32_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-2147483648, -1, 0, 7, 2147483647] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1, 0, 3, 5, 2] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": [1, 0, 4, 2, 1, 3, 1, 0, 4, 2, 1, 3, 1, 0, 4, 2, 1, 3, 1, 0, 4, 2, 1, 3, 1, 0, 4, 2, 1, 3, 1, 0, 4]
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 11, 5, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_uint32_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "uint32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_uint32_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [4294967295, 0, 2147483648, 7, 2147483647] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 6, 5, 5] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_uint32_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "uint32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_uint32_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "uint32",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 7, 2147483647, 2147483648, 4294967295] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1, 3, 5, 2, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_uint32_finite_mask7_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 5, 5, 6, 11] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_int16_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int16_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int16",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-32768, 32767, -1, 0, 7] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 6, 5, 5] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_int16_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int16_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int16",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-32768, -1, 0, 7, 32767] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 2, 3, 5, 1] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int16_finite_mask7_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 5, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_int8_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int8",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int8_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int8",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-128, 127, -1, 0, 7] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 6, 5, 5] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_int8_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int8",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int8_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int8",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-128, -1, 0, 7, 127] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 2, 3, 5, 1] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int16_finite_mask7_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 5, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_uint8_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "uint8",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_uint8_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "uint8",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [255, 0, 128, 7, 127] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 1, 2, 3, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_int32_finite_mask7_flat_sorted0_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [11, 6, 6, 5, 5] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_uint8_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "uint8",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_uint8_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "uint8",
+          "shape": [1, 5, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 7, 127, 128, 255] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1, 3, 5, 2, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_uint32_finite_mask7_axis_sorted1_output_inverse_indices" }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [5],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 5, 5, 6, 11] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_bool_finite_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "bool",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_bool_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "bool", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [1, 0] } },
+        "indices": { "dtype": "uint32", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [0, 1] } },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]
+          }
+        },
+        "counts": { "dtype": "uint32", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [22, 11] } }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_bool_finite_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "bool",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_bool_finite_mask7_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "bool", "shape": [1, 2, 1], "tolerance": 0, "data": { "kind": "values", "values": [0, 1] } },
+        "indices": { "dtype": "uint32", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [1, 0] } },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_bool_finite_mask7_flat_sorted0_input_x" }
+          }
+        },
+        "counts": { "dtype": "uint32", "shape": [2], "tolerance": 0, "data": { "kind": "values", "values": [11, 22] } }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_later_nan_mask4_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 1.0, 3.0, -2.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 6, 5, 16] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_later_nan_mask4_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-2.0, 1.0, 3.0, 5.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [16, 6, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_later_nan_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 1.0, 3.0, -2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 2, 4, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask7_flat_sorted0_output_inverse_indices"
+            }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 6, 5, 16] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_later_nan_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-2.0, 1.0, 3.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 2, 4, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask7_axis_sorted1_output_inverse_indices"
+            }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [16, 6, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_leading_nan_mask5_axis_sorted0",
+      "attrs": { "sorted": 0, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_leading_nan_mask7_axis_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 1, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN"] },
+          "allowNaN": true
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [0] } },
+        "counts": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [33] } }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float32_leading_nan_mask5_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_leading_nan_mask7_axis_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 1, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN"] },
+          "allowNaN": true
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [0] } },
+        "counts": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [33] } }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_later_nan_mask4_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 1.0, 3.0, -2.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 6, 5, 16] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_later_nan_mask4_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-2.0, 1.0, 3.0, 5.0] }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [16, 6, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_later_nan_mask7_flat_sorted0",
+      "attrs": { "sorted": 0 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 1.0, 3.0, -2.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0, 2, 4, 5] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask7_flat_sorted0_output_inverse_indices"
+            }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [6, 6, 5, 16] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_later_nan_mask7_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask4_flat_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-2.0, 1.0, 3.0, 5.0] }
+        },
+        "indices": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 2, 4, 0] }
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [33],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/scalar_hash_float32_later_nan_mask7_axis_sorted1_output_inverse_indices"
+            }
+          }
+        },
+        "counts": {
+          "dtype": "uint32",
+          "shape": [4],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [16, 6, 5, 6] }
+        }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_leading_nan_mask5_axis_sorted0",
+      "attrs": { "sorted": 0, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_leading_nan_mask7_axis_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 1, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN"] },
+          "allowNaN": true
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [0] } },
+        "counts": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [33] } }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "scalar_hash_float16_leading_nan_mask5_axis_sorted1",
+      "attrs": { "sorted": 1, "axis": -2 },
+      "tunables": {
+        "PARALLEL_SCAN_MIN_CHUNKS": 0,
+        "LOCAL_SORT_CROSSOVER": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [1, 33, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_float32_leading_nan_mask7_axis_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 1, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN"] },
+          "allowNaN": true
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [0] } },
+        "counts": { "dtype": "uint32", "shape": [1], "tolerance": 0, "data": { "kind": "values", "values": [33] } }
+      },
+      "provenance": {
+        "notes": "Exact ordered-insertion expectations for all scalar output masks. Integer -1/max uint32 exercises EMPTY side storage; float signed zero retains its first representative. Leading NaN exercises the exact one-class contract."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_head_later_inner_sorted0",
+      "attrs": { "axis": 0, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_head_later_inner_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 0.0, 1.0, 0.0, 3.0, 0.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_suffix_ignored_by_head_inner_sorted0",
+      "attrs": { "axis": 0, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_ignored_by_head_inner_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, "NaN", 2.0, 0.0, 3.0, 9.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted0",
+      "attrs": { "axis": -1, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 3],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, 1.0, 0.0, 5.0, 3.0, 0.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted0",
+      "attrs": { "axis": -1, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN", 3.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_head_later_inner_sorted1",
+      "attrs": { "axis": 0, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_head_later_inner_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, 0.0, 3.0, 0.0, 5.0, 0.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_suffix_ignored_by_head_inner_sorted1",
+      "attrs": { "axis": 0, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_ignored_by_head_inner_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, "NaN", 2.0, 0.0, 3.0, 9.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted1",
+      "attrs": { "axis": -1, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 3],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0.0, 1.0, 1.0, 0.0, 3.0, 5.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted1",
+      "attrs": { "axis": -1, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN", 3.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_head_later_inner_sorted0",
+      "attrs": { "axis": 0, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_head_later_inner_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 0.0, 1.0, 0.0, 3.0, 0.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_suffix_ignored_by_head_inner_sorted0",
+      "attrs": { "axis": 0, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_ignored_by_head_inner_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, "NaN", 2.0, 0.0, 3.0, 9.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_suffix_later_outer_sorted0",
+      "attrs": { "axis": -1, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [2, 3],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, 1.0, 0.0, 5.0, 3.0, 0.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_leading_single_bucket_outer_sorted0",
+      "attrs": { "axis": -1, "sorted": 0 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN", 3.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_head_later_inner_sorted1",
+      "attrs": { "axis": 0, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_head_later_inner_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, 0.0, 3.0, 0.0, 5.0, 0.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_suffix_ignored_by_head_inner_sorted1",
+      "attrs": { "axis": 0, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [33, 2],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_ignored_by_head_inner_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [3, 2],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, "NaN", 2.0, 0.0, 3.0, 9.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_suffix_later_outer_sorted1",
+      "attrs": { "axis": -1, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_suffix_later_outer_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [2, 3],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [0.0, 1.0, 1.0, 0.0, 3.0, 5.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "axis_nan_ordered_y_float16_nan_leading_single_bucket_outer_sorted1",
+      "attrs": { "axis": -1, "sorted": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": {
+          "dtype": "float16",
+          "shape": [2, 33],
+          "data": {
+            "kind": "values",
+            "values": {
+              "$ref": "#/fixtureArrays/axis_nan_ordered_y_float32_nan_leading_single_bucket_outer_sorted0_input_x"
+            }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": ["NaN", 3.0] },
+          "allowNaN": true
+        }
+      },
+      "provenance": {
+        "notes": "Y-only multi-element axis ordered-map reference with NaN at the deciding coordinate, after an earlier decisive coordinate, or in the initial representative. Outer/inner layouts preserve the same lexicographic slice values."
+      }
+    },
+    {
+      "name": "scalar_hash_scan_float32_n31_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 1, 31, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_scan_float32_n31_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 1, 30, 1],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": [0.0, 7.0, 14.0, 21.0, 28.0, 5.0, 12.0, 19.0, 26.0, 3.0, 10.0, 17.0, 24.0, 1.0, 8.0, 15.0, 22.0, 29.0, 6.0, 13.0, 20.0, 27.0, 4.0, 11.0, 18.0, 25.0, 2.0, 9.0, 16.0, 23.0]
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_scan_float32_n31_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 1, 31, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_scan_float32_n31_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 1, 30, 1],
+          "tolerance": 0,
+          "data": {
+            "kind": "values",
+            "values": [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0]
+          }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_scan_float32_n32_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 1, 32, 1],
+          "data": {
+            "kind": "values",
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+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_scan_float32_n257_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 256,
+        "SORT_WORKGROUP": 256,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 1, 257, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_scan_float32_n257_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 1, 256, 1],
+          "tolerance": 0,
+          "data": {
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+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_prefix_chunks_sparse_heads_n1023_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
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+          "dtype": "int32",
+          "shape": [1, 1, 1023, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_prefix_chunks_sparse_heads_n1023_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 3, 7, 1] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_prefix_chunks_sparse_heads_n1023_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 1023, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_prefix_chunks_sparse_heads_n1023_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1, 3, 5, 7] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_prefix_chunks_sparse_heads_n1024_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 1024, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_prefix_chunks_sparse_heads_n1024_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 3, 7, 1] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_prefix_chunks_sparse_heads_n1024_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 1024, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_prefix_chunks_sparse_heads_n1024_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1, 3, 5, 7] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_prefix_chunks_sparse_heads_n1025_sorted0",
+      "attrs": { "axis": -2, "sorted": 0 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 1025, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_prefix_chunks_sparse_heads_n1025_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5, 3, 7, 1] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_prefix_chunks_sparse_heads_n1025_sorted1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 512,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 1025, 1],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/scalar_hash_prefix_chunks_sparse_heads_n1025_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 4, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1, 3, 5, 7] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_hybrid_tile1",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 1,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 35, 1],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/scalar_hash_hybrid_tile1_input_x" } }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 6, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-1, 0, 2, 5, 7, 9] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_hybrid_tile2",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 2,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 35, 1],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/scalar_hash_hybrid_tile1_input_x" } }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 6, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-1, 0, 2, 5, 7, 9] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_hybrid_tile4",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 4,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 35, 1],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/scalar_hash_hybrid_tile1_input_x" } }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 6, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-1, 0, 2, 5, 7, 9] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_hybrid_tile32",
+      "attrs": { "axis": -2, "sorted": 1 },
+      "tunables": {
+        "LOCAL_SORT_CROSSOVER": 1,
+        "HASH_MIN_INPUT": 1,
+        "WORKGROUP_SIZE": 32,
+        "SORT_WORKGROUP": 32,
+        "GLOBAL_SORT_TILE": 32,
+        "PARALLEL_SCAN_MIN_CHUNKS": 0
+      },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1, 1, 35, 1],
+          "data": { "kind": "values", "values": { "$ref": "#/fixtureArrays/scalar_hash_hybrid_tile1_input_x" } }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "int32",
+          "shape": [1, 1, 6, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [-1, 0, 2, 5, 7, 9] }
+        }
+      },
+      "provenance": {
+        "notes": "Round4 scratch boundary matrix: exact scalar-axis shape proof, first-occurrence semantics, scan tails, and sort padding. Small crossover forces the scalable family without a large oracle workload."
+      }
+    },
+    {
+      "name": "scalar_hash_y_float32_axis_scalar_later_nan_sorted0",
+      "attrs": { "sorted": 0, "axis": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "HASH_MIN_INPUT": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": { "dtype": "float32", "shape": [1, 3, 1], "data": { "kind": "values", "values": [5.0, "NaN", 1.0] } }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 1.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Minimal ordered-map later-NaN Y-only witness. A NaN creates no new bucket; scalar axis and flattening have identical value semantics. Forced small crossover reaches existing hash families."
+      }
+    },
+    {
+      "name": "scalar_hash_y_float32_axis_scalar_later_nan_sorted1",
+      "attrs": { "sorted": 1, "axis": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "HASH_MIN_INPUT": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": { "dtype": "float32", "shape": [1, 3, 1], "data": { "kind": "values", "values": [5.0, "NaN", 1.0] } }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [1, 2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, 5.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Minimal ordered-map later-NaN Y-only witness. A NaN creates no new bucket; scalar axis and flattening have identical value semantics. Forced small crossover reaches existing hash families."
+      }
+    },
+    {
+      "name": "scalar_hash_y_float16_axis_scalar_later_nan_sorted0",
+      "attrs": { "sorted": 0, "axis": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "HASH_MIN_INPUT": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": { "dtype": "float16", "shape": [1, 3, 1], "data": { "kind": "values", "values": [5.0, "NaN", 1.0] } }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [5.0, 1.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Minimal ordered-map later-NaN Y-only witness. A NaN creates no new bucket; scalar axis and flattening have identical value semantics. Forced small crossover reaches existing hash families."
+      }
+    },
+    {
+      "name": "scalar_hash_y_float16_axis_scalar_later_nan_sorted1",
+      "attrs": { "sorted": 1, "axis": 1 },
+      "tunables": { "LOCAL_SORT_CROSSOVER": 1, "HASH_MIN_INPUT": 1, "WORKGROUP_SIZE": 32, "SORT_WORKGROUP": 32 },
+      "inputs": {
+        "x": { "dtype": "float16", "shape": [1, 3, 1], "data": { "kind": "values", "values": [5.0, "NaN", 1.0] } }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float16",
+          "shape": [1, 2, 1],
+          "tolerance": 0,
+          "data": { "kind": "values", "values": [1.0, 5.0] }
+        }
+      },
+      "provenance": {
+        "notes": "Minimal ordered-map later-NaN Y-only witness. A NaN creates no new bucket; scalar axis and flattening have identical value semantics. Forced small crossover reaches existing hash families."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask0",
+      "attrs": { "axis": 1, "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 5, 3],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/single_class_axis1_outer2_inner3_mask0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask1",
+      "attrs": { "axis": 1, "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 5, 3],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/single_class_axis1_outer2_inner3_mask0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [0] }, "tolerance": 0 }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask2",
+      "attrs": { "axis": 1, "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [1],
+          "data": { "kind": "values", "values": [0] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask3",
+      "attrs": { "axis": 1, "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [0] }, "tolerance": 0 },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [1],
+          "data": { "kind": "values", "values": [0] },
+          "tolerance": 0
+        }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask4",
+      "attrs": { "axis": 1, "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 5, 3],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/single_class_axis1_outer2_inner3_mask0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "counts": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [5] }, "tolerance": 0 }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask5",
+      "attrs": { "axis": 1, "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 5, 3],
+          "data": {
+            "kind": "values",
+            "values": { "$ref": "#/fixtureArrays/single_class_axis1_outer2_inner3_mask0_input_x" }
+          }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [0] }, "tolerance": 0 },
+        "counts": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [5] }, "tolerance": 0 }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask6",
+      "attrs": { "axis": 1, "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [1],
+          "data": { "kind": "values", "values": [0] },
+          "tolerance": 0
+        },
+        "counts": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [1] }, "tolerance": 0 }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "single_class_axis1_outer2_inner3_mask7",
+      "attrs": { "axis": 1, "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] }
+        }
+      },
+      "outputs": {
+        "y": {
+          "dtype": "float32",
+          "shape": [2, 1, 3],
+          "data": { "kind": "values", "values": [7.0, 2.0, 5.0, 11.0, 3.0, 2.0] },
+          "tolerance": 0
+        },
+        "indices": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [0] }, "tolerance": 0 },
+        "inverse_indices": {
+          "dtype": "uint32",
+          "shape": [1],
+          "data": { "kind": "values", "values": [0] },
+          "tolerance": 0
+        },
+        "counts": { "dtype": "uint32", "shape": [1], "data": { "kind": "values", "values": [1] }, "tolerance": 0 }
+      },
+      "provenance": {
+        "notes": "The required one-class output extent proves every full axis slice belongs to its first representative; nonuniform coordinates check outer/inner copy indexing."
+      }
+    },
+    {
+      "name": "scalar_f32_metadata_mask7_sorted0_n16385_u13",
+      "attrs": { "axis": 1, "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 16385, 1],
+          "data": { "kind": "cycle", "values": [5.0, 2.0, 7.0, 1.0, 3.0, 11.0, 0.0, 4.0, 6.0, 8.0, 9.0, 10.0, 12.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 13, 1] },
+        "indices": { "dtype": "uint32", "shape": [13] },
+        "inverse_indices": { "dtype": "uint32", "shape": [16385] },
+        "counts": { "dtype": "uint32", "shape": [13] }
+      },
+      "provenance": {
+        "notes": "Natural full-size sibling confirms the default resource-derived parallel selection and all metadata outputs without overriding the crossover."
+      }
+    },
+    {
+      "name": "scalar_f32_metadata_mask7_sorted1_n16385_u13",
+      "attrs": { "axis": 1, "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1, 16385, 1],
+          "data": { "kind": "cycle", "values": [5.0, 2.0, 7.0, 1.0, 3.0, 11.0, 0.0, 4.0, 6.0, 8.0, 9.0, 10.0, 12.0] }
+        }
+      },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1, 13, 1] },
+        "indices": { "dtype": "uint32", "shape": [13] },
+        "inverse_indices": { "dtype": "uint32", "shape": [16385] },
+        "counts": { "dtype": "uint32", "shape": [13] }
+      },
+      "provenance": {
+        "notes": "Natural full-size sibling confirms the default resource-derived parallel selection and all metadata outputs without overriding the crossover."
+      }
+    },
+    {
+      "name": "single_class_f32_n65537_mask7",
+      "inputs": { "x": { "dtype": "float32", "shape": [65537], "data": { "kind": "constant", "value": 3.0 } } },
+      "outputs": {
+        "y": { "dtype": "float32", "shape": [1] },
+        "indices": { "dtype": "uint32", "shape": [1] },
+        "inverse_indices": { "dtype": "uint32", "shape": [65537] },
+        "counts": { "dtype": "uint32", "shape": [1] }
+      },
+      "provenance": {
+        "notes": "Natural full-size sibling confirms the default resource-derived parallel selection and all metadata outputs without overriding the crossover."
+      }
+    },
+    {
+      "name": "flat_global_crossover_i32_n2049_u2049_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [2049],
+          "data": {
+            "kind": "cycle",
+            "values": { "$ref": "#/fixtureArrays/flat_global_crossover_int32_n4097_u2049_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [2049], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural flat large-output crossover: first-seen or sorted integer representatives without tuning overrides. The new hash route replaces quadratic duplicate detection."
+      }
+    },
+    {
+      "name": "flat_global_crossover_i32_n2049_u2049_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [2049],
+          "data": {
+            "kind": "cycle",
+            "values": { "$ref": "#/fixtureArrays/flat_global_crossover_int32_n4097_u2049_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [2049], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural flat large-output crossover: first-seen or sorted integer representatives without tuning overrides. The new hash route replaces quadratic duplicate detection."
+      }
+    },
+    {
+      "name": "flat_global_crossover_int32_n4097_u2049_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [4097],
+          "data": {
+            "kind": "cycle",
+            "values": { "$ref": "#/fixtureArrays/flat_global_crossover_int32_n4097_u2049_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [2049], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural flat large-output crossover: first-seen or sorted integer representatives without tuning overrides. The new hash route replaces quadratic duplicate detection."
+      }
+    },
+    {
+      "name": "flat_global_crossover_int32_n4097_u2049_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [4097],
+          "data": {
+            "kind": "cycle",
+            "values": { "$ref": "#/fixtureArrays/flat_global_crossover_int32_n4097_u2049_sorted0_input_x" }
+          }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [2049], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural flat large-output crossover: first-seen or sorted integer representatives without tuning overrides. The new hash route replaces quadratic duplicate detection."
+      }
+    },
+    {
+      "name": "output_span_int32_n257_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [257],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n257_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [257], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_int32_n257_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [257],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n257_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [257], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_float32_n257_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [257],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n257_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [257], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_float32_n257_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [257],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n257_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [257], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_int32_n1025_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1025],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n1025_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [1025], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_int32_n1025_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [1025],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n1025_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [1025], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_float32_n1025_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1025],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n1025_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [1025], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_float32_n1025_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "float32",
+          "shape": [1025],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n1025_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [1025], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_int32_n2048_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [2048],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n2048_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [2048], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "output_span_int32_n2048_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": {
+          "dtype": "int32",
+          "shape": [2048],
+          "data": { "kind": "cycle", "values": { "$ref": "#/fixtureArrays/output_span_int32_n2048_sorted0_input_x" } }
+        }
+      },
+      "outputs": { "y": { "dtype": "int32", "shape": [2048], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural distinct-output boundary across effective sort workgroup widths. Descending first occurrence separates sorted from unsorted behavior; hashing avoids the quadratic or serial fallback without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float32_n15_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": { "dtype": "float32", "shape": [15], "data": { "kind": "linspace", "start": 14.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [15], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float32_n15_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": { "dtype": "float32", "shape": [15], "data": { "kind": "linspace", "start": 14.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [15], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float32_n16_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": { "dtype": "float32", "shape": [16], "data": { "kind": "linspace", "start": 15.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [16], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float32_n16_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": { "dtype": "float32", "shape": [16], "data": { "kind": "linspace", "start": 15.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float32", "shape": [16], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float16_n15_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": { "dtype": "float16", "shape": [15], "data": { "kind": "linspace", "start": 14.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [15], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float16_n15_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": { "dtype": "float16", "shape": [15], "data": { "kind": "linspace", "start": 14.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [15], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float16_n16_sorted0",
+      "attrs": { "sorted": 0 },
+      "inputs": {
+        "x": { "dtype": "float16", "shape": [16], "data": { "kind": "linspace", "start": 15.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [16], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
+    },
+    {
+      "name": "float_hash_work_boundary_float16_n16_sorted1",
+      "attrs": { "sorted": 1 },
+      "inputs": {
+        "x": { "dtype": "float16", "shape": [16], "data": { "kind": "linspace", "start": 15.0, "end": 0.0 } }
+      },
+      "outputs": { "y": { "dtype": "float16", "shape": [16], "tolerance": 0 } },
+      "provenance": {
+        "notes": "Natural comparison-work admission boundary; descending inputs distinguish sorted output from first-occurrence order without tuning overrides."
+      }
     }
   ]
 }