{ "schema": "lp-basis-pair-partition-sharing-bundle-v1", "snapshot": "2026-08-05", "code_count": 19, "exact_distance_count": 18, "interval_count": 1, "kenta_comparison": { "url": "https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_20260714.html", "checked": "2026-08-05", "scope": "parameter-level comparison against the live verified-code table" }, "codes": [ { "metric_id": "PP53J4L18", "name": "PP_J4_L18_P53_S000_A013", "catalogue_location": "main table, page 2", "P": 53, "L": 18, "Jx": 4, "Jz": 4, "N": 954, "K": 536, "rank_X": 209, "rank_Z": 209, "rate": 0.5618448637316562, "check_weight": 18, "degree_X": 4, "degree_Z": 4, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 14, "lower": 14, "upper": 14 }, "proof_summary": "Complete two-sided exclusion through weight 12, even-kernel parity, and a verified weight-14 logical.", "kenta_relation": "No [[954,536,14]] row found in the live verified-code table on 2026-08-05.", "E": [ [ 1, 27, 3, 10, 47, 45, 32, 11, 1, 42, 31, 29, 3, 27, 32, 9, 5, 4 ], [ 31, 10, 10, 52, 44, 50, 34, 5, 38, 10, 40, 15, 34, 41, 6, 41, 16, 23 ], [ 33, 13, 50, 41, 4, 28, 39, 19, 30, 17, 33, 38, 20, 42, 31, 4, 16, 8 ], [ 21, 25, 31, 48, 8, 11, 35, 28, 47, 38, 47, 33, 5, 45, 18, 19, 18, 36 ] ], "D": [ [ 30, 26, 23, 11, 49, 35, 4, 23, 20, 9, 3, 28, 46, 46, 44, 11, 34, 5 ], [ 39, 3, 42, 24, 29, 7, 10, 5, 44, 3, 25, 44, 34, 13, 14, 47, 48, 33 ], [ 37, 47, 14, 39, 9, 24, 2, 37, 49, 21, 14, 2, 18, 47, 27, 20, 34, 27 ], [ 10, 47, 21, 1, 22, 21, 48, 46, 51, 51, 51, 47, 47, 2, 8, 25, 40, 1 ] ], "source": { "path": "seed_spectroscopy_letter/search_pair_partition_shape_frontier_qdist_20260723/data/initial_candidates/PP_J4_L18_P53_S000_A013.json", "sha256": "c5c4208cdbd3d5793d4fb7ccc4d633ba3e686022599cd2625c705905b7ff2a12", "note": "construction record; distance claim updated by the catalogue evidence" }, "file": "codes/PP53J4L18_n954_k536_d14.cpm", "bundle_sha256": "66d116b9a0c1a53c9f6b571bf418fa9fe51de98cb765ef58dd707fe5fd9dc225", "display_parameters": "[[954,536,14]]" }, { "metric_id": "PP113", "name": "j3l8_p113_g8_00001", "catalogue_location": "main table, page 2 and exact comparison appendix", "P": 113, "L": 8, "Jx": 3, "Jz": 3, "N": 904, "K": 230, "rank_X": 337, "rank_Z": 337, "rate": 0.25442477876106195, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 8, "girth_Z": 8, "distance": { "status": "exact", "d": 20, "lower": 20, "upper": 20 }, "proof_summary": "Complete lower certificates and verified minimum-weight logical witnesses.", "kenta_relation": "No [[904,230,20]] row found in the live verified-code table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 83, 25, 111, 19, 1, 107, 92 ], [ 0, 70, 96, 34, 24, 91, 75, 10 ] ], "D": [ [ 0, 92, 24, 3, 24, 0, 3, 92 ], [ 0, 1, 6, 10, 0, 1, 6, 10 ], [ 0, 60, 91, 19, 19, 91, 60, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/pair_partition_exact_registry.json", "registry_key": "PP113", "registry_sha256": "2db777b24356d1e52d56ec7cf4c83023b28c89530b897d6d1876b81763fb27fc", "original_code_path": "02_WORKING_DIRECTORIES/Kasai_Girth8_Distance_Ladder_v1/codes/p113_d20.cpm", "original_code_sha256": "41563aa53c8da41d22442553bf6bcb68020eba09426e129e587f27e699b1bc1c" }, "file": "codes/PP113_n904_k230_d20.cpm", "bundle_sha256": "41563aa53c8da41d22442553bf6bcb68020eba09426e129e587f27e699b1bc1c", "display_parameters": "[[904,230,20]]" }, { "metric_id": "PP37J5L20", "name": "PP_J5_L20_P37_S000_A001", "catalogue_location": "main table, page 2", "P": 37, "L": 20, "Jx": 5, "Jz": 5, "N": 740, "K": 378, "rank_X": 181, "rank_Z": 181, "rate": 0.5108108108108108, "check_weight": 20, "degree_X": 5, "degree_Z": 5, "girth_X": 6, "girth_Z": 6, "distance": { "status": "interval", "d": null, "lower": 16, "upper": 20 }, "proof_summary": "Complete two-sided exclusion through weight 14 and even-kernel parity give d>=16; independently verified weight-20 logical operators on both CSS sides give d<=20.", "kenta_relation": "No [[740,378,d]] row found in the live verified-code table on 2026-08-05.", "E": [ [ 20, 29, 6, 30, 20, 6, 15, 22, 15, 35, 22, 1, 35, 21, 31, 20, 6, 4, 22, 14 ], [ 2, 28, 20, 2, 11, 10, 33, 20, 12, 23, 25, 9, 4, 36, 21, 9, 6, 14, 33, 19 ], [ 19, 22, 24, 14, 18, 12, 15, 31, 7, 20, 35, 35, 22, 26, 26, 31, 14, 30, 5, 10 ], [ 29, 15, 16, 36, 19, 27, 9, 18, 30, 26, 35, 18, 3, 25, 23, 13, 31, 28, 1, 26 ], [ 5, 30, 15, 27, 27, 30, 7, 24, 9, 19, 17, 19, 34, 27, 11, 18, 14, 20, 22, 26 ] ], "D": [ [ 23, 35, 26, 29, 4, 30, 8, 23, 26, 32, 28, 21, 34, 8, 28, 23, 27, 34, 23, 25 ], [ 12, 10, 33, 1, 19, 30, 13, 27, 36, 20, 7, 22, 3, 19, 18, 19, 14, 31, 3, 6 ], [ 31, 4, 11, 24, 15, 7, 1, 22, 12, 19, 17, 22, 32, 21, 25, 6, 11, 16, 33, 15 ], [ 13, 17, 5, 31, 4, 13, 29, 19, 27, 24, 21, 2, 5, 14, 6, 8, 32, 25, 36, 11 ], [ 34, 26, 13, 28, 20, 30, 25, 11, 18, 7, 9, 15, 32, 28, 4, 18, 32, 7, 31, 14 ] ], "source": { "path": "seed_spectroscopy_letter/search_pair_partition_shape_frontier_qdist_20260723/data/initial_candidates/PP_J5_L20_P37_S000_A001.json", "sha256": "c0f29234e0f3b54815f4696c967571a1da2b8c94f135d8ebc97a0588a7de3900", "note": "construction record; distance claim updated by the catalogue evidence" }, "file": "codes/PP37J5L20_n740_k378_d16to20.cpm", "bundle_sha256": "88f76bb4b0580c04d14df3c591edb2f2d342c8ed310d56881c75438347c7c288", "display_parameters": "[[740,378,d]], 16 <= d <= 20" }, { "metric_id": "PP61", "name": "qc_488_126_16_a", "catalogue_location": "main table, page 2 and exact comparison appendix", "P": 61, "L": 8, "Jx": 3, "Jz": 3, "N": 488, "K": 126, "rank_X": 181, "rank_Z": 181, "rate": 0.2581967213114754, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 8, "girth_Z": 8, "distance": { "status": "exact", "d": 16, "lower": 16, "upper": 16 }, "proof_summary": "Complete lower certificates and verified minimum-weight logical witnesses.", "kenta_relation": "The live table lists [[488,126,14]] at girth 6; this local instance is exact distance 16 with girth 8.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 28, 40, 8, 10, 7, 1, 58 ], [ 0, 44, 34, 50, 33, 18, 32, 45 ] ], "D": [ [ 0, 21, 10, 32, 10, 0, 32, 21 ], [ 0, 33, 2, 7, 33, 7, 0, 2 ], [ 0, 18, 1, 19, 0, 18, 1, 19 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/pair_partition_exact_registry.json", "registry_key": "PP61", "registry_sha256": "2db777b24356d1e52d56ec7cf4c83023b28c89530b897d6d1876b81763fb27fc", "original_code_path": "03_EXTRACTED_RELEASES/Kasai_Table_Improvements_J3L8_v1/Kasai_Table_Improvements_J3L8_v1/codes/qc_488_126_16_a.cpm", "original_code_sha256": "b02e4addcca758bdf462bdcd1da19c94d2c7890f96d45149596a750bb3064d3c" }, "file": "codes/PP61_n488_k126_d16.cpm", "bundle_sha256": "b02e4addcca758bdf462bdcd1da19c94d2c7890f96d45149596a750bb3064d3c", "display_parameters": "[[488,126,16]]" }, { "metric_id": "PP59", "name": "qc_472_122_16", "catalogue_location": "main table, page 2 and exact comparison appendix", "P": 59, "L": 8, "Jx": 3, "Jz": 3, "N": 472, "K": 122, "rank_X": 175, "rank_Z": 175, "rate": 0.2584745762711864, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 8, "girth_Z": 8, "distance": { "status": "exact", "d": 16, "lower": 16, "upper": 16 }, "proof_summary": "Complete lower certificates and verified minimum-weight logical witnesses.", "kenta_relation": "The live table now lists the same parameters and girth. The downloaded exponent arrays differ; equivalence is unresolved, and there is no novelty claim on the parameter row.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 19, 36, 17, 28, 52, 3, 48 ], [ 0, 20, 46, 6, 43, 31, 35, 22 ] ], "D": [ [ 0, 48, 43, 32, 43, 0, 32, 48 ], [ 0, 52, 8, 22, 0, 52, 8, 22 ], [ 0, 57, 31, 28, 28, 31, 57, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/pair_partition_exact_registry.json", "registry_key": "PP59", "registry_sha256": "2db777b24356d1e52d56ec7cf4c83023b28c89530b897d6d1876b81763fb27fc", "original_code_path": "03_EXTRACTED_RELEASES/Kasai_Table_Improvements_J3L8_v1/Kasai_Table_Improvements_J3L8_v1/codes/qc_472_122_16.cpm", "original_code_sha256": "21fda532d9a34fe6ddf0bc2cf3417b7c0b345aefb9af8f79ba3c55bed4006003" }, "file": "codes/PP59_n472_k122_d16.cpm", "bundle_sha256": "21fda532d9a34fe6ddf0bc2cf3417b7c0b345aefb9af8f79ba3c55bed4006003", "display_parameters": "[[472,122,16]]" }, { "metric_id": "PPS296", "name": "j3l8_p37_g8_orbit_00001", "catalogue_location": "exact small-code appendix", "P": 37, "L": 8, "Jx": 3, "Jz": 3, "N": 296, "K": 78, "rank_X": 109, "rank_Z": 109, "rate": 0.2635135135135135, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 8, "girth_Z": 8, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "The frozen audit excludes both logical sides through weight 10; even kernels exclude the next odd weight, and replayed weight-12 logicals close the bound.", "kenta_relation": "The downloaded arrays differ. The live table lists girth 6 for the same parameters; this local realization has girth 8.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 20, 6, 26, 4, 1, 25, 22 ], [ 0, 33, 12, 8, 5, 11, 34, 3 ] ], "D": [ [ 0, 22, 5, 27, 5, 0, 27, 22 ], [ 0, 1, 2, 3, 0, 1, 2, 3 ], [ 0, 30, 11, 4, 4, 11, 30, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS296", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_296_78_12.cpm", "original_code_sha256": "0313e95f1059f1f62d406791948c79fcbd3f88d06b942e4dbee540539937bd0a" }, "file": "codes/PPS296_n296_k78_d12.cpm", "bundle_sha256": "0313e95f1059f1f62d406791948c79fcbd3f88d06b942e4dbee540539937bd0a", "display_parameters": "[[296,78,12]]" }, { "metric_id": "PPS276", "name": "j4l12_p23_g6_c0002", "catalogue_location": "exact small-code appendix", "P": 23, "L": 12, "Jx": 4, "Jz": 4, "N": 276, "K": 98, "rank_X": 89, "rank_Z": 89, "rate": 0.35507246376811596, "check_weight": 12, "degree_X": 4, "degree_Z": 4, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 14, "lower": 14, "upper": 14 }, "proof_summary": "Complete searches exclude both sides through weight 12; even kernels exclude weight 13, and a replayed weight-14 logical closes the bound.", "kenta_relation": "The live table lists the same parameters and girth; the CPM bytes differ, but code equivalence is unresolved.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 15, 19, 18, 6, 8, 5, 17, 10, 11, 14, 9 ], [ 0, 20, 17, 15, 19, 3, 11, 1, 9, 7, 2, 21 ], [ 0, 22, 7, 4, 12, 11, 10, 18, 6, 5, 16, 1 ] ], "D": [ [ 0, 17, 6, 13, 2, 19, 0, 17, 6, 13, 2, 19 ], [ 0, 1, 15, 9, 7, 18, 15, 18, 1, 7, 0, 9 ], [ 0, 11, 21, 1, 18, 16, 1, 0, 18, 11, 16, 21 ], [ 0, 5, 1, 14, 10, 15, 10, 1, 0, 15, 14, 5 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS276", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/cluster/small_frontier_20260803/hits/j4l12_p23_orbit0002_exact14/code.cpm", "original_code_sha256": "989af29ac594596d0c8fa78e50c383fdb9517af5fa5a943b125e36bb01108195" }, "file": "codes/PPS276_n276_k98_d14.cpm", "bundle_sha256": "989af29ac594596d0c8fa78e50c383fdb9517af5fa5a943b125e36bb01108195", "display_parameters": "[[276,98,14]]" }, { "metric_id": "PPS248", "name": "j3l8_p31_g8_orbit_00000", "catalogue_location": "exact small-code appendix", "P": 31, "L": 8, "Jx": 3, "Jz": 3, "N": 248, "K": 66, "rank_X": 91, "rank_Z": 91, "rate": 0.2661290322580645, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 8, "girth_Z": 8, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "The frozen audit excludes both logical sides through weight 10; even kernels exclude the next odd weight, and replayed weight-12 logicals close the bound.", "kenta_relation": "The downloaded arrays differ. The live table lists girth 6 for the same parameters; this local realization has girth 8.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 14, 6, 20, 4, 1, 19, 16 ], [ 0, 27, 12, 8, 5, 11, 28, 3 ] ], "D": [ [ 0, 16, 5, 21, 5, 0, 21, 16 ], [ 0, 1, 2, 3, 0, 1, 2, 3 ], [ 0, 24, 11, 4, 4, 11, 24, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS248", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_248_66_12.cpm", "original_code_sha256": "3c1be1d131f4495d4e45ab0423e82581b6af37f6e5036b0eee03885fdf64efa9" }, "file": "codes/PPS248_n248_k66_d12.cpm", "bundle_sha256": "3c1be1d131f4495d4e45ab0423e82581b6af37f6e5036b0eee03885fdf64efa9", "display_parameters": "[[248,66,12]]" }, { "metric_id": "PPS232", "name": "j3l8_p29_g8_orbit_05025", "catalogue_location": "exact small-code appendix", "P": 29, "L": 8, "Jx": 3, "Jz": 3, "N": 232, "K": 62, "rank_X": 85, "rank_Z": 85, "rate": 0.2672413793103448, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "The frozen audit excludes both logical sides through weight 10; even kernels exclude the next odd weight, and replayed weight-12 logicals close the bound.", "kenta_relation": "The live table lists the same parameters and girth. The downloaded arrays differ; full code equivalence is unresolved.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 5, 4, 18, 2, 1, 8, 16 ], [ 0, 10, 24, 15, 3, 23, 11, 12 ] ], "D": [ [ 0, 16, 3, 19, 3, 0, 19, 16 ], [ 0, 1, 2, 12, 0, 1, 2, 12 ], [ 0, 27, 23, 2, 2, 23, 27, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS232", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_232_62_12.cpm", "original_code_sha256": "dcff877cae3a0fa2e4ce9ffb8aa2fe5196c5940213baac90a5bc4bddacbed81f" }, "file": "codes/PPS232_n232_k62_d12.cpm", "bundle_sha256": "dcff877cae3a0fa2e4ce9ffb8aa2fe5196c5940213baac90a5bc4bddacbed81f", "display_parameters": "[[232,62,12]]" }, { "metric_id": "PPS228", "name": "j4l12_p19_s001_c001", "catalogue_location": "exact small-code appendix", "P": 19, "L": 12, "Jx": 4, "Jz": 4, "N": 228, "K": 82, "rank_X": 73, "rank_Z": 73, "rate": 0.35964912280701755, "check_weight": 12, "degree_X": 4, "degree_Z": 4, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "Complete searches exclude both logical sides through weight 11; independently replayed weight-12 logicals prove exact distance 12.", "kenta_relation": "No [[228,82,12]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 17, 14, 9, 4, 8, 15, 6, 16, 5, 7, 3 ], [ 0, 4, 17, 1, 12, 3, 8, 11, 7, 9, 16, 5 ], [ 0, 9, 5, 11, 1, 14, 3, 4, 6, 13, 12, 2 ] ], "D": [ [ 0, 6, 9, 13, 16, 17, 0, 6, 9, 13, 16, 17 ], [ 0, 15, 8, 4, 5, 10, 15, 4, 10, 0, 8, 5 ], [ 0, 5, 6, 3, 7, 18, 3, 0, 7, 5, 18, 6 ], [ 0, 3, 10, 12, 8, 1, 8, 10, 0, 1, 12, 3 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS228", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/results/small_frontier_100_300_v1/found_qc_228_82_12_v1/codes/qc_228_82_12.cpm", "original_code_sha256": "564e40bfa7443f6fa2361fb4061fb53d15df3267a2939f2566440f2f59d4714e" }, "file": "codes/PPS228_n228_k82_d12.cpm", "bundle_sha256": "564e40bfa7443f6fa2361fb4061fb53d15df3267a2939f2566440f2f59d4714e", "display_parameters": "[[228,82,12]]" }, { "metric_id": "PPS190", "name": "j5l10_p19_c0000", "catalogue_location": "exact small-code appendix", "P": 19, "L": 10, "Jx": 5, "Jz": 5, "N": 190, "K": 8, "rank_X": 91, "rank_Z": 91, "rate": 0.042105263157894736, "check_weight": 10, "degree_X": 5, "degree_Z": 5, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 18, "lower": 18, "upper": 18 }, "proof_summary": "Complete Z-side exclusion through weight 16; a replay-verified weight-preserving X/Z involution transfers that exclusion to X; all logical weights are even; and independently validated weight-18 logicals close both upper bounds. Therefore d_X=d_Z=d=18.", "kenta_relation": "No [[190,8,18]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 17, 1, 14, 2, 12, 8, 15, 5, 13 ], [ 0, 13, 12, 16, 14, 1, 9, 6, 2, 18 ], [ 0, 10, 16, 12, 1, 15, 2, 7, 11, 4 ], [ 0, 9, 10, 13, 17, 3, 14, 18, 6, 8 ] ], "D": [ [ 0, 3, 11, 18, 8, 3, 8, 0, 11, 18 ], [ 0, 8, 15, 6, 5, 15, 0, 6, 5, 8 ], [ 0, 14, 7, 2, 13, 0, 14, 7, 2, 13 ], [ 0, 6, 2, 1, 15, 1, 2, 15, 6, 0 ], [ 0, 18, 4, 9, 12, 12, 9, 18, 0, 4 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS190", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/cluster/small_frontier_20260803/hits/j5l10_p19_orbit0000_exact18/code.cpm", "original_code_sha256": "b16ee9d2d4133c1e201b84e01f3d0f85f1dbdfa01602fce7b1af0cefc77cf598" }, "file": "codes/PPS190_n190_k8_d18.cpm", "bundle_sha256": "b16ee9d2d4133c1e201b84e01f3d0f85f1dbdfa01602fce7b1af0cefc77cf598", "display_parameters": "[[190,8,18]]" }, { "metric_id": "PPS184", "name": "j3l8_p23_00156", "catalogue_location": "exact small-code appendix", "P": 23, "L": 8, "Jx": 3, "Jz": 3, "N": 184, "K": 50, "rank_X": 67, "rank_Z": 67, "rate": 0.2717391304347826, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 10, "lower": 10, "upper": 10 }, "proof_summary": "The frozen audit excludes both logical sides through weight 8; even kernels exclude the next odd weight, and replayed weight-10 logicals close the bound.", "kenta_relation": "No [[184,50,10]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 12, 8, 21, 6, 1, 19, 15 ], [ 0, 9, 18, 11, 7, 17, 10, 4 ] ], "D": [ [ 0, 15, 7, 22, 7, 0, 22, 15 ], [ 0, 1, 2, 4, 0, 1, 2, 4 ], [ 0, 5, 17, 6, 6, 17, 5, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS184", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_184_50_10.cpm", "original_code_sha256": "01a3d2940b7ee66a8ceea5407e371117df96080fdf827439f490dbd7aa3849c0" }, "file": "codes/PPS184_n184_k50_d10.cpm", "bundle_sha256": "01a3d2940b7ee66a8ceea5407e371117df96080fdf827439f490dbd7aa3849c0", "display_parameters": "[[184,50,10]]" }, { "metric_id": "PPS170", "name": "j5l10_p17_c0000", "catalogue_location": "exact small-code appendix", "P": 17, "L": 10, "Jx": 5, "Jz": 5, "N": 170, "K": 8, "rank_X": 81, "rank_Z": 81, "rate": 0.047058823529411764, "check_weight": 10, "degree_X": 5, "degree_Z": 5, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 20, "lower": 20, "upper": 20 }, "proof_summary": "A complete cutoff-16 exclusion, side isometry, and even kernels give d>=18. The verified hidden generalized-bicycle equivalence and Wang--Pryadko asymmetric-bicycle identity reduce weight 18 to 60 exact graph cases; their complete aggregate has no witness. A directly replayed weight-20 logical closes the bound. Therefore d_X=d_Z=d=20.", "kenta_relation": "No [[170,8,20]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 15, 4, 3, 8, 7, 6, 5, 10, 2 ], [ 0, 16, 12, 5, 3, 1, 10, 14, 13, 15 ], [ 0, 10, 11, 12, 4, 9, 3, 16, 8, 1 ], [ 0, 6, 10, 16, 15, 11, 1, 2, 9, 7 ] ], "D": [ [ 0, 11, 8, 15, 6, 11, 6, 0, 8, 15 ], [ 0, 7, 9, 14, 10, 9, 0, 14, 10, 7 ], [ 0, 1, 16, 13, 2, 0, 1, 16, 13, 2 ], [ 0, 9, 3, 1, 5, 1, 3, 5, 9, 0 ], [ 0, 2, 1, 10, 7, 7, 10, 2, 0, 1 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS170", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/cluster/small_frontier_20260803/hits/j5l10_p17_orbit0000_prospective_exact20/code.cpm", "original_code_sha256": "4dbb0cbdfb14734094f05e6eda96b006f9379dcfbdc6200d262c72f09b337f14" }, "file": "codes/PPS170_n170_k8_d20.cpm", "bundle_sha256": "4dbb0cbdfb14734094f05e6eda96b006f9379dcfbdc6200d262c72f09b337f14", "display_parameters": "[[170,8,20]]" }, { "metric_id": "PPS152", "name": "j3l8_p19_00016", "catalogue_location": "exact small-code appendix", "P": 19, "L": 8, "Jx": 3, "Jz": 3, "N": 152, "K": 42, "rank_X": 55, "rank_Z": 55, "rate": 0.27631578947368424, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 8, "lower": 8, "upper": 8 }, "proof_summary": "The frozen audit excludes both logical sides through weight 6; even kernels exclude the next odd weight, and replayed weight-8 logicals close the bound.", "kenta_relation": "No [[152,42,8]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 10, 9, 3, 7, 1, 18, 15 ], [ 0, 12, 17, 14, 8, 16, 13, 6 ] ], "D": [ [ 0, 15, 8, 4, 8, 0, 4, 15 ], [ 0, 1, 2, 6, 0, 1, 2, 6 ], [ 0, 6, 16, 7, 7, 16, 6, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS152", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_152_42_8.cpm", "original_code_sha256": "2c0b11059910a4353a746713100720db0e73214abcdd204973206d5af954a897" }, "file": "codes/PPS152_n152_k42_d8.cpm", "bundle_sha256": "2c0b11059910a4353a746713100720db0e73214abcdd204973206d5af954a897", "display_parameters": "[[152,42,8]]" }, { "metric_id": "PPS136", "name": "j3l8_p17_00010", "catalogue_location": "exact small-code appendix", "P": 17, "L": 8, "Jx": 3, "Jz": 3, "N": 136, "K": 38, "rank_X": 49, "rank_Z": 49, "rate": 0.27941176470588236, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 8, "lower": 8, "upper": 8 }, "proof_summary": "The frozen audit excludes both logical sides through weight 6; even kernels exclude the next odd weight, and replayed weight-8 logicals close the bound.", "kenta_relation": "No [[136,38,8]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 8, 10, 4, 1, 9, 6 ], [ 0, 16, 13, 12, 7, 10, 2, 5 ] ], "D": [ [ 0, 6, 7, 13, 7, 0, 13, 6 ], [ 0, 1, 4, 5, 0, 1, 4, 5 ], [ 0, 11, 10, 4, 4, 10, 11, 0 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS136", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_136_38_8.cpm", "original_code_sha256": "2e91f898d06edf32773bc3a37129f17b2309ced5e24d21b384043d5d2740b2e3" }, "file": "codes/PPS136_n136_k38_d8.cpm", "bundle_sha256": "2e91f898d06edf32773bc3a37129f17b2309ced5e24d21b384043d5d2740b2e3", "display_parameters": "[[136,38,8]]" }, { "metric_id": "PPS110A", "name": "j5l10_p11_c0002", "catalogue_location": "exact small-code appendix", "P": 11, "L": 10, "Jx": 5, "Jz": 5, "N": 110, "K": 8, "rank_X": 51, "rank_Z": 51, "rate": 0.07272727272727272, "check_weight": 10, "degree_X": 5, "degree_Z": 5, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "Both logical sides are excluded through weight 10 by the archived search and an independent replay; evenness excludes weight 11, and a replayed weight-12 X logical closes the bound.", "kenta_relation": "No [[110,8,12]] row found in the live table on 2026-08-05; exact instance A.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 6, 3, 10, 9, 5, 7, 8, 2 ], [ 0, 8, 4, 2, 3, 1, 6, 9, 5, 7 ], [ 0, 5, 8, 4, 6, 7, 2, 10, 3, 1 ], [ 0, 10, 5, 8, 1, 6, 9, 2, 4, 3 ] ], "D": [ [ 0, 6, 3, 7, 5, 6, 5, 0, 3, 7 ], [ 0, 3, 7, 9, 8, 7, 0, 9, 8, 3 ], [ 0, 9, 10, 5, 2, 0, 9, 10, 5, 2 ], [ 0, 4, 2, 1, 7, 1, 2, 7, 4, 0 ], [ 0, 2, 1, 6, 9, 9, 6, 2, 0, 1 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS110A", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/cluster/small_frontier_20260803/corpora/j5l10_p11_lowrate_matrixwave_seed2026080411_9/codes/j5l10_p11_c0002.cpm", "original_code_sha256": "8c416007d500bee14be415d1ddf94178f7f713d4517b394ca2a5bf43d5633881" }, "file": "codes/PPS110A_n110_k8_d12.cpm", "bundle_sha256": "8c416007d500bee14be415d1ddf94178f7f713d4517b394ca2a5bf43d5633881", "display_parameters": "[[110,8,12]]" }, { "metric_id": "PPS110B", "name": "j5l10_p11_c0007", "catalogue_location": "exact small-code appendix", "P": 11, "L": 10, "Jx": 5, "Jz": 5, "N": 110, "K": 8, "rank_X": 51, "rank_Z": 51, "rate": 0.07272727272727272, "check_weight": 10, "degree_X": 5, "degree_Z": 5, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "Both logical sides are excluded through weight 10 by the archived search and an independent replay; evenness excludes weight 11, and a replayed weight-12 X logical closes the bound.", "kenta_relation": "No [[110,8,12]] row found in the live table on 2026-08-05; exact instance B.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 9, 8, 7, 3, 4, 10, 2, 5, 6 ], [ 0, 10, 4, 9, 7, 1, 2, 8, 3, 5 ], [ 0, 2, 3, 4, 8, 6, 9, 5, 1, 7 ], [ 0, 5, 2, 10, 9, 8, 7, 1, 6, 4 ] ], "D": [ [ 0, 8, 1, 5, 10, 8, 10, 0, 1, 5 ], [ 0, 4, 6, 8, 5, 6, 0, 8, 5, 4 ], [ 0, 7, 5, 3, 6, 0, 7, 5, 3, 6 ], [ 0, 6, 9, 1, 2, 1, 9, 2, 6, 0 ], [ 0, 1, 7, 2, 4, 4, 2, 1, 0, 7 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS110B", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/cluster/small_frontier_20260803/corpora/j5l10_p11_lowrate_matrixwave_seed2026080411_9/codes/j5l10_p11_c0007.cpm", "original_code_sha256": "e91085ac12bb85f4e7fc1de43ee8526acb2e6f739f813ba7480f696eaa4b8277" }, "file": "codes/PPS110B_n110_k8_d12.cpm", "bundle_sha256": "e91085ac12bb85f4e7fc1de43ee8526acb2e6f739f813ba7480f696eaa4b8277", "display_parameters": "[[110,8,12]]" }, { "metric_id": "PPS110C", "name": "j5l10_p11_c0008", "catalogue_location": "exact small-code appendix", "P": 11, "L": 10, "Jx": 5, "Jz": 5, "N": 110, "K": 8, "rank_X": 51, "rank_Z": 51, "rate": 0.07272727272727272, "check_weight": 10, "degree_X": 5, "degree_Z": 5, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 12, "lower": 12, "upper": 12 }, "proof_summary": "Both logical sides are excluded through weight 10 by the archived search and an independent replay; evenness excludes weight 11, and a replayed weight-12 X logical closes the bound.", "kenta_relation": "No [[110,8,12]] row found in the live table on 2026-08-05; exact instance C.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 10, 4, 9, 7, 5, 3, 2, 1, 8 ], [ 0, 5, 2, 10, 9, 1, 8, 6, 4, 7 ], [ 0, 1, 7, 2, 4, 10, 9, 3, 8, 6 ], [ 0, 8, 1, 5, 10, 9, 2, 4, 6, 3 ] ], "D": [ [ 0, 9, 8, 7, 3, 9, 3, 0, 8, 7 ], [ 0, 3, 10, 6, 1, 10, 0, 6, 1, 3 ], [ 0, 2, 3, 4, 8, 0, 2, 3, 4, 8 ], [ 0, 6, 9, 1, 2, 1, 9, 2, 6, 0 ], [ 0, 4, 6, 8, 5, 5, 8, 4, 0, 6 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS110C", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "07_ACTIVE_SEARCH_FRAMEWORK/cluster/small_frontier_20260803/corpora/j5l10_p11_lowrate_matrixwave_seed2026080411_9/codes/j5l10_p11_c0008.cpm", "original_code_sha256": "396ec469b6dd93f97e7de634d6da1f3bbfd8bab85bdea51ced26dcf1ea064314" }, "file": "codes/PPS110C_n110_k8_d12.cpm", "bundle_sha256": "396ec469b6dd93f97e7de634d6da1f3bbfd8bab85bdea51ced26dcf1ea064314", "display_parameters": "[[110,8,12]]" }, { "metric_id": "PPS104", "name": "j3l8_p13_00382", "catalogue_location": "exact small-code appendix", "P": 13, "L": 8, "Jx": 3, "Jz": 3, "N": 104, "K": 30, "rank_X": 37, "rank_Z": 37, "rate": 0.28846153846153844, "check_weight": 8, "degree_X": 3, "degree_Z": 3, "girth_X": 6, "girth_Z": 6, "distance": { "status": "exact", "d": 8, "lower": 8, "upper": 8 }, "proof_summary": "The frozen audit excludes both logical sides through weight 6; even kernels exclude the next odd weight, and replayed weight-8 logicals close the bound.", "kenta_relation": "No [[104,30,8]] row found in the live table on 2026-08-05.", "E": [ [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 7, 11, 5, 2, 12, 6, 3 ], [ 0, 2, 7, 9, 1, 5, 4, 8 ] ], "D": [ [ 0, 4, 12, 3, 3, 12, 4, 0 ], [ 0, 1, 3, 4, 1, 4, 0, 3 ], [ 0, 5, 6, 11, 0, 5, 6, 11 ] ], "source": { "path": "seed_spectroscopy_letter/good_code_catalogue_20260710/small_pair_partition_exact_registry.json", "registry_key": "PPS104", "registry_sha256": "deb2265878578a46bd5d697d5a854b992c6079b13fa87f9a6fdabcf62c52b5f5", "original_code_path": "02_WORKING_DIRECTORIES/Small_PairPartition_Codes_n104_n348_v1/codes/qc_104_30_8.cpm", "original_code_sha256": "f40ebdb9f2a12e39ccecd49c5b7e537ef0b989cbb19a8cab8e4782b31a640753" }, "file": "codes/PPS104_n104_k30_d8.cpm", "bundle_sha256": "f40ebdb9f2a12e39ccecd49c5b7e537ef0b989cbb19a8cab8e4782b31a640753", "display_parameters": "[[104,30,8]]" } ] }