candidate_id stringlengths 20 20 | categories listlengths 1 1 | construction dict | distance dict | evidence_class stringclasses 3
values | first_seen_round int64 1 4 | fom dict | matrices dict | matrix_checks dict | novelty dict | parameters dict | release_schema_version int64 1 1 | representation_id stringclasses 1
value | run_id stringclasses 1
value | snapshot_sealed_through_round int64 4 4 | target dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
158bf9b332c9012345f8 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
8,
1
],
[
14,
2
]
],
"B_terms": [
[
4,
1
],
[
8,
2
],
[
10,
0
]
],
"ell": 15,
"family": "css-bb",
"geometry": null,
"m": 3
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 10,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 2 | {
"bp_osd_distance_upper_bound_advisory": 8,
"bp_osd_fom_upper_bound_advisory": 8.533333333333333,
"exact": null,
"lower_bound": 3.3333333333333335,
"upper_bound": 13.333333333333334
} | {
"hx_content_sha256": "62f98b22f86d9f797653dc7674d349f71c716c558c3cbb5d8511cb80bf2cc18c",
"hx_file_sha256": "65396b30286bf0fd32de51f532f163f7823450967b54d2d4414e790a3efd30e7",
"hx_path": "matrices/158bf9b332c9012345f8/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "5fe3dd1655f3cd92c7b2db9... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 39,
"rank_z": 39,
"tanner_components": 1
} | {
"canonical_digest": "7c83a42826b859463a39cace747fd794453ba09cd7fd5002e18488eb51bb3b4f",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 10,
"strict_inequality": "k*d^2 > 12*n"
} |
50c0e573b498edce4055 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
3,
5
],
[
4,
5
],
[
6,
0
]
],
"B_terms": [
[
1,
0
],
[
6,
0
]
],
"ell": 9,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 23,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": 9,
"bp_osd_fom_upper_bound_advisory": 9,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 58.77777777777778
} | {
"hx_content_sha256": "82f523f20e0ca162b77db0ebbe02a21e8f141929fef95a7045ec9d8e142fd93a",
"hx_file_sha256": "760ad3a197864f410ff67c9ba8c35ad18fb8a80e2856f4e39fef7a205f4f89e6",
"hx_path": "matrices/50c0e573b498edce4055/Hx.mtx.gz",
"hx_shape": [
54,
108
],
"hz_content_sha256": "c3dcf4162cb937a3dfa893... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 48,
"rank_z": 48,
"tanner_components": 1
} | {
"canonical_digest": "e7065ec3b5c359f792bf77ba3122d6c21cef5f37a8d19dc9dc1eb7f6f9666a51",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 108
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
fa9eb9fa4548126df910 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
5,
2
],
[
9,
1
],
[
14,
2
]
],
"B_terms": [
[
0,
0
],
[
10,
1
]
],
"ell": 15,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 18,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 36
} | {
"hx_content_sha256": "58c261df62a01bf5de6dc44606dca4d3a6cca1ed35dc922f41f702440a3b4db1",
"hx_file_sha256": "67e077a7898a6354b868865ea0d2a846d4ff11dbed4cddc583d580a1725813f2",
"hx_path": "matrices/fa9eb9fa4548126df910/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "bec9a056290b9c4139a6db1... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 40,
"rank_z": 40,
"tanner_components": 1
} | {
"canonical_digest": "249274442688dfd4f0514166da1fcd6929d7f44c8f2f22d3360576f19e8999fd",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 10,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
c4a8463fd209cf16ad32 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
5,
2
],
[
9,
1
],
[
14,
2
]
],
"B_terms": [
[
0,
0
],
[
10,
1
]
],
"ell": 15,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 16,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 4 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 28.444444444444443
} | {
"hx_content_sha256": "752b5b12ba9fa1401e046123ced33d482f17fcf1bf506cfcf924094e40337482",
"hx_file_sha256": "5c7318e46720a7c3663f8b6166a3e83eacdc99d17d147eeea7a6f400e9015ba2",
"hx_path": "matrices/c4a8463fd209cf16ad32/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "78db596d999baaa5ca7f6b6... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 40,
"rank_z": 40,
"tanner_components": 1
} | {
"canonical_digest": "c69cbb8161a22a8ec70a881ce0e6f88f0e158fe1830fe4f794e95f2b403bfad0",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 10,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
4374e4bdca6836ff3bd2 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
1,
2
],
[
3,
1
],
[
8,
2
]
],
"B_terms": [
[
2,
0
],
[
11,
0
]
],
"ell": 15,
"family": "css-bb",
"geometry": null,
"m": 3
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 16,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 28.444444444444443
} | {
"hx_content_sha256": "bccb9d3379c289a2f48b0859a60cba855b734ce085dc432f1b06cead3f2cbfc2",
"hx_file_sha256": "bd1165f2876b23bdb7b7c705e7951ce2daa31d59a96333a9ac4eae0b68786ccd",
"hx_path": "matrices/4374e4bdca6836ff3bd2/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "565e04a5bc5ed169a07c92a... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 40,
"rank_z": 40,
"tanner_components": 1
} | {
"canonical_digest": "ea418e9e612349f783aa7bc8e6e5a5dd103a5df50ac4e7a2008decffe6ad9172",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 10,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
b5df3326a3b35f644ffd | [
"formal_open"
] | {
"A_terms": [
[
0,
1
],
[
0,
5
],
[
3,
0
]
],
"B_terms": [
[
0,
3
],
[
1,
0
],
[
2,
0
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 14,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 21.77777777777778
} | {
"hx_content_sha256": "b1939f5a2dde1fe6d361e1157c2bbe14aea4043b2859a847d32ada33830072ca",
"hx_file_sha256": "02dcb979651f929f4519ed366e14464bb579164a3877cacc67f247c10c165471",
"hx_path": "matrices/b5df3326a3b35f644ffd/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "41b5a783a63391d53bfb823... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 32,
"rank_z": 32,
"tanner_components": 1
} | {
"canonical_digest": "ae8e36ec6904c38f4b94d63934804d3f9bc3f585a8b9d5dcbef86023e7f5858f",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
4924b80973546f9d4dba | [
"formal_open"
] | {
"A_terms": [
[
7,
2
],
[
9,
0
],
[
10,
0
],
[
12,
2
]
],
"B_terms": [
[
0,
0
],
[
6,
0
]
],
"ell": 15,
"family": "css-bb",
"geometry": null,
"m": 3
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 13,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 18.77777777777778
} | {
"hx_content_sha256": "44ab38ebf858c82712664ddef251467583c6fee73daef091afd157d4e8a428ba",
"hx_file_sha256": "f124e141244b800b3745e07b4c0a7acf454854b3f51a52b4144f7cf87a9faa00",
"hx_path": "matrices/4924b80973546f9d4dba/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "754e61b274ae8d9391e056d... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 40,
"rank_z": 40,
"tanner_components": 1
} | {
"canonical_digest": "ea418e9e612349f783aa7bc8e6e5a5dd103a5df50ac4e7a2008decffe6ad9172",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 10,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
0579b59ae2df3098975c | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
7,
2
],
[
13,
1
],
[
14,
0
]
],
"B_terms": [
[
7,
1
],
[
13,
1
]
],
"ell": 15,
"family": "css-bb",
"geometry": null,
"m": 3
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 13,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 18.77777777777778
} | {
"hx_content_sha256": "89ce7a5200005df5448e043c1e28a10a0284dc07d39be336d03af19c3e5627d2",
"hx_file_sha256": "aa60eb391f2c9c4e5bc8bd0313b16587b0641522caa6d99d59a397910a1b77c4",
"hx_path": "matrices/0579b59ae2df3098975c/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "7def1e5166ea061d09a265b... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 40,
"rank_z": 40,
"tanner_components": 1
} | {
"canonical_digest": "f90b1f9aeeed43e933e4b7e8c514a4616e0870f93b0b92a96fb76c742f886c18",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 10,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
f18d1f42955e077f129c | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
4,
5
],
[
5,
2
]
],
"B_terms": [
[
3,
3
],
[
4,
2
],
[
5,
4
]
],
"ell": 6,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 12,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 4 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 16
} | {
"hx_content_sha256": "df7f5ca5a1b2abc274793cc8dafcf7f12700bb0b3bc239493d81e50aa802788e",
"hx_file_sha256": "6d87d1843dfaa8e397866571bb1bf31dafafc9302082b43c850d8c5eaedf0d62",
"hx_path": "matrices/f18d1f42955e077f129c/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "5f44a4bf96656963cb75b6d... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 32,
"rank_z": 32,
"tanner_components": 1
} | {
"canonical_digest": "260c92d1bfc9d17787951f714fa61429b2c61839ec567102a7430c288d81469c",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
54edb806f10491ae809b | [
"formal_open"
] | {
"A_terms": [
[
0,
4
],
[
1,
1
],
[
2,
1
]
],
"B_terms": [
[
0,
0
],
[
1,
4
],
[
5,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 12,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 16
} | {
"hx_content_sha256": "023bc3e6b3799b9ef2a315c1299b8c350c72d7e9dc567bf6c0e7a4aef46425ef",
"hx_file_sha256": "19c39cdcdb0f4e6be485f4c25a4a68411f3d83840c3751fa2f381d28c1f64d88",
"hx_path": "matrices/54edb806f10491ae809b/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "9b768bce2b3151503d8414b... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 32,
"rank_z": 32,
"tanner_components": 1
} | {
"canonical_digest": "b3e553149c93701ea4095c579c4eaea82e22738a7838e9e1ada1918fcaaf1fc0",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
407e924ed5097c20234c | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
4,
5
],
[
5,
3
]
],
"B_terms": [
[
0,
2
],
[
1,
4
],
[
2,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 12,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 16
} | {
"hx_content_sha256": "b023d73efd1183e7e34db9ffb51acafc3aa31646ef1bffc2f0fea81cfd3f114d",
"hx_file_sha256": "cc0787214e44f2171a14d89d12e40d4055d3de016f78ef46663b4246e68889d6",
"hx_path": "matrices/407e924ed5097c20234c/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "cc4d409aff7a80d9f76107c... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 32,
"rank_z": 32,
"tanner_components": 1
} | {
"canonical_digest": "260c92d1bfc9d17787951f714fa61429b2c61839ec567102a7430c288d81469c",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
249517eba0a7d90c336b | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
1,
2
],
[
1,
4
],
[
3,
1
]
],
"B_terms": [
[
2,
1
],
[
3,
2
]
],
"ell": 6,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 12,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.7777777777777777,
"upper_bound": 16
} | {
"hx_content_sha256": "dd2ab425237b98f929a775198d006dbe700b6a0e30d1b11aa66a2e158bd86478",
"hx_file_sha256": "7ca0b38ec7434dda1f5580002f22150383a994d22f0a26934f72dad54d7f8aed",
"hx_path": "matrices/249517eba0a7d90c336b/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "47d35400634a81699b7f600... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 32,
"rank_z": 32,
"tanner_components": 1
} | {
"canonical_digest": "27274214d2cbab919638b96573db7ad12bcaf64ef77dc18d9d3b2763e5898681",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 11,
"strict_inequality": "k*d^2 > 12*n"
} |
fd1058c7eb0400bc1033 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
4,
0
],
[
5,
4
],
[
7,
1
]
],
"B_terms": [
[
3,
1
],
[
6,
4
]
],
"ell": 9,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 22,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.314814814814815,
"upper_bound": 44.81481481481482
} | {
"hx_content_sha256": "4ded13f13aae8361e03e56b1fd352fc20fa3a2a47dd330232df08b09dec5698d",
"hx_file_sha256": "e2e7c4fa474437fa95f14a51697b5ecacb72021356b52803c4234766f1207755",
"hx_path": "matrices/fd1058c7eb0400bc1033/Hx.mtx.gz",
"hx_shape": [
54,
108
],
"hz_content_sha256": "7d51fffc7b434c7e74c319... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 49,
"rank_z": 49,
"tanner_components": 1
} | {
"canonical_digest": "49c278b636aff9b68180faab723496dd804a83e643fb720defb7a27f101ebfd0",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 10,
"n": 108
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 12,
"strict_inequality": "k*d^2 > 12*n"
} |
b4b7100379a62ba92a04 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
0,
9
],
[
5,
2
],
[
5,
3
]
],
"B_terms": [
[
2,
6
],
[
2,
8
]
],
"ell": 12,
"family": "css-bb",
"geometry": null,
"m": 12
} | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 12,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.2569444444444446,
"upper_bound": 13
} | {
"hx_content_sha256": "68c9495ca9b2c1ffd075b8591c0602b58d0a33c81b55c18f11013cf479bb58c9",
"hx_file_sha256": "026e8e19bbdaa6301c96eb1e1d39dbab7e467af61d22e1c1bf15a21c71f2082b",
"hx_path": "matrices/b4b7100379a62ba92a04/Hx.mtx.gz",
"hx_shape": [
144,
288
],
"hz_content_sha256": "53bfc8c9ba5db1148cfb2... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 131,
"rank_z": 131,
"tanner_components": 1
} | {
"canonical_digest": "6651926eca7e563f5d2bf4038fa323fe650cabfba528ce20b001344630ceb560",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 26,
"n": 288
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 12,
"strict_inequality": "k*d^2 > 12*n"
} |
2a3df5ca15c8c65e0a61 | [
"formal_open"
] | {
"A_terms": [
[
0,
0
],
[
0,
9
],
[
5,
2
],
[
5,
3
]
],
"B_terms": [
[
2,
6
],
[
2,
8
]
],
"ell": 12,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 12,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": 2.2569444444444446,
"upper_bound": 13
} | {
"hx_content_sha256": "76aca72b4bbc3a5231aa5546c005387f3221289cb9150bd2a8492eb8705216cc",
"hx_file_sha256": "e3d88eff745c7638086e25bc859d01aa63c15dfd42f7d27e0f5159b947f39dcd",
"hx_path": "matrices/2a3df5ca15c8c65e0a61/Hx.mtx.gz",
"hx_shape": [
144,
288
],
"hz_content_sha256": "7893fe1cc8c9491f5ce8b... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 131,
"rank_z": 131,
"tanner_components": 1
} | {
"canonical_digest": "f13e0dd84ac96f7310b1ccadf4e1de40b26aade832a92c5c6a0c1fc46169c91c",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 26,
"n": 288
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 12,
"strict_inequality": "k*d^2 > 12*n"
} |
f40799ccba3e96d86a46 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
0
],
[
1,
11
],
[
2,
9
]
],
"B_terms": [
[
1,
9
],
[
2,
4
],
[
3,
10
]
],
"ell": 12,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 36,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": 22,
"bp_osd_fom_upper_bound_advisory": 26.88888888888889,
"exact": null,
"lower_bound": 1.3888888888888888,
"upper_bound": 72
} | {
"hx_content_sha256": "956867df1e31b2387d8c753eeb997dcc0667887e7c532659aae7732b7d79f01a",
"hx_file_sha256": "b1e88b6b905ba0dbda88d2c247180e2bf584ef4b9205b7307f31cf77761415ee",
"hx_path": "matrices/f40799ccba3e96d86a46/Hx.mtx.gz",
"hx_shape": [
144,
288
],
"hz_content_sha256": "bcd7dd9392d59590f5bf1... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 136,
"rank_z": 136,
"tanner_components": 1
} | {
"canonical_digest": "8b6153dfc51d23cb396de52e0259a51fae6704a965448a515259ba7ad4ff07ba",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 16,
"n": 288
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 15,
"strict_inequality": "k*d^2 > 12*n"
} |
fb5d5da1f7d3e95a3fb8 | [
"heuristic_signal"
] | {
"A_terms": [
[
3,
15
],
[
4,
17
],
[
5,
14
]
],
"B_terms": [
[
0,
0
],
[
1,
9
],
[
5,
4
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 68,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 3 | {
"bp_osd_distance_upper_bound_advisory": 46,
"bp_osd_fom_upper_bound_advisory": 94.04444444444445,
"exact": null,
"lower_bound": 1.1111111111111112,
"upper_bound": 205.51111111111112
} | {
"hx_content_sha256": "0c3e49a1b63c2a57de716fd33aa1710648b1417daf699930c2483690d9eb69e1",
"hx_file_sha256": "4d24a3a2b862c67d78fd81152cec0d6a62a6e0fe95368ff395b2577a84c271ac",
"hx_path": "matrices/fb5d5da1f7d3e95a3fb8/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "f3588124bfb90f362e3b6... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 172,
"rank_z": 172,
"tanner_components": 1
} | {
"canonical_digest": "cbe7c06e6bf8e7f73c1f0f3c6a9316e1e617ed67c15dcbe1831534e43311b72b",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 16,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 17,
"strict_inequality": "k*d^2 > 12*n"
} |
61a1d17554cc6503a4c2 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
1
],
[
0,
2
],
[
3,
0
]
],
"B_terms": [
[
0,
11
],
[
1,
8
],
[
2,
8
]
],
"ell": 12,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versi... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 22,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 4 | {
"bp_osd_distance_upper_bound_advisory": 20,
"bp_osd_fom_upper_bound_advisory": 16.666666666666668,
"exact": null,
"lower_bound": 1.0416666666666667,
"upper_bound": 20.166666666666668
} | {
"hx_content_sha256": "de987c6e32c63ee98ea1a780aef4d3bf7c08f5889ee6426b7ce65941b5a1fc50",
"hx_file_sha256": "5de51c4c20de25547e120604f0949be1fd934f1bb921fe9dd8e35ed619083c5d",
"hx_path": "matrices/61a1d17554cc6503a4c2/Hx.mtx.gz",
"hx_shape": [
144,
288
],
"hz_content_sha256": "d8b216d4c7fb679a8d206... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 138,
"rank_z": 138,
"tanner_components": 1
} | {
"canonical_digest": "90f09902e22d0381d6859fe69f13d01351696151b3324731c11a712d77880c2b",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 288
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 17,
"strict_inequality": "k*d^2 > 12*n"
} |
7e8650c686e1c0ebc6f8 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
1
],
[
0,
2
],
[
3,
18
]
],
"B_terms": [
[
0,
3
],
[
1,
0
],
[
2,
0
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 30,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 28,
"bp_osd_fom_upper_bound_advisory": 26.133333333333333,
"exact": null,
"lower_bound": 0.8333333333333334,
"upper_bound": 30
} | {
"hx_content_sha256": "a4017919efcaf411a83d3661765179ed184f79d366b7c5880e809462f620bf5f",
"hx_file_sha256": "9f5d147eebf41f89b027cd2a077c4f24c1fd7200e2dcf1f02489165ffcb70082",
"hx_path": "matrices/7e8650c686e1c0ebc6f8/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "8b2c945407b9a34f492e7... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 174,
"rank_z": 174,
"tanner_components": 1
} | {
"canonical_digest": "892a430d83cee7f7ec011b59888c69c6da4041c5c5434d0020e4faa009aba9fd",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 19,
"strict_inequality": "k*d^2 > 12*n"
} |
d0667e048b4a349788cb | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
1
],
[
0,
2
],
[
3,
0
]
],
"B_terms": [
[
0,
6
],
[
1,
3
],
[
2,
3
]
],
"ell": 12,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 36,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 30,
"bp_osd_fom_upper_bound_advisory": 25,
"exact": null,
"lower_bound": 0.6944444444444444,
"upper_bound": 36
} | {
"hx_content_sha256": "dcd2143bf4bbae47922399a75132dad41535272c62b9ac9f2dc6855592caaf8c",
"hx_file_sha256": "f827e139b52d2c292700350cbf3cd0814fc7eb39c0cf0aba8b315f4fec7912e9",
"hx_path": "matrices/d0667e048b4a349788cb/Hx.mtx.gz",
"hx_shape": [
144,
288
],
"hz_content_sha256": "cc114656c0df2c8d7333b... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 140,
"rank_z": 140,
"tanner_components": 1
} | {
"canonical_digest": "164064c43fe7baff2c02012a22948f4f9fd4aa37be4c79c4eefa83d0639b1a46",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 288
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 21,
"strict_inequality": "k*d^2 > 12*n"
} |
e28b88c1b0aaa9f7520d | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
0
],
[
0,
17
],
[
5,
1
]
],
"B_terms": [
[
2,
14
],
[
4,
11
],
[
5,
10
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_ver... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 74,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 38,
"bp_osd_fom_upper_bound_advisory": 32.08888888888889,
"exact": null,
"lower_bound": 0.5555555555555556,
"upper_bound": 121.68888888888888
} | {
"hx_content_sha256": "9076e5141b02b2e23d4122fa3d6a368921ccf294a5ccd683cd33c370ce0af979",
"hx_file_sha256": "bd2881f1f10ddf99618517e2e0e64bdc26cc280495ffee13017d4e21ffe414ae",
"hx_path": "matrices/e28b88c1b0aaa9f7520d/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "666ceee0f9e06efbdc59e... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 176,
"rank_z": 176,
"tanner_components": 1
} | {
"canonical_digest": "e2aebb6b075a7429b16843057be5ef5731d7ddc69e02f402de68bbfe44ebce21",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 24,
"strict_inequality": "k*d^2 > 12*n"
} |
884685711ba275f945da | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
0
],
[
1,
23
],
[
2,
13
]
],
"B_terms": [
[
2,
14
],
[
3,
11
],
[
4,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_ver... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 64,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 42,
"bp_osd_fom_upper_bound_advisory": 39.2,
"exact": null,
"lower_bound": 0.5555555555555556,
"upper_bound": 91.02222222222223
} | {
"hx_content_sha256": "30f2562d22b26e2d380647291729ecd4578d3f6108963ec7e429d01e872d0283",
"hx_file_sha256": "34af978ea459f32d3b245f4ceaf846c51398bd56ebc8994d59738e9f0fac38cc",
"hx_path": "matrices/884685711ba275f945da/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "59b13bfc45d9ebc0c6271... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 176,
"rank_z": 176,
"tanner_components": 1
} | {
"canonical_digest": "522e10cbc368e729089ebc4044652655a2308a42c068faec357d458ed60f4cba",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 24,
"strict_inequality": "k*d^2 > 12*n"
} |
b06eaf5bbc75671b17a0 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
1
],
[
0,
2
],
[
3,
0
]
],
"B_terms": [
[
0,
3
],
[
1,
0
],
[
2,
0
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 56,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 38,
"bp_osd_fom_upper_bound_advisory": 32.08888888888889,
"exact": null,
"lower_bound": 0.5555555555555556,
"upper_bound": 69.68888888888888
} | {
"hx_content_sha256": "03b53c39b9ef32d5211d5a9f0129f83417b0838fba6794569ee8e83c5ddc7f19",
"hx_file_sha256": "f7cf1d9147db18ec4f30a787faa82f1c4045bc2f786530bc1681371773303633",
"hx_path": "matrices/b06eaf5bbc75671b17a0/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "ad5b67ca505a66aed0c41... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 176,
"rank_z": 176,
"tanner_components": 1
} | {
"canonical_digest": "707ce66df0eeaec6700179b771d1848423dc0b9852b56f0350b1220bb84510fe",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 24,
"strict_inequality": "k*d^2 > 12*n"
} |
1afd1547591d65165f71 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
4
],
[
0,
8
],
[
3,
0
]
],
"B_terms": [
[
0,
3
],
[
1,
27
],
[
2,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 44,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 36,
"bp_osd_fom_upper_bound_advisory": 28.8,
"exact": null,
"lower_bound": 0.5555555555555556,
"upper_bound": 43.022222222222226
} | {
"hx_content_sha256": "76db5c9e43f48e2839f2996b165ee45ae64b3477456600fa1ffdf1250fee92cc",
"hx_file_sha256": "2bd6d4547994464106860a286f49afca3608982f76b5d23b071bbd21e715ae27",
"hx_path": "matrices/1afd1547591d65165f71/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "d8bd2e9ac238d7bfec2af... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 176,
"rank_z": 176,
"tanner_components": 1
} | {
"canonical_digest": "6f1dac308608acb05b1756a84b3f3578fb196bbd7be650e7116418528c4f24be",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 24,
"strict_inequality": "k*d^2 > 12*n"
} |
af12e9a536e777c30cc9 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
0
],
[
3,
29
],
[
4,
9
]
],
"B_terms": [
[
0,
0
],
[
3,
11
],
[
4,
27
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 42,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 36,
"bp_osd_fom_upper_bound_advisory": 28.8,
"exact": null,
"lower_bound": 0.5555555555555556,
"upper_bound": 39.2
} | {
"hx_content_sha256": "5ebeafbeb98b49a59d70cefc42bb01fd44e1df74baed9e303f440d60036cf8ef",
"hx_file_sha256": "03a5e4388e7a914ced18b662d3acceb8fb28d8e421a3c7e9e94ca2b97ce240e2",
"hx_path": "matrices/af12e9a536e777c30cc9/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "32dfc8fa246e8e2c017b5... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 176,
"rank_z": 176,
"tanner_components": 1
} | {
"canonical_digest": "2a9b81a87430f56aea75fd3d84655fddaff1633c8ee237a775c1181079cd4fb1",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 8,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 24,
"strict_inequality": "k*d^2 > 12*n"
} |
893e0883e3cda30e0032 | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
0
],
[
1,
9
],
[
1,
11
]
],
"B_terms": [
[
2,
1
],
[
3,
0
],
[
3,
28
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versi... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 84,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 1 | {
"bp_osd_distance_upper_bound_advisory": 48,
"bp_osd_fom_upper_bound_advisory": 25.6,
"exact": null,
"lower_bound": 0.2777777777777778,
"upper_bound": 78.4
} | {
"hx_content_sha256": "055fc50d99453fc337e994b7b48f3779581b692eb521ed6d71269d700d586220",
"hx_file_sha256": "8e8030804b661166888ad1adc66104e55705fad8d136697757ae19338c86fe84",
"hx_path": "matrices/893e0883e3cda30e0032/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "f82c81c6938158f47606b... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 178,
"rank_z": 178,
"tanner_components": 1
} | {
"canonical_digest": "78b2eb2b04d16414b6d84eabdc86ffe44d70750b46132978b648f5777041a2df",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 4,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 33,
"strict_inequality": "k*d^2 > 12*n"
} |
cb086df42f84cc48498a | [
"heuristic_signal"
] | {
"A_terms": [
[
0,
0
],
[
0,
1
],
[
5,
0
]
],
"B_terms": [
[
0,
14
],
[
0,
21
],
[
1,
0
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versi... | {
"exact": null,
"lower_bound": 5,
"lower_bound_source": "sealed_search_oracle_unsat",
"upper_bound": 78,
"upper_bound_source": "replayed_logical_basis_witness"
} | FORMAL_OPEN_LOWER_BOUND | 4 | {
"bp_osd_distance_upper_bound_advisory": 60,
"bp_osd_fom_upper_bound_advisory": 40,
"exact": null,
"lower_bound": 0.2777777777777778,
"upper_bound": 67.6
} | {
"hx_content_sha256": "b24fa6a0a99d84c4cc6913e033d8e9427c53ea98aebe2be18cf153e72d892d61",
"hx_file_sha256": "b7409818c08de40dea5cab27fea60018e2ff66f7ae95658b06725b12e767cbe1",
"hx_path": "matrices/cb086df42f84cc48498a/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "dc7fe82505a64063ae142... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 178,
"rank_z": 178,
"tanner_components": 1
} | {
"canonical_digest": "b06a1a76ea42533cfa160b9467774143ad8e003405b9a3d39b5b7f35b4629347",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 4,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 33,
"strict_inequality": "k*d^2 > 12*n"
} |
eace300f0179ee2f421d | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
6,
1
]
],
"B_terms": [
[
4,
5
],
[
5,
2
],
[
10,
0
],
[
11,
3
]
],
"ell": 12,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": 2,
"lower_bound": 2,
"lower_bound_source": "sealed_trusted_exact_audit",
"upper_bound": 2,
"upper_bound_source": "sealed_trusted_audit"
} | EXACT_NON_WIN | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": 2,
"lower_bound": 2,
"upper_bound": 2
} | {
"hx_content_sha256": "84e074921b0e04a1f802424962620dae5b2054f6a9cb70385e5722e2d2590c8d",
"hx_file_sha256": "28b6847ad36f7158fb7abaf4a504a00abc6b725306bbca9eae3cf51cd9818c06",
"hx_path": "matrices/eace300f0179ee2f421d/Hx.mtx.gz",
"hx_shape": [
72,
144
],
"hz_content_sha256": "fc63710355abe06413cccb... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 36,
"rank_z": 36,
"tanner_components": 1
} | {
"canonical_digest": "363c7b55d72e6c5e2e5ddb27e0d3be91cd3643288783e73526c99d20152db343",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 72,
"n": 144
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 5,
"strict_inequality": "k*d^2 > 12*n"
} |
1a92317e4c91644009d0 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
3
]
],
"B_terms": [
[
0,
2
],
[
0,
5
],
[
1,
0
],
[
1,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": 2,
"lower_bound": 2,
"lower_bound_source": "sealed_trusted_exact_audit",
"upper_bound": 2,
"upper_bound_source": "sealed_trusted_audit"
} | EXACT_NON_WIN | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": 2,
"lower_bound": 2,
"upper_bound": 2
} | {
"hx_content_sha256": "62e30c75b1ca9b2e2266f88bb0ad67f23d088ec628ef2a3ff89bddb1ca749bd9",
"hx_file_sha256": "9ab0e63a1ed0b277f5e4894cca14a0c001d5e442819e2a96d5ebc4562958f620",
"hx_path": "matrices/1a92317e4c91644009d0/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "e18b4602c90b9ec3b58ae4d... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 18,
"rank_z": 18,
"tanner_components": 1
} | {
"canonical_digest": "735448f9f2b6f56d65a014df59e265f9214b02b14c5ffed7d74876affa4138cd",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 36,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 5,
"strict_inequality": "k*d^2 > 12*n"
} |
4972b76678ee3d914550 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
3,
2
]
],
"B_terms": [
[
1,
2
],
[
2,
0
],
[
4,
4
],
[
5,
5
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": 2,
"lower_bound": 2,
"lower_bound_source": "sealed_trusted_exact_audit",
"upper_bound": 2,
"upper_bound_source": "sealed_trusted_audit"
} | EXACT_NON_WIN | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": 1,
"lower_bound": 1,
"upper_bound": 1
} | {
"hx_content_sha256": "db54e2ab63c7bb814bf726b0b11c9cbd4dadcf98df3695e682db1de2610d362c",
"hx_file_sha256": "316d2921a6004b1635ceb0723d19f2e17675992702c610c9494f99a0aeb15aea",
"hx_path": "matrices/4972b76678ee3d914550/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "bda1aaddb0060725c0f07eb... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 27,
"rank_z": 27,
"tanner_components": 1
} | {
"canonical_digest": "f684a7238de2b6b949df59fa5c956ca788aa922525c119963de157defb28d1bc",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
dec8d7bc73c6c8e48a1f | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
3,
2
],
[
4,
1
],
[
11,
4
]
],
"B_terms": [
[
7,
3
],
[
11,
4
]
],
"ell": 12,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 8,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 4 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 10.666666666666666
} | {
"hx_content_sha256": "f6b4b033c86fd405c3aec103b58e618dc3c3b5d97accc8424e8bdcceca8c1e9e",
"hx_file_sha256": "424e044a003a03fe928dbbb36fdb2daadbe909b46ee8a185912177473ae00775",
"hx_path": "matrices/dec8d7bc73c6c8e48a1f/Hx.mtx.gz",
"hx_shape": [
72,
144
],
"hz_content_sha256": "3b068907f1d292068aaa89... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 60,
"rank_z": 60,
"tanner_components": 1
} | {
"canonical_digest": "7656f1edbeccddf57b5d295d3ea3b481f1f496040e0ed6ae051ee83484653d67",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 24,
"n": 144
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
f34c90a5a110c3584210 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
4
],
[
5,
4
],
[
5,
5
]
],
"B_terms": [
[
0,
1
],
[
0,
5
]
],
"ell": 9,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 6,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 6
} | {
"hx_content_sha256": "bbce466e048c91d7eae53f3f4b4c7185d91dcb29d4d019032fb9559f6d39b405",
"hx_file_sha256": "010179a1e0f0b3cb7a5f9089416535dc441e80230096144f86646c6e5d5e23bd",
"hx_path": "matrices/f34c90a5a110c3584210/Hx.mtx.gz",
"hx_shape": [
54,
108
],
"hz_content_sha256": "f80e343ed8c7102e418ca5... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 45,
"rank_z": 45,
"tanner_components": 1
} | {
"canonical_digest": "cac5ac1fa487c876ab6e9fed8bc98e5fea530fe526910c6cb52b9a53b907b306",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 108
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
e10efc640acbf0900a89 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
3,
3
],
[
4,
2
],
[
4,
5
],
[
5,
2
]
],
"B_terms": [
[
0,
0
],
[
0,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 6,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 6
} | {
"hx_content_sha256": "33a824f62ea698b4689a0f8581cb3285f704b5af710e1fa8146b5f6c5a40a90d",
"hx_file_sha256": "27d2913fd34ca21c31968bdbeb2902b15eee17eddd135f0fad991344478795b4",
"hx_path": "matrices/e10efc640acbf0900a89/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "414693eb2789fe6a9854dfd... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 30,
"rank_z": 30,
"tanner_components": 1
} | {
"canonical_digest": "c36383b37b5553d809ff8905d2af9451892b5d72684f0ae7adea3fe824accd3b",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
fe0e327abe20b2648e47 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
5
],
[
5,
1
],
[
5,
4
]
],
"B_terms": [
[
0,
1
],
[
0,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 5,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 4.861111111111111
} | {
"hx_content_sha256": "fb4c7a00c342a4e2414f228a6da203449feaa7cc147732bee67b79e4a2da09d6",
"hx_file_sha256": "a0f710dd60e6383e495524189f794d8cbf48fef7c56923fc347456806d268f27",
"hx_path": "matrices/fe0e327abe20b2648e47/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "867660f6939f7be2ba5fbf6... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 29,
"rank_z": 29,
"tanner_components": 1
} | {
"canonical_digest": "993779c638eed01c6d54660d42ae7fcfc2270110ade1c277fc9a0ec3c8e3190f",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 14,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 8,
"strict_inequality": "k*d^2 > 12*n"
} |
d7e98ed4292e5d3580fb | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
18
],
[
3,
8
],
[
3,
35
]
],
"B_terms": [
[
0,
3
],
[
0,
30
]
],
"ell": 5,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 4,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 4
} | {
"hx_content_sha256": "abf3cf50fd7ac5f317cf5b35610c04e9c6c15effc370db6bf855bdaf16e42ef9",
"hx_file_sha256": "fe860c790476d9760e65b9649de2d3f5d6aa11f08f70ed40240e9b7129549ef1",
"hx_path": "matrices/d7e98ed4292e5d3580fb/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "4448ea32451e1b663571f... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 135,
"rank_z": 135,
"tanner_components": 1
} | {
"canonical_digest": "47eb7c0839ac9cc038e134e33199f33b5f39ca0b01ac06809d9d8401565b035e",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 90,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
e788b450cc0e09d249b1 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
1,
1
],
[
4,
2
],
[
6,
2
]
],
"B_terms": [
[
0,
1
],
[
3,
2
]
],
"ell": 15,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 4,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 3.2
} | {
"hx_content_sha256": "e6d2d9af53256d4b27dfcde1f4477aa556815cd1088075de58de95f16a9cc156",
"hx_file_sha256": "7d7699a6107701fb2c9721d1e2c0b2fa5ce4225c7ca1b39fa47d50bb51edc996",
"hx_path": "matrices/e788b450cc0e09d249b1/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "b66e26dfb8e007615cdf64a... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 36,
"rank_z": 36,
"tanner_components": 1
} | {
"canonical_digest": "6b943240e6df2be1d4d72754593b5935ed40707904364606f3239fe13ef83a0f",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 8,
"strict_inequality": "k*d^2 > 12*n"
} |
f024b0fb4b0a05098aa4 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
2,
1
],
[
2,
5
]
],
"B_terms": [
[
2,
0
],
[
2,
2
],
[
3,
3
],
[
3,
5
]
],
"ell": 9,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 3
} | {
"hx_content_sha256": "1654c971fedce5c2ec54b7f182530474ebeae3270f1deda8ebcdcd60ba6c505e",
"hx_file_sha256": "1d6b13b4afee252ab6079339afb4f2a26e4a7fca6ebcb78a7d61ac5ffa9d1cb1",
"hx_path": "matrices/f024b0fb4b0a05098aa4/Hx.mtx.gz",
"hx_shape": [
54,
108
],
"hz_content_sha256": "2e6f711ea0cb2bb0d30ba3... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 36,
"rank_z": 36,
"tanner_components": 1
} | {
"canonical_digest": "d942a3b0f65cd0be21bd4d5da3e221dce3d09155abb4f8da0852923f282688e6",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 36,
"n": 108
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
df1d16a2e8186164a3e7 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
3,
2
]
],
"B_terms": [
[
1,
1
],
[
3,
4
],
[
6,
0
],
[
7,
5
]
],
"ell": 9,
"family": "css-bb",
"geometry": null,
"m": 6
} | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 3 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 3
} | {
"hx_content_sha256": "38ec0401d6d64c1194ab1d9cf7d1291b9452944b9ff7d673e78bebbfda64ec4b",
"hx_file_sha256": "9af1932f3a4501cea5a794978b97907d204789cf6530277ca2cca9eb292b2840",
"hx_path": "matrices/df1d16a2e8186164a3e7/Hx.mtx.gz",
"hx_shape": [
54,
108
],
"hz_content_sha256": "9c15cb67a20f2fb0f86b39... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 36,
"rank_z": 36,
"tanner_components": 1
} | {
"canonical_digest": "124fb56da6bb2e07166725c1d73cd699bc637d8a99a0774cffd6b6761ac3ee36",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 36,
"n": 108
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
da558563d690cc5da167 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
1
]
],
"B_terms": [
[
0,
0
],
[
0,
2
],
[
8,
0
],
[
8,
2
]
],
"ell": 15,
"family": "css-bb",
"geometry": null,
"m": 3
} | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 3
} | {
"hx_content_sha256": "383d7a10bcaf7daa300ffbfd57c03929d859ba61249fa01230e531ab3d6fb4c9",
"hx_file_sha256": "6560e910f0718d1a357cd6a1a37cae585f1e41e2aa265a06d98777db831401e3",
"hx_path": "matrices/da558563d690cc5da167/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "be2f3755f2d55a8aa494844... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 30,
"rank_z": 30,
"tanner_components": 1
} | {
"canonical_digest": "9c4d3e1d87d257fd0ef8a1da9decaa2bebb0149621e95ea7ca92d059f3222c22",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 30,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
cb3ab01590a9484b97a7 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
2
]
],
"B_terms": [
[
0,
0
],
[
0,
2
],
[
1,
1
],
[
1,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 3
} | {
"hx_content_sha256": "066fd4a5e5e9a9d2cf5ffd2d0b997a01327473e98c51f5fb9a36266ee966cc7a",
"hx_file_sha256": "251c2b598d01c829f695e8d4c50bc824eaf8ca7b7eda45ced42aaf018f531acc",
"hx_path": "matrices/cb3ab01590a9484b97a7/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "8e1276c17a79883250e6a1a... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 24,
"rank_z": 24,
"tanner_components": 1
} | {
"canonical_digest": "a23e9c9da923998ba6ff95459f791d8e4492497f6466e02ca9c5c6f0199f9290",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 24,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
6225c816c4ff8c855c61 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
1,
2
],
[
4,
4
],
[
5,
0
]
],
"B_terms": [
[
3,
5
],
[
5,
4
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 3
} | {
"hx_content_sha256": "66975a7c727e5ca73010f9bdb8213dcb67ffd7d65ed7b3b0f504d4531c5537ec",
"hx_file_sha256": "19860f961a8be2e2dc1750b418ea6212b1ab2000f5a44576ef8887a2bcf47a4b",
"hx_path": "matrices/6225c816c4ff8c855c61/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "8f16cd2caaa00b1a72fe3db... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 24,
"rank_z": 24,
"tanner_components": 1
} | {
"canonical_digest": "8a723ea8557e7300c1592f97788bd91fb354b57fc02de46730f81f9074e79d68",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 24,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
ebac15b6336935ab059f | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
0,
3
]
],
"B_terms": [
[
0,
0
],
[
0,
1
],
[
1,
0
],
[
1,
3
]
],
"ell": 45,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 2.25
} | {
"hx_content_sha256": "f903c28011e6649f2ddaf4d2fa9c01bccb2f2ebf15c7a60e2651e8f37e416f26",
"hx_file_sha256": "3a8082a52f090a1c5562398a2930df884268b6529ae26ab728ff50d2d6848fda",
"hx_path": "matrices/ebac15b6336935ab059f/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "ee5e23f57dea2653079f6... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 135,
"rank_z": 135,
"tanner_components": 1
} | {
"canonical_digest": "ca7d5739e1dc4cead332fe48189e16f3e9d950dd365674c350fb023031e23a47",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 90,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
dc5339a8def3b549a111 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
11,
2
],
[
11,
3
]
],
"B_terms": [
[
23,
0
],
[
23,
1
],
[
37,
0
],
[
37,
1
]
],
"ell": 45,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 2.25
} | {
"hx_content_sha256": "79d5501a0833245167d597015e328bcfdc48923bfcd6fd3d66e13698d27c1b94",
"hx_file_sha256": "8f2b1f401525a66c99aa98142e178de3627d477c3cedba430a5aa3c2e0faf019",
"hx_path": "matrices/dc5339a8def3b549a111/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "2956caea4b7ac21f14d40... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 135,
"rank_z": 135,
"tanner_components": 1
} | {
"canonical_digest": "fb5e486467d20a63b75abb5f9d2807dbf6d22ada7225a80485de35434e95df19",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 90,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
c327165b75c36b30beae | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
45,
1
]
],
"B_terms": [
[
0,
1
],
[
44,
0
],
[
45,
0
],
[
89,
0
]
],
"ell": 90,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_ve... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 2.25
} | {
"hx_content_sha256": "2afe4046367dd8acb5bc132aa42508dcdd6440f37d37f318df8f8ae56e23f3fb",
"hx_file_sha256": "b38e178753c4f50384ece625b0616125073120516a10cca3290701fd21c3b59d",
"hx_path": "matrices/c327165b75c36b30beae/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "106f9e9e2909931ef71b7... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 135,
"rank_z": 135,
"tanner_components": 1
} | {
"canonical_digest": "aa808ff74e441c49949d8a2b73ca831f8760c895caf71eeb1a0261808f5e98db",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 90,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
b7369b8176da61224b25 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
1,
0
],
[
3,
1
],
[
4,
1
]
],
"B_terms": [
[
0,
3
],
[
3,
4
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 2.25
} | {
"hx_content_sha256": "a50fef671ca742105502a1b7da3d94d971af8f9f12b03b3f05a47c9d57dcb2a0",
"hx_file_sha256": "a60c1a1e2bce717675642d8dd8db051a4d764ec7c36ebb3c10a789e36a954ddb",
"hx_path": "matrices/b7369b8176da61224b25/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "0289cb0eaad1cf6c898f84e... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 27,
"rank_z": 27,
"tanner_components": 1
} | {
"canonical_digest": "6db8fd64b0a0c958858958d332ab2d4cc6bc45a25c30a5e1c36a24aa632c31ff",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
0a3cdf4c4b7a11672dff | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
3,
5
]
],
"B_terms": [
[
1,
1
],
[
2,
1
],
[
4,
0
],
[
5,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 2.25
} | {
"hx_content_sha256": "c5c33aed1457faacff00a96249080b279f6067bc9529db1a0466984d65a28448",
"hx_file_sha256": "7424ecb716bc55297af6b61bfe8efde6a3d4c573f87645dc2e4497e90b710727",
"hx_path": "matrices/0a3cdf4c4b7a11672dff/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "ef707cd2ced70f397666a27... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 27,
"rank_z": 27,
"tanner_components": 1
} | {
"canonical_digest": "4411d34d3bda636ffdf4312a81df1b2776c290d5a76e1433b42e35d6ccdd4883",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 7,
"strict_inequality": "k*d^2 > 12*n"
} |
646c13a5d7242ffbe3fb | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
1,
2
],
[
3,
1
],
[
4,
0
]
],
"B_terms": [
[
6,
1
],
[
9,
2
]
],
"ell": 15,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_versio... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 1.8
} | {
"hx_content_sha256": "45947252d760e223a5907334679c86cfd72755457f7a16244afc12848e468f93",
"hx_file_sha256": "ff74862a75d8c3da0926a40a247eb289ef0193ec5af4d6c9c733519770bd0495",
"hx_path": "matrices/646c13a5d7242ffbe3fb/Hx.mtx.gz",
"hx_shape": [
45,
90
],
"hz_content_sha256": "c38582597467c6328859add... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 36,
"rank_z": 36,
"tanner_components": 1
} | {
"canonical_digest": "14d0c5b943d86897befc5ee069ca4437c8bceefa9cdd5db02641c71cfbd6eb3f",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 90
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 8,
"strict_inequality": "k*d^2 > 12*n"
} |
e0efec4d2a6df12a827a | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
0,
0
],
[
3,
5
]
],
"B_terms": [
[
0,
0
],
[
1,
4
],
[
3,
3
],
[
4,
3
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 2 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 1.5
} | {
"hx_content_sha256": "447f16a54ded11b61756f778fe319d6fcb6a4934c8b034426c47c8ad8f30f27e",
"hx_file_sha256": "65d941dec444d6e5c732debaf8ad2df8006288be1c14685f16ed45cb820ccd49",
"hx_path": "matrices/e0efec4d2a6df12a827a/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "8401c1391eb8265819df8f2... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 30,
"rank_z": 30,
"tanner_components": 1
} | {
"canonical_digest": "7e6482a017a4263baba90ccfc9bf5e77569502ff740251835793635e6ea6ee83",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
bce79b5541ffe926d495 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
2,
2
],
[
2,
3
]
],
"B_terms": [
[
2,
4
],
[
2,
5
],
[
3,
1
],
[
3,
2
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 1.5
} | {
"hx_content_sha256": "6211d66380a11374e69f163cf4bd2833e8b8b7ab2d60a49730fd64f057a5b285",
"hx_file_sha256": "ed86d70ed4816bd7b70260da1508e3478ffa425d39ecea3379f963e6e0618c15",
"hx_path": "matrices/bce79b5541ffe926d495/Hx.mtx.gz",
"hx_shape": [
36,
72
],
"hz_content_sha256": "114a53499159b9cfeeacf4e... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 30,
"rank_z": 30,
"tanner_components": 1
} | {
"canonical_digest": "6a25c79bf19e3b22112e9991797294cf082efafe7b338790d74c77025fd95c05",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 12,
"n": 72
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
6d1b1f80def0f0fdd96e | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
1,
1
],
[
1,
6
]
],
"B_terms": [
[
1,
17
],
[
1,
22
],
[
2,
9
],
[
2,
14
]
],
"ell": 6,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_vers... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 1 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 1.5
} | {
"hx_content_sha256": "e80e07f72b106bd47c0cedba2b311a76212090e3871d541176d1b389cb8c146c",
"hx_file_sha256": "0d9210f0341e2088a5df863b29a5cf1f02b4ebb33fcf10f121be1359062a13f7",
"hx_path": "matrices/6d1b1f80def0f0fdd96e/Hx.mtx.gz",
"hx_shape": [
180,
360
],
"hz_content_sha256": "1ba5f0a91d6b25a231d39... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 150,
"rank_z": 150,
"tanner_components": 1
} | {
"canonical_digest": "bf45d4eeb5ac8aabf080273e0a67745d93f0eff6f27d2d762a9c0de247315e58",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 60,
"n": 360
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
64af511ac73874d20330 | [
"sealed_trusted_audit"
] | {
"A_terms": [
[
4,
3
],
[
4,
4
],
[
6,
2
],
[
6,
3
]
],
"B_terms": [
[
0,
0
],
[
0,
1
]
],
"ell": 9,
"family": "css-bb",
"geometry": {
"family": "twisted_torus",
"schema_version... | {
"exact": null,
"lower_bound": null,
"lower_bound_source": null,
"upper_bound": 3,
"upper_bound_source": "sealed_trusted_audit"
} | REJECTED_WITH_WITNESS | 4 | {
"bp_osd_distance_upper_bound_advisory": null,
"bp_osd_fom_upper_bound_advisory": null,
"exact": null,
"lower_bound": null,
"upper_bound": 1.5
} | {
"hx_content_sha256": "ac025620f31b0f1a255bc8f6c4d6e5909a7e24038ce35196c0789949de0c4775",
"hx_file_sha256": "ba53e7aee78910b829d660448195df0ca46696610b72966a50be412174c2cb48",
"hx_path": "matrices/64af511ac73874d20330/Hx.mtx.gz",
"hx_shape": [
54,
108
],
"hz_content_sha256": "328efd4ae1638e29d81035... | {
"commutation_violations": 0,
"css_commutation": true,
"max_check_weight": 6,
"max_qubit_degree": 6,
"rank_x": 45,
"rank_z": 45,
"tanner_components": 1
} | {
"canonical_digest": "3e48e00450fcf1fe6968363d96a891183fdb0efcd552da34f373f964b97f9b19",
"matched_reference": null,
"relation": null,
"scope": "pinned known-code registry at sealed structural replay",
"status": "novel"
} | {
"k": 18,
"n": 108
} | 1 | css-bb-twisted-torus-generator-v1 | qcode-coset-two-block-paper-auto-family-v2-gpt56sol-20260811.esc.css-bb-twisted-torus-generator-v1.96ab25fc3ebc | 4 | {
"certified_win": false,
"mode": "scalar-fom-strict-v1",
"required_distance": 9,
"strict_inequality": "k*d^2 > 12*n"
} |
QLDPC FOM>12 Search Evidence
This is a human-review snapshot, not a winner announcement. It contains a compact selection of twisted-torus CSS quantum-code candidates, their check matrices, replay-oriented evidence summaries, and a readable description of the automated five-stage search pipeline.
Status at snapshot: in progress. Sealed rounds: 1–4. Certified novel candidates with exact
FOM > 12: 0.
Snapshot summary
| Item | Value |
|---|---|
| Selected candidates | 51 |
| Sealed trusted audits | 24 |
| Exact non-winners | 3 |
| Rejected with replayable witness | 21 |
| Formally open lower-bound candidates | 27 |
| Advisory upper-bound-only signals | 0 |
Exact FOM > 12 |
0 |
Exact FOM = 12 |
0 |
Best formally open item in this snapshot: 158bf9b332c9012345f8: [[90,12,d]], 5 ≤ d ≤ 10, FOM ∈ [3.33333, 13.3333]. “Open” means the current rigorous interval has not excluded the target; it is not a proof of high distance.
Objective
For a quantum code [[n,k,d]], this project uses
FOM = k d² / n.
The strict target is checked with integer arithmetic: k*d*d > 12*n. Equality is not a win. A candidate is promoted only when its distance evidence and novelty checks cross the appropriate trust boundary.
Read this first
docs/PIPELINE.md— what each automated stage does.docs/METRICS.md— lower bounds, upper bounds, exact values, and search-only scores.docs/EXPERT_REVIEW_CHECKLIST.md— concrete independent checks.data/candidates.jsonl— one compact record per selected code.evidence/proofs.jsonlandmatrices/— evidence andH_X/H_Zmatrices.
Run python -B scripts/verify_dataset.py . to validate every checksum, matrix, CSS commutation relation, reconstructed k, FOM field, and included logical witness.
中文说明
这是供人类专家复核的进行中快照，不是“已经发现新纪录码”的声明。数据集收录精选 twisted-torus CSS 候选、H_X/H_Z、证据等级、FOM 区间、每轮统计和五阶段流水线说明。当前没有任何新候选被严格认证为 FOM>12。BP/OSD 的较大数值只是启发式距离上界，不能当作性能下界或最终结果。
Attribution and non-endorsement
The challenge target follows Shuxiang Cao's public gist. Publishing this dataset does not imply that Shuxiang Cao, NVIDIA, or any cited author has reviewed or endorsed these candidates.
- Downloads last month
- 34