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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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The source records specify the construction and exact tensor identification.","name":"Rep(S3) x Rep(S3)","existence":"unitary","model_reference":"unitary realization exists","model_reference_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_file":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_location":"R9_1_13","report_url":"./papers/rank9-rank10-m1.pdf","case_url":"./case.html?id=R9_1_13","fusion_tensor":[[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[0,1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,1,0,0,1]],[[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1],[1,0,1,0,0,1,0,0,0],[0,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,1,0,1]],[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,1,0],[1,0,1,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,1,0,1]],[[0,0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,0,1]],[[0,0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,0,0,1],[0,0,0,1,0,0,1,0,1],[0,0,0,1,0,0,1,0,1],[0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,1],[1,1,1,1,1,1,1,1,1]]],"tensor_sha256":"8fc7fdc7fbc9f7ed79b59e8c9d09853515e07cb4b1ed8ca7b6914ca057838972","basis":["X0","X1","X2","X3","X4","X5","X6","X7","X8"],"unit_index":0,"tensor_convention":"N[i][j][k] is the coefficient of X_k in X_i * X_j. 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,1,2,3,4,5,6,7,8],"invertible_indices":[0,1,2,7],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999987,0.9999999999999998,2.0000000000000004,2.0000000000000004,2.0,2.0000000000000004,0.9999999999999998,4.000000000000001],"global_fp_dimension_approx":36.000000000000014,"central_casimir_polynomial":"(t - 36)*(t - 18)**2*(t - 12)**2*(t - 9)*(t - 6)**2*(t - 4)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 36)*(t - 18)**2*(t - 12)**2*(t - 9)*(t - 6)**2*(t - 4)"},"research":[{"title":"Current accepted case 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The source records specify the construction and exact tensor identification."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}]},"download_url":"./downloads/fusion-tensors/R9_1_16.txt","investigation_deferred":false},{"id":"R9_1_17","rank":9,"multiplicity":1,"status":"excluded","summary":"General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates.","name":"R9_1_17","existence":"excluded","model_reference":"","model_reference_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_file":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_location":"R9_1_17","report_url":"./papers/rank9-rank10-m1.pdf","case_url":"./case.html?id=R9_1_17","fusion_tensor":[[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[1,0,0,1,1,1,1,1,0],[0,0,0,1,1,1,1,0,1],[0,0,0,1,1,1,1,0,1],[0,1,1,1,1,1,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,1,0,0,0]],[[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,1,1,1,0,1],[1,0,1,1,1,1,1,0,0],[0,1,0,1,1,1,1,1,0],[0,0,0,1,1,1,1,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,1,0,0]],[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,1,1,1,0,1],[0,1,0,1,1,1,1,1,0],[1,0,1,1,1,1,1,0,0],[0,0,0,1,1,1,1,0,1],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,1,0,0]],[[0,0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,1,1,1,1,1,0,0],[0,0,0,1,1,1,1,0,1],[0,0,0,1,1,1,1,0,1],[1,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,0,0]],[[0,0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,0,0,0],[0,0,0,1,0,0,1,0,0],[0,0,0,1,0,0,1,0,0],[0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,1,0]]],"tensor_sha256":"999ef408e6632782f4280032464e13c67c9affc4429be84960aca03c987c7060","basis":["X0","X1","X2","X3","X4","X5","X6","X7","X8"],"unit_index":0,"tensor_convention":"N[i][j][k] is the coefficient of X_k in X_i * X_j. 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,1,2,3,4,5,6,7,8],"invertible_indices":[0,1,2,7],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999976,1.0000000000000002,4.44948974278318,4.44948974278318,4.44948974278318,4.44948974278318,0.9999999999999991,2.0000000000000004],"global_fp_dimension_approx":87.1918358845309,"central_casimir_polynomial":"(t - 16)**2*(t - 8)**4*(t - 4)*(t**2 - 96*t + 768)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 16)**2*(t - 8)**4*(t - 4)*(t**2 - 96*t + 768)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R9_1_17","rank":9,"input_line":17,"status":"excluded","tensor_sha256_compact_json":"999ef408e6632782f4280032464e13c67c9affc4429be84960aca03c987c7060","tensor_sha256_uint8_flattened":"0b9efb30e07991c999f99c23c6d44bb51e0bfb49c17554bce9b6a45da09efe56","commutative":true,"dual":[0,1,2,3,4,5,6,7,8],"fp_dimensions_approx":[1.0,0.9999999999999976,1.0000000000000002,4.44948974278318,4.44948974278318,4.44948974278318,4.44948974278318,0.9999999999999991,2.0000000000000004],"fp_dimension_approx":87.1918358845309,"exclusions":[{"criterion":"central restriction: quadratic","scope":"no fusion category over 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work/resolve_rank9_irrational/quadratic_exact.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/resolve_rank9_irrational/proofs.tex","path":"evidence/rank9_rank10_m1_20261023/work/resolve_rank9_irrational/proofs.tex","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/resolve_rank9_irrational/proofs.tex","sha256":"5fad2e5a6c09994aa704b2a667d5aa93d997c213655db40f2fa092251f16f201"},{"label":"work/resolve_rank9_irrational/quadratic_certificates.json","path":"evidence/rank9_rank10_m1_20261023/work/resolve_rank9_irrational/quadratic_certificates.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/resolve_rank9_irrational/quadratic_certificates.json","sha256":"d12d50c2b004cd63013b9b19c78a529bdc5846faac46bf4b02fdbecc2a3eb246"},{"label":"work/resolve_rank9_irrational/quadratic_exact.py","path":"evidence/rank9_rank10_m1_20261023/work/resolve_rank9_irrational/quadratic_exact.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/resolve_rank9_irrational/quadratic_exact.py","sha256":"ef31e4c5e353d2b936b5f790305265db505e0bf5fa37aa17cab3206ad3dd2d05"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,1,2,3,4,5,6,7,8],"invertible_indices":[0,1],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999989,1.9999999999999993,1.9999999999999991,1.9999999999999991,1.999999999999999,1.999999999999999,1.999999999999999,1.9999999999999991],"global_fp_dimension_approx":29.999999999999975,"central_casimir_polynomial":"(t - 30)*(t - 15)**7*(t - 2)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 30)*(t - 15)**7*(t - 2)"},"research":[{"title":"Current accepted case 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,3,4,5,6,7,8],"invertible_indices":[0,1,2,8],"commutative":false,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999969,0.9999999999999997,5.156325174658663,5.156325174658663,4.962388608184033,5.156325174658663,5.1563251746586625,0.9999999999999993],"global_fp_dimension_approx":134.97605792590943,"central_casimir_polynomial":"(t - 8)**6*(t**3 - 152*t**2 + 2368*t - 9472)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package."},"research":[{"title":"Current accepted case 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,3,4,5,6,7,8],"invertible_indices":[0,3,4,5],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,4.000000000000001,3.9999999999999987,0.9999999999999998,0.9999999999999997,0.9999999999999997,2.0,1.9999999999999996,2.0],"global_fp_dimension_approx":48.0,"central_casimir_polynomial":"(t - 48)*(t - 24)*(t - 16)*(t - 8)**5*(t - 4)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 48)*(t - 24)*(t - 16)*(t - 8)**5*(t - 4)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R9_1_87","rank":9,"input_line":87,"status":"excluded","tensor_sha256_compact_json":"7bc8a9944bfec23ed79151020fb07157f4e2f3bc13b0f909c25bbe83b7c489b8","tensor_sha256_uint8_flattened":"af31325e72b3e86b4614cf0dbf7071df66a47ee1cb95beb5728ec2619c7f65ba","commutative":true,"dual":[0,2,1,3,4,5,6,7,8],"fp_dimensions_approx":[1.0,4.000000000000001,3.9999999999999987,0.9999999999999998,0.9999999999999997,0.9999999999999997,2.0,1.9999999999999996,2.0],"fp_dimension_approx":48.0,"exclusions":[{"criterion":"Complete dimension-48 solvable-category reduction: near-group, triality, and characteristic central boson branches","scope":"no fusion category over C","proof":"work/resolve_rank9_integral/D48_EXCLUSIONS.tex","certificate":"work/resolve_rank9_integral/d48_exclusions_receipt.json","verifier":"python work/resolve_rank9_integral/verify_d48_exclusions.py"}],"models":[]}},{"title":"Completed research and remaining scope","source":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","source_sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491","data":{"findings":["Solvability and trivial universal grading force a C2 equivariantization. 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The exclusion does not depend on the completeness of an external quotient 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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The source records specify the construction and exact tensor identification.","name":"C(F2^2 semidirect S3,Omega,C2,1)","existence":"unitary","model_reference":"unitary realization exists","model_reference_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_file":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_location":"R9_1_92","report_url":"./papers/rank9-rank10-m1.pdf","case_url":"./case.html?id=R9_1_92","fusion_tensor":[[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]],[[0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]],[[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,0,0],[1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,1,0,1,0],[0,1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0]],[[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,1],[0,0,0,1,0,1,0,0,0],[0,0,0,1,0,0,1,0,0],[0,1,1,0,1,0,0,0,0],[0,0,0,0,0,1,1,0,0],[0,0,0,0,1,0,0,0,0]],[[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,0,0],[0,0,0,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,1],[0,0,0,1,0,0,0,1,0],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,1,0,0,0]],[[0,0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,1,1,0,0,0,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,1,0,0,1,0],[1,0,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,1,0,0]],[[0,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,1,0,0],[0,1,1,0,1,0,0,0,0],[0,0,0,1,0,0,1,0,0],[0,0,0,1,0,1,0,0,0],[1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,1,0]],[[0,0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0]]],"tensor_sha256":"76518b5b6c24a3cdc818e5c309882a70a845d544624349fab1fc205cb1b87ea5","basis":["X0","X1","X2","X3","X4","X5","X6","X7","X8"],"unit_index":0,"tensor_convention":"N[i][j][k] is the coefficient of X_k in X_i * X_j. 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,5,6,7,8],"invertible_indices":[0,1,2,8],"commutative":false,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999989,0.9999999999999986,3.5615528128088307,3.5615528128088307,2.0,3.5615528128088316,3.5615528128088307,0.9999999999999996],"global_fp_dimension_approx":58.73863375370598,"central_casimir_polynomial":"(t - 16)**4*(t - 8)*(t - 4)**2*(t**2 - 68*t + 544)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package."},"research":[{"title":"Current accepted case 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The source records specify the construction and exact tensor identification.","name":"C4-subextension of (Ising x Ising) crossed C2_swap","existence":"unitary","model_reference":"unitary realization exists","model_reference_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_file":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_location":"R9_1_102","report_url":"./papers/rank9-rank10-m1.pdf","case_url":"./case.html?id=R9_1_102","fusion_tensor":[[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,1,0,0,0,0]],[[0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0]],[[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,1,0,0,0,0]],[[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,1,0,1,0,0,0,0,0]],[[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],[[0,0,0,0,0,0,0,0,1],[0,0,1,0,1,0,0,0,0],[0,1,0,1,0,0,0,0,0],[0,0,1,0,1,0,0,0,0],[0,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,1,1,0]]],"tensor_sha256":"acac184950e0242f308e71a7f3d275bb2cdc8868d15240bbc8a96da66247c0a6","basis":["X0","X1","X2","X3","X4","X5","X6","X7","X8"],"unit_index":0,"tensor_convention":"N[i][j][k] is the coefficient of X_k in X_i * X_j. 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,5,6,7,8],"invertible_indices":[0,6,7,8],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,1.414213562373095,1.4142135623730951,1.4142135623730951,1.414213562373095,2.0,1.0,1.0,1.0],"global_fp_dimension_approx":16.0,"central_casimir_polynomial":"(t - 16)**4*(t - 8)**4*(t - 4)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 16)**4*(t - 8)**4*(t - 4)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R9_1_103","rank":9,"input_line":103,"status":"unitarily_realized","tensor_sha256_compact_json":"001bb9bbe66f99f0bd1e29bde5687be90bada6a78d26082892b97afcafb47562","tensor_sha256_uint8_flattened":"c61d03ed52a4b20d412902f05351faa37b3c7808b9c43c807dd91ea922d6207a","commutative":true,"dual":[0,2,1,4,3,5,6,7,8],"fp_dimensions_approx":[1.0,1.414213562373095,1.4142135623730951,1.4142135623730951,1.414213562373095,2.0,1.0,1.0,1.0],"fp_dimension_approx":16.0,"exclusions":[],"models":[{"model":"C2-zest(Ising x Ising; h=4, degree=[0, 0, 1, 0, 0, 1, 1, 1, 0])","scope":"unitary realization exists","proof":"work/audit_models/THEORY.md","certificate":"work/audit_models/selected_models.json","verifier":"python work/audit_models/verify_models.py"}]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/audit_models/THEORY.md","path":"evidence/rank9_rank10_m1_20261023/work/audit_models/THEORY.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/audit_models/THEORY.md","sha256":"340ad52ce81d25b05b933c0b8a98a067715bba1c180f349a21c77c97dac04678"},{"label":"work/audit_models/selected_models.json","path":"evidence/rank9_rank10_m1_20261023/work/audit_models/selected_models.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/audit_models/selected_models.json","sha256":"2cd851dee505ff7e2a3ab5773ebc7238db683b135f6b01cb92d27d9d623f5a1b"},{"label":"work/audit_models/verify_models.py","path":"evidence/rank9_rank10_m1_20261023/work/audit_models/verify_models.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/audit_models/verify_models.py","sha256":"44706f202cf12ea6cb2c557aee8efb7086f82d7e163544c3e768afbdc7a68b04"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"}],"categorification_scope":{"general_status":"realized","level_status":{"general":"realized","pivotal":"realized","spherical":"realized","pseudo_unitary":"realized","unitary":"realized"},"strongest_excluded":null,"same_category_implications":[],"existence_implications":[],"notes":["A unitary categorification is identified: C2-zest(Ising x Ising; 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The source records specify the construction and exact tensor identification."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}]},"download_url":"./downloads/fusion-tensors/R9_1_103.txt","investigation_deferred":false},{"id":"R9_1_104","rank":9,"multiplicity":1,"status":"unitarily_realized","summary":"A unitary categorification is identified: C2-zest(SU(2)_8; h=8, degree=[0, 1, 0, 1, 0, 1, 0, 1, 0]). 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,5,6,7,8],"invertible_indices":[0,5],"commutative":false,"frobenius_perron_dimensions_approx":[1.0,5.37228132326901,5.372281323269015,5.372281323269015,5.372281323269015,0.9999999999999974,5.372281323269016,6.372281323269016,6.372281323269017],"global_fp_dimension_approx":227.5189716074916,"central_casimir_polynomial":"(t - 24)**2*(t - 8)**5*(t**2 - 231*t + 792)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package."},"research":[{"title":"Current accepted case 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,6,5,7,8],"invertible_indices":[0,1,2,8],"commutative":false,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999976,1.0000000000000002,5.156325174658661,5.156325174658661,5.15632517465866,5.15632517465866,4.96238860818403,0.9999999999999997],"global_fp_dimension_approx":134.9760579259093,"central_casimir_polynomial":"(t - 8)**6*(t**3 - 152*t**2 + 2368*t - 9472)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package."},"research":[{"title":"Current accepted case 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,1,2,3,4,5,6,7,8,9],"invertible_indices":[0,1,2,9],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999991,0.9999999999999997,2.9122291784843983,3.5688496095315094,3.9122291784843988,3.912229178484399,3.5688496095315094,2.9122291784843983,1.0000000000000002],"global_fp_dimension_approx":77.04660693690766,"central_casimir_polynomial":"(t - 20)*(t - 4)**2*(t**3 - 102*t**2 + 2056*t - 10280)*(t**4 - 74*t**3 + 1968*t**2 - 22216*t + 88864)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 20)*(t - 4)**2*(t**3 - 102*t**2 + 2056*t - 10280)*(t**4 - 74*t**3 + 1968*t**2 - 22216*t + 88864)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R10_1_3","rank":10,"input_line":3,"status":"excluded","tensor_sha256_compact_json":"9475641124c4d02886be9d0aa5be9ba6b35a9dd796be9937179dd170479c8118","tensor_sha256_uint8_flattened":"1b9fa5626d9dae1f5e6580e5e3251541f6d723113ceac7546ff53497c819c2f7","commutative":true,"dual":[0,1,2,3,4,5,6,7,8,9],"fp_dimensions_approx":[1.0,0.9999999999999991,0.9999999999999997,2.9122291784843983,3.5688496095315094,3.9122291784843988,3.912229178484399,3.5688496095315094,2.9122291784843983,1.0000000000000002],"fp_dimension_approx":77.04660693690766,"exclusions":[{"criterion":"casimir_dnumber","scope":"no fusion category over 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/spectra/one_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","sha256":"48949357159efe774e9f172f7b548e8b115df5703e1dc5bdb7e48dfc58cfedbc"},{"label":"work/obstructions/spectra/zero_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","sha256":"7785ae431e1be9de125c7a62e7412ce2b05c427797515a6a0f62e6a579db4306"},{"label":"work/obstructions/structural.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/structural.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/structural.json","sha256":"e8252b5e25428924f5ef7ee9d33e10e8d48c7bde4cc64bbf07acefb532c35e6e"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/spectra/one_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","sha256":"48949357159efe774e9f172f7b548e8b115df5703e1dc5bdb7e48dfc58cfedbc"},{"label":"work/obstructions/spectra/zero_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","sha256":"7785ae431e1be9de125c7a62e7412ce2b05c427797515a6a0f62e6a579db4306"},{"label":"work/obstructions/structural.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/structural.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/structural.json","sha256":"e8252b5e25428924f5ef7ee9d33e10e8d48c7bde4cc64bbf07acefb532c35e6e"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/spectra/one_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","sha256":"48949357159efe774e9f172f7b548e8b115df5703e1dc5bdb7e48dfc58cfedbc"},{"label":"work/obstructions/spectra/zero_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","sha256":"7785ae431e1be9de125c7a62e7412ce2b05c427797515a6a0f62e6a579db4306"},{"label":"work/obstructions/structural.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/structural.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/structural.json","sha256":"e8252b5e25428924f5ef7ee9d33e10e8d48c7bde4cc64bbf07acefb532c35e6e"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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is the coefficient of X_k in X_i * X_j. Indices are zero-based; X_0 is the unit. The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,1,2,3,4,5,6,7,8,9],"invertible_indices":[0,1],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999998,6.608033764809964,6.6080337648099645,2.9770989448207006,3.8860191824318195,4.705945480318242,5.4181006610891105,6.006175619653366,6.456702818935363],"global_fp_dimension_approx":242.56137819080598,"central_casimir_polynomial":"(t - 4)**2*(t**8 - 365*t**7 + 35876*t**6 - 1665414*t**5 + 43148822*t**4 - 659550384*t**3 + 5898770485*t**2 - 28447885264*t + 56895770528)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 4)**2*(t**8 - 365*t**7 + 35876*t**6 - 1665414*t**5 + 43148822*t**4 - 659550384*t**3 + 5898770485*t**2 - 28447885264*t + 56895770528)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R10_1_50","rank":10,"input_line":50,"status":"excluded","tensor_sha256_compact_json":"ef5d60c5ffd33c49c418cbdd1d6dfd1e01079398048b767273eea883425129a5","tensor_sha256_uint8_flattened":"443a46f416c8eed881c603120083366b28e61fed68848c35269075e309fedee5","commutative":true,"dual":[0,1,2,3,4,5,6,7,8,9],"fp_dimensions_approx":[1.0,0.9999999999999998,6.608033764809964,6.6080337648099645,2.9770989448207006,3.8860191824318195,4.705945480318242,5.4181006610891105,6.006175619653366,6.456702818935363],"fp_dimension_approx":242.56137819080598,"exclusions":[{"criterion":"casimir_dnumber","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/arithmetic.json","verifier":"python work/root_audit/verify_baseline.py"},{"criterion":"cyclotomic","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/arithmetic.json","verifier":"python work/root_audit/verify_baseline.py"},{"criterion":"zero_spectrum","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/spectra/zero_spectrum.json","verifier":"python work/root_audit/verify_baseline.py"},{"criterion":"one_spectrum","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/spectra/one_spectrum.json","verifier":"python work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/spectra/one_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","sha256":"48949357159efe774e9f172f7b548e8b115df5703e1dc5bdb7e48dfc58cfedbc"},{"label":"work/obstructions/spectra/zero_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","sha256":"7785ae431e1be9de125c7a62e7412ce2b05c427797515a6a0f62e6a579db4306"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/spectra/one_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","sha256":"48949357159efe774e9f172f7b548e8b115df5703e1dc5bdb7e48dfc58cfedbc"},{"label":"work/obstructions/spectra/zero_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","sha256":"7785ae431e1be9de125c7a62e7412ce2b05c427797515a6a0f62e6a579db4306"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/spectra/one_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/one_spectrum.json","sha256":"48949357159efe774e9f172f7b548e8b115df5703e1dc5bdb7e48dfc58cfedbc"},{"label":"work/obstructions/spectra/zero_spectrum.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/spectra/zero_spectrum.json","sha256":"7785ae431e1be9de125c7a62e7412ce2b05c427797515a6a0f62e6a579db4306"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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is the coefficient of X_k in X_i * X_j. 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,5,6,7,8,9],"invertible_indices":[0,1,2,3,4,7,8,9],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999988,0.9999999999999988,0.9999999999999992,0.9999999999999992,3.23606797749979,3.23606797749979,0.9999999999999994,0.9999999999999994,0.9999999999999994],"global_fp_dimension_approx":28.944271909999152,"central_casimir_polynomial":"(t - 16)**2*(t - 8)**6*(t**2 - 40*t + 320)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 16)**2*(t - 8)**6*(t**2 - 40*t + 320)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R10_1_99","rank":10,"input_line":99,"status":"excluded","tensor_sha256_compact_json":"4e2521dc326b1b1631038d1d6531e3c02fe56cabf9b4da436ba3fee1a5695c5a","tensor_sha256_uint8_flattened":"4eb09e1940729845def303d3620d53e86e172c8ca07a815bab8d0e375b6aee0b","commutative":true,"dual":[0,2,1,4,3,5,6,7,8,9],"fp_dimensions_approx":[1.0,0.9999999999999988,0.9999999999999988,0.9999999999999992,0.9999999999999992,3.23606797749979,3.23606797749979,0.9999999999999994,0.9999999999999994,0.9999999999999994],"fp_dimension_approx":28.944271909999152,"exclusions":[{"criterion":"generalized_near_group_divisibility","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/gng.json","verifier":"python work/root_audit/verify_baseline.py"},{"criterion":"two_dimension_induction","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/two_dimension_induction.json","verifier":"python work/root_audit/verify_baseline.py"},{"criterion":"involution_module","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/module3.json","verifier":"python work/root_audit/verify_baseline.py"},{"criterion":"involution_module","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/module_all.json","verifier":"python work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/gng.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/gng.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/gng.json","sha256":"b651b8027cb0071bb9c9f113d6a52a558d2195c4b512e6bb2eaa92172d4d44f0"},{"label":"work/obstructions/module3.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/module3.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/module3.json","sha256":"265b6be3971e886943c67e1dd9d860f6f6526822dc16e7ec6fce9425f123b095"},{"label":"work/obstructions/module_all.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/module_all.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/module_all.json","sha256":"61946be8c0f50e064d3e4e16b8af21b54e1d8e9d9d06fd4a5fd2ae772f92a8be"},{"label":"work/obstructions/two_dimension_induction.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/two_dimension_induction.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/two_dimension_induction.json","sha256":"c3a5b36e87cb6fc329332ff6bd58689da3d7937793c3aaa08cf26b70681706b0"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to two ordinary-factor swap descents: one has fusion multiplicity two, and the other has invertible group C2×C2, incompatible with this ring's C4."],"audit_sources":[{"label":"General complex exclusion proof","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","sha256":"2b38e38ed6b444d95ecbef7404ff58ff94f20cd5f7000cb1ff53461c4eed4033"}],"braided":{"status":"excluded","explanation":"General complex nonexistence also excludes braided categorifications.","sources":[{"label":"new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","sha256":"2b38e38ed6b444d95ecbef7404ff58ff94f20cd5f7000cb1ff53461c4eed4033"}]}},"download_url":"./downloads/fusion-tensors/R10_1_114.txt","investigation_deferred":false},{"id":"R10_1_115","rank":10,"multiplicity":1,"status":"excluded","summary":"No complex fusion categorification exists. 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Indices are zero-based; X_0 is the unit. The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,5,6,7,8,9],"invertible_indices":[0,1,2,9],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999941,0.9999999999999952,5.82842712474619,5.82842712474619,4.828427124746189,4.828427124746189,5.828427124746188,5.82842712474619,0.9999999999999968],"global_fp_dimension_approx":186.50966799187802,"central_casimir_polynomial":"(t - 16)**3*(t - 8)**5*(t**2 - 192*t + 1024)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 16)**3*(t - 8)**5*(t**2 - 192*t + 1024)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","source_sha256":"a4075e19d489ff9daaa405647c3be5aa8b8bed321e15d75f1ad53dbf9eb47ebe","data":{"id":"R10_1_115","rank":10,"input_line":115,"status":"excluded","tensor_sha256_compact_json":"0e57e37801e8a5135ad03dfe156ba842ef019488637a08d30c200682bc109679","tensor_sha256_uint8_flattened":"36c9c0e8d7a7eb802bd21e04a35dcc720a399f33309562b6679e103bfae0af87","commutative":true,"dual":[0,2,1,4,3,5,6,7,8,9],"fp_dimensions_approx":[1.0,0.9999999999999941,0.9999999999999952,5.82842712474619,5.82842712474619,4.828427124746189,4.828427124746189,5.828427124746188,5.82842712474619,0.9999999999999968],"fp_dimension_approx":186.50966799187802,"exclusions":[{"criterion":"ordinary_factor_swap_descent","scope":"general complex fusion categories","proof":"new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","certificate":"verification_summary.json","verifier":"python new/rank16_dual/verify_subcategories.py; see README.md for the full exact replay"}],"models":[]}},{"title":"Proof and remaining scope","source":"evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","source_sha256":"2b38e38ed6b444d95ecbef7404ff58ff94f20cd5f7000cb1ff53461c4eed4033","data":{"findings":["No complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to two ordinary-factor swap descents: one has fusion multiplicity two, and the other has invertible group C2×C2, incompatible with this ring's C4.","The categorical proof and the exact finite reconstruction have independent agent audits; independent human verification remains pending."]}}],"evidence":[{"label":"README.md","path":"evidence/rank10_m1_exclusions_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/README.md","sha256":"4bd56073df729bd025e943b3168ae339f439de0fea7647318c182d6d505751a2"},{"label":"accepted_ledger.json","path":"evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","sha256":"a4075e19d489ff9daaa405647c3be5aa8b8bed321e15d75f1ad53dbf9eb47ebe"},{"label":"classification_updates.json","path":"evidence/rank10_m1_exclusions_20261023/classification_updates.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/classification_updates.json","sha256":"fedd7c61239a3e708852b2962f06b2f05d914f43bbb9f99e158dcd263ebc0b87"},{"label":"verification_summary.json","path":"evidence/rank10_m1_exclusions_20261023/verification_summary.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/verification_summary.json","sha256":"75579544ab2c180dc3e0e76e3619d7df9094ef8603fcd9dd37890dd03d3aebb0"},{"label":"new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","sha256":"2b38e38ed6b444d95ecbef7404ff58ff94f20cd5f7000cb1ff53461c4eed4033"},{"label":"new/quadratic_obstructions/MORITA_REDUCTION.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/MORITA_REDUCTION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/MORITA_REDUCTION.md","sha256":"cc6552523de1a64488450e2534e638b75e9f7ee2d8583c7759d42946ba3e6852"},{"label":"new/quadratic_obstructions/REDUCTION_AUDIT.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/REDUCTION_AUDIT.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/REDUCTION_AUDIT.md","sha256":"24bc793086ebdbfed976f54d9c1738669a2ed6b00eabe44c8fda62759b726a40"},{"label":"new/rank16_dual/RELATIVE_FACTORIZATION.md","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/RELATIVE_FACTORIZATION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/RELATIVE_FACTORIZATION.md","sha256":"2f358456f3d8cf19bbd423f71bac0b7233091c2af2f350631cca4d417c93d28f"},{"label":"new/quadratic_obstructions/R10_1_115_dual_tensor.json","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/R10_1_115_dual_tensor.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/R10_1_115_dual_tensor.json","sha256":"48354801594fcacef954e542c22fa68fcdc923649b6c7c4023a4732a02268bbc"},{"label":"new/quadratic_obstructions/commutant_completeness_receipt.json","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/commutant_completeness_receipt.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/commutant_completeness_receipt.json","sha256":"6c8263c3a2639fb94e7a8cd49fbee76d0ecf52964df199701061842208426db8"},{"label":"new/rank16_dual/verify_subcategories.py","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/verify_subcategories.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/verify_subcategories.py","sha256":"770d3a93d365c4b2f3b939c886bcee59cc89d0874a28392ff872dc52f19cf1cc"},{"label":"new/rank16_dual/subcategories_receipt.json","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/subcategories_receipt.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/subcategories_receipt.json","sha256":"6dbcd2507b8df923878f7b17195ec6d0895224eb10bcf848bed4ed86444d99d9"},{"label":"new/rank16_dual/ORDINARY_DESCENT_AUDIT.md","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/ORDINARY_DESCENT_AUDIT.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/ORDINARY_DESCENT_AUDIT.md","sha256":"2362c915a6b39565a8cca528b0b80d83ffa07d22db534192605edf17940566c0"},{"label":"work/audit_signed/AUDI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complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to two ordinary-factor swap descents: one has fusion multiplicity two, and the other has invertible group C2×C2, incompatible with this ring's C4."],"audit_sources":[{"label":"General complex exclusion proof","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","sha256":"2b38e38ed6b444d95ecbef7404ff58ff94f20cd5f7000cb1ff53461c4eed4033"}],"braided":{"status":"excluded","explanation":"General complex nonexistence also excludes braided categorifications.","sources":[{"label":"new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_models/ORDINARY_FACTOR_EXCLUSION.md","sha256":"2b38e38ed6b444d95ecbef7404ff58ff94f20cd5f7000cb1ff53461c4eed4033"}]}},"download_url":"./downloads/fusion-tensors/R10_1_115.txt","investigation_deferred":false},{"id":"R10_1_116","rank":10,"multiplicity":1,"status":"unitarily_realized","summary":"A unitary categorification is identified: Fib x TY(C4). 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The forced Morita dual and relative factorization reduce the problem to a central fermion in a pseudo-PSU(2)6 factor. 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complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to a central fermion in a pseudo-PSU(2)6 factor. Its odd-evaluation rank-two superfusion quotient is excluded by the published finite superpentagon calculation."],"audit_sources":[{"label":"General complex exclusion proof","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","sha256":"8e1b9e706d8fa1763748fb7135f67d7031627c8f082019033c32d4d609dca47b"}],"braided":{"status":"excluded","explanation":"General complex nonexistence also excludes braided categorifications.","sources":[{"label":"new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","sha256":"8e1b9e706d8fa1763748fb7135f67d7031627c8f082019033c32d4d609dca47b"}]}},"download_url":"./downloads/fusion-tensors/R10_1_152.txt","investigation_deferred":false},{"id":"R10_1_153","rank":10,"multiplicity":1,"status":"excluded","summary":"No complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to a central fermion in a pseudo-PSU(2)6 factor. Its odd-evaluation rank-two superfusion quotient is excluded by the published finite superpentagon calculation.","name":"R10_1_153","existence":"excluded","model_reference":"","model_reference_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","source_file":"evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","source_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","source_location":"R10_1_153","report_url":"./papers/rank9-rank10-m1.pdf","case_url":"./case.html?id=R10_1_153","fusion_tensor":[[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]],[[0,0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]],[[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,1,1,1,1,1,1,1],[1,0,0,1,1,1,1,1,1,0],[0,0,0,1,1,1,0,1,1,0],[0,0,0,1,1,0,1,1,1,0],[0,1,0,1,1,1,1,1,1,0],[0,0,1,1,1,1,1,1,1,0],[0,0,0,0,1,0,0,0,0,0]],[[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[1,0,0,1,1,1,1,1,1,0],[0,0,0,1,1,1,1,1,1,1],[0,0,0,1,1,1,0,1,1,0],[0,0,0,1,1,0,1,1,1,0],[0,0,1,1,1,1,1,1,1,0],[0,1,0,1,1,1,1,1,1,0],[0,0,0,1,0,0,0,0,0,0]],[[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,1,1,1,0,1,1,0],[0,0,0,1,1,1,0,1,1,0],[0,1,1,0,0,1,1,1,1,0],[1,0,0,1,1,1,1,0,0,1],[0,0,0,1,1,0,1,1,1,0],[0,0,0,1,1,0,1,1,1,0],[0,0,0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,1,1,0,1,1,1,0],[0,0,0,1,1,0,1,1,1,0],[1,0,0,1,1,1,1,0,0,1],[0,1,1,0,0,1,1,1,1,0],[0,0,0,1,1,1,0,1,1,0],[0,0,0,1,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0]],[[0,0,0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,1,0,1,1,1,1,1,1,0],[0,0,1,1,1,1,1,1,1,0],[0,0,0,1,1,0,1,1,1,0],[0,0,0,1,1,1,0,1,1,0],[1,0,0,1,1,1,1,1,1,0],[0,0,0,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,0,1,0]],[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,1,1,1,1,1,1,0],[0,1,0,1,1,1,1,1,1,0],[0,0,0,1,1,0,1,1,1,0],[0,0,0,1,1,1,0,1,1,0],[0,0,0,1,1,1,1,1,1,1],[1,0,0,1,1,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0]],[[0,0,0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0,0,0]]],"tensor_sha256":"791fe583f226d11f1730dae7aa965d26e160df9be654920d68aa7c7c9162ea7c","basis":["X0","X1","X2","X3","X4","X5","X6","X7","X8","X9"],"unit_index":0,"tensor_convention":"N[i][j][k] is the coefficient of X_k in X_i * X_j. Indices are zero-based; X_0 is the unit. The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,6,5,7,8,9],"invertible_indices":[0,1,2,9],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999941,0.9999999999999952,5.82842712474619,5.82842712474619,4.828427124746189,4.828427124746189,5.828427124746188,5.82842712474619,0.9999999999999968],"global_fp_dimension_approx":186.50966799187802,"central_casimir_polynomial":"(t - 16)**3*(t - 8)**5*(t**2 - 192*t + 1024)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 16)**3*(t - 8)**5*(t**2 - 192*t + 1024)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","source_sha256":"a4075e19d489ff9daaa405647c3be5aa8b8bed321e15d75f1ad53dbf9eb47ebe","data":{"id":"R10_1_153","rank":10,"input_line":153,"status":"excluded","tensor_sha256_compact_json":"791fe583f226d11f1730dae7aa965d26e160df9be654920d68aa7c7c9162ea7c","tensor_sha256_uint8_flattened":"50d532dd5ea91099a6e42ac017e7c904265e2bb0f029496580fd21b6482a5440","commutative":true,"dual":[0,2,1,4,3,6,5,7,8,9],"fp_dimensions_approx":[1.0,0.9999999999999941,0.9999999999999952,5.82842712474619,5.82842712474619,4.828427124746189,4.828427124746189,5.828427124746188,5.82842712474619,0.9999999999999968],"fp_dimension_approx":186.50966799187802,"exclusions":[{"criterion":"pseudo_factor_odd_superpentagon","scope":"general complex fusion categories","proof":"new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","certificate":"verification_summary.json","verifier":"python new/rank16_dual/verify_subcategories.py; see README.md for the full exact replay"}],"models":[]}},{"title":"Proof and remaining scope","source":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","source_sha256":"8e1b9e706d8fa1763748fb7135f67d7031627c8f082019033c32d4d609dca47b","data":{"findings":["No complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to a central fermion in a pseudo-PSU(2)6 factor. 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,6,5,7,8,9],"invertible_indices":[0,1,2],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,1.0000000000000007,1.0000000000000018,3.75801626271987,3.75801626271987,5.606653705427284,5.606653705427285,6.098572130859925,5.606653705427285,3.75801626271987],"global_fp_dimension_approx":176.86433804564692,"central_casimir_polynomial":"(t**3 - 42*t**2 + 441*t - 1323)**2*(t**4 - 214*t**3 + 6945*t**2 - 67833*t + 203499)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t**3 - 42*t**2 + 441*t - 1323)**2*(t**4 - 214*t**3 + 6945*t**2 - 67833*t + 203499)"},"research":[{"title":"Current accepted case 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,6,5,7,8,9],"invertible_indices":[0,7,8,9],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,4.828427124746186,4.828427124746189,5.828427124746189,5.82842712474619,5.82842712474619,5.82842712474619,0.9999999999999976,0.9999999999999976,0.9999999999999976],"global_fp_dimension_approx":186.50966799187802,"central_casimir_polynomial":"(t - 16)**3*(t - 8)**5*(t**2 - 192*t + 1024)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 16)**3*(t - 8)**5*(t**2 - 192*t + 1024)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","source_sha256":"a4075e19d489ff9daaa405647c3be5aa8b8bed321e15d75f1ad53dbf9eb47ebe","data":{"id":"R10_1_179","rank":10,"input_line":179,"status":"excluded","tensor_sha256_compact_json":"4e1c7e3806c930837f93d3b0426f1dbe63adc3552ba83e82c667bb10e53fd148","tensor_sha256_uint8_flattened":"2754c3290d83f03b6429af5ce185a1d046ab2e3f787217fe43b91e119c72582c","commutative":true,"dual":[0,2,1,4,3,6,5,7,8,9],"fp_dimensions_approx":[1.0,4.828427124746186,4.828427124746189,5.828427124746189,5.82842712474619,5.82842712474619,5.82842712474619,0.9999999999999976,0.9999999999999976,0.9999999999999976],"fp_dimension_approx":186.50966799187802,"exclusions":[{"criterion":"pseudo_factor_odd_superpentagon","scope":"general complex fusion categories","proof":"new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","certificate":"verification_summary.json","verifier":"python new/rank16_dual/verify_subcategories.py; see README.md for the full exact replay"}],"models":[]}},{"title":"Proof and remaining scope","source":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","source_sha256":"8e1b9e706d8fa1763748fb7135f67d7031627c8f082019033c32d4d609dca47b","data":{"findings":["No complex fusion categorification exists. The forced Morita dual and relative factorization reduce the problem to a central fermion in a pseudo-PSU(2)6 factor. Its odd-evaluation rank-two superfusion quotient is excluded by the published finite superpentagon calculation.","The categorical proof and the exact finite reconstruction have independent agent audits; independent human verification remains pending.","The final finite superpentagon exclusion is imported from Chang–Chen–Xu, Section 3; their unrestricted rank-two classification conjecture is not used, and their calculation was not independently rerun here."]}}],"evidence":[{"label":"README.md","path":"evidence/rank10_m1_exclusions_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/README.md","sha256":"4bd56073df729bd025e943b3168ae339f439de0fea7647318c182d6d505751a2"},{"label":"accepted_ledger.json","path":"evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/accepted_ledger.json","sha256":"a4075e19d489ff9daaa405647c3be5aa8b8bed321e15d75f1ad53dbf9eb47ebe"},{"label":"classification_updates.json","path":"evidence/rank10_m1_exclusions_20261023/classification_updates.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/classification_updates.json","sha256":"fedd7c61239a3e708852b2962f06b2f05d914f43bbb9f99e158dcd263ebc0b87"},{"label":"verification_summary.json","path":"evidence/rank10_m1_exclusions_20261023/verification_summary.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/verification_summary.json","sha256":"75579544ab2c180dc3e0e76e3619d7df9094ef8603fcd9dd37890dd03d3aebb0"},{"label":"new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/PSEUDO_BRANCH_EXCLUSION.md","sha256":"8e1b9e706d8fa1763748fb7135f67d7031627c8f082019033c32d4d609dca47b"},{"label":"new/quadratic_obstructions/MORITA_REDUCTION.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/MORITA_REDUCTION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/MORITA_REDUCTION.md","sha256":"cc6552523de1a64488450e2534e638b75e9f7ee2d8583c7759d42946ba3e6852"},{"label":"new/quadratic_obstructions/REDUCTION_AUDIT.md","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/REDUCTION_AUDIT.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/REDUCTION_AUDIT.md","sha256":"24bc793086ebdbfed976f54d9c1738669a2ed6b00eabe44c8fda62759b726a40"},{"label":"new/rank16_dual/RELATIVE_FACTORIZATION.md","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/RELATIVE_FACTORIZATION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/RELATIVE_FACTORIZATION.md","sha256":"2f358456f3d8cf19bbd423f71bac0b7233091c2af2f350631cca4d417c93d28f"},{"label":"new/quadratic_obstructions/R10_1_179_dual_tensor.json","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/R10_1_179_dual_tensor.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/R10_1_179_dual_tensor.json","sha256":"e565fadc80b40c2a698393e034134e67785f1da129895d900d77c7288714dabe"},{"label":"new/quadratic_obstructions/commutant_completeness_receipt.json","path":"evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/commutant_completeness_receipt.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/quadratic_obstructions/commutant_completeness_receipt.json","sha256":"6c8263c3a2639fb94e7a8cd49fbee76d0ecf52964df199701061842208426db8"},{"label":"new/rank16_dual/verify_subcategories.py","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/verify_subcategories.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/verify_subcategories.py","sha256":"770d3a93d365c4b2f3b939c886bcee59cc89d0874a28392ff872dc52f19cf1cc"},{"label":"new/rank16_dual/subcategories_receipt.json","path":"evidence/rank10_m1_exclusions_20261023/new/rank16_dual/subcategories_receipt.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/rank16_dual/subcategories_receipt.json","sha256":"6dbcd2507b8df923878f7b17195ec6d0895224eb10bcf848bed4ed86444d99d9"},{"label":"new/pseudo_psu_central_fermion_audit.md","path":"evidence/rank10_m1_exclusions_20261023/new/pseudo_psu_central_fermion_audit.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/pseudo_psu_central_fermion_audit.md","sha256":"8cbc8dd48ccae2e8b6047c58c25c67af9e78ed915b4afc808ab60153fa8668d2"},{"label":"work/audit_signed/AUDIT.md","path":"evidence/rank9_r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complex fusion categorification exists. 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With beta=F(010), g=tau_2 and x=tau_5 beta, the ten simples satisfy g^5=1, gx=xg, x*=x and x^2=1+(g+g^2+g^3+g^4)x. 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Indices are zero-based; X_0 is the unit. The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,6,5,8,7,9],"invertible_indices":[0,1,2,7,8],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999994,0.9999999999999998,4.236067977499793,4.236067977499793,4.236067977499793,4.236067977499794,0.9999999999999998,0.9999999999999998,4.236067977499794],"global_fp_dimension_approx":94.72135954999597,"central_casimir_polynomial":"(t**2 - 100*t + 500)*(t**2 - 25*t + 125)**4","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t**2 - 100*t + 500)*(t**2 - 25*t + 125)**4"},"research":[{"title":"Current accepted case decision","source":"evidence/unresolved_retry_20261024/rank9_rank10_m1_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/rank9_rank10_m1_ledger.json","source_sha256":"6c53d65604523c54e8ccd4f7474826cd55f1f6b0d184be3dbd4ddda7139396e2","data":{"id":"R10_1_189","rank":10,"input_line":189,"status":"unitarily_realized","tensor_sha256_compact_json":"c44e21d1844ded91dba30cd6c691180afa4d4f1be1c4f27806bbc12c8c8292f4","tensor_sha256_uint8_flattened":"cae3e2a0497f434d336c30a9a5a53432ad12d774318f7b7009c691011291a2e9","commutative":true,"dual":[0,2,1,4,3,6,5,8,7,9],"fp_dimensions_approx":[1.0,0.9999999999999994,0.9999999999999998,4.236067977499793,4.236067977499793,4.236067977499793,4.236067977499794,0.9999999999999998,0.9999999999999998,4.236067977499794],"fp_dimension_approx":94.72135954999597,"exclusions":[],"models":[{"model":"Charge-zero component of SU(4)_6 modules for SU(4)_6 subset SU(10)_1","construction":"conformal_embedding_subcategory","scope":"unitary","proof":"proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","basis_normal_to_source":[0,1,8,7,2,9,4,6,5,3],"tensor_sha256":"c44e21d1844ded91dba30cd6c691180afa4d4f1be1c4f27806bbc12c8c8292f4","novelty":"Recognition in a classical construction; no new tensor-category claim"}]}},{"title":"Current theoretical continuation","source":"evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","source_sha256":"aa14f37c79f5e7171465819f5ba9eca567082fabf08a2e55bef18087eb5d4f44","data":{"findings":["An actual unitary model is the charge-zero component of the category of modules over B=000+060+202+222 supplied by the known conformal embedding SU(4)_6 inside SU(10)_1.","With beta=F(010), g=tau_2 and x=tau_5 beta, the ten simples satisfy g^5=1, gx=xg, x*=x and x^2=1+(g+g^2+g^3+g^4)x. All 1,000 census coefficients match exactly.","The accompanying rank-fourteen modular category and the actual algebra 1+U are constructed within the same known WZW category. No existence inference from candidate modular data is required.","This recognizes a classical construction; it is not a claim of a new tensor category. The unitary model is unbraided, consistently with the retained braided obstruction."],"status_changed":true,"remaining_gap":null}},{"title":"Proof and remaining scope","source":"evidence/rank10_m1_exclusions_20261023/new/case189/STRUCTURAL_PROGRESS.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/case189/STRUCTURAL_PROGRESS.md","source_sha256":"fa94bfc67d23a596308950e15ddb7c65391765b4da8bac2a8c67cd4c568aa944","data":{"findings":["General complex categorifiability remains unresolved. The pointed subcategory must be untwisted Vec(C5), the regular-algebra Morita dual must have the same fusion ring, and no braided categorification exists. These restrictions provide neither a model nor a general exclusion.","The pointed-associator theorem rules out every nonzero H³(C5,C×) class.","Based-ring equality of the Morita dual does not imply a tensor equivalence or a central lift.","The necessary twist orders divide 1600. Surviving integer Gram data are not categorical models."]}}],"evidence":[{"label":"Current accepted rank-nine/ten decisions","path":"evidence/unresolved_retry_20261024/rank9_rank10_m1_ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/rank9_rank10_m1_ledger.json","sha256":"6c53d65604523c54e8ccd4f7474826cd55f1f6b0d184be3dbd4ddda7139396e2"},{"label":"Actual unitary construction","path":"evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","sha256":"aa14f37c79f5e7171465819f5ba9eca567082fabf08a2e55bef18087eb5d4f44"},{"label":"Categorical proof 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actual unitary model is the charge-zero component of the category of modules over B=000+060+202+222 supplied by the known conformal embedding SU(4)_6 inside SU(10)_1.","With beta=F(010), g=tau_2 and x=tau_5 beta, the ten simples satisfy g^5=1, gx=xg, x*=x and x^2=1+(g+g^2+g^3+g^4)x. All 1,000 census coefficients match exactly.","The accompanying rank-fourteen modular category and the actual algebra 1+U are constructed within the same known WZW category. No existence inference from candidate modular data is required.","This recognizes a classical construction; it is not a claim of a new tensor category. The unitary model is unbraided, consistently with the retained braided obstruction."],"audit_sources":[{"label":"Actual unitary construction","path":"evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/CONFORMAL_MODEL.md","sha256":"aa14f37c79f5e7171465819f5ba9eca567082fabf08a2e55bef18087eb5d4f44"},{"label":"Categorical proof PDF","path":"evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/rank10_conformal_model.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/rank10_conformal_model.pdf","sha256":"1a87486a6c505f297d81ea515a00c8c70d2e3fb53713ee8afb2c2c1a5a7ec2b4"},{"label":"Exact 1,000-coefficient certificate","path":"evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/conformal_model_certificate.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/unresolved_retry_20261024/proofs/unresolved11_retry_20261024/rank10/conformal_model_certificate.json","sha256":"1d20ec13974532ebe84cb9fd9cb8e7c2627f7f494079a77f5d3769a78a94d053"}],"braided":{"status":"excluded","explanation":"Schopieray's irrational braided generalized-near-group classification excludes the noninvertible dimension 2+√5.","sources":[{"label":"new/case189/STRUCTURAL_PROGRESS.md","path":"evidence/rank10_m1_exclusions_20261023/new/case189/STRUCTURAL_PROGRESS.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank10_m1_exclusions_20261023/new/case189/STRUCTURAL_PROGRESS.md","sha256":"fa94bfc67d23a596308950e15ddb7c65391765b4da8bac2a8c67cd4c568aa944"},{"label":"Schopieray, Theorem 3.6","url":"https://doi.org/10.4153/S0008439523000334"}]}},"download_url":"./downloads/fusion-tensors/R10_1_189.txt","investigation_deferred":false},{"id":"R10_1_190","rank":10,"multiplicity":1,"status":"excluded","summary":"General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates.","name":"R10_1_190","existence":"excluded","model_reference":"","model_reference_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_file":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_location":"R10_1_190","report_url":"./papers/rank9-rank10-m1.pdf","case_url":"./case.html?id=R10_1_190","fusion_tensor":[[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0]],[[0,0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]],[[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,1,1,1,1,1,0,1],[1,0,0,1,1,1,1,0,0,1],[0,0,0,1,1,1,1,0,1,1],[0,1,0,1,1,1,1,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,1,1,1,1,1,0,0,1]],[[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,1,1,1,1,0,0,1],[0,0,0,1,1,1,1,0,1,1],[0,0,1,1,1,1,1,0,0,1],[0,0,0,1,1,1,1,1,0,1],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,1,0,1,1,1,1,0,0,1]],[[0,0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,1,1,1,1,0,1,1],[0,0,1,1,1,1,1,0,0,1],[0,1,0,1,1,1,1,0,0,1],[1,0,0,1,1,1,1,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,1,1,1,1,0,1]],[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,1,0,1,1,1,1,0,0,1],[0,0,0,1,1,1,1,1,0,1],[1,0,0,1,1,1,1,0,0,1],[0,0,1,1,1,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0,0,0],[0,0,0,1,1,1,1,0,1,1]],[[0,0,0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0]],[[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,1,1,1,1,0,0,1],[0,1,0,1,1,1,1,0,0,1],[0,0,0,1,1,1,1,1,0,1],[0,0,0,1,1,1,1,0,1,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[1,0,0,1,1,1,1,0,0,1]]],"tensor_sha256":"e1c150784ecb829ebafceae6f182d955372064b7921645f4e0d93e0c1c2bc375","basis":["X0","X1","X2","X3","X4","X5","X6","X7","X8","X9"],"unit_index":0,"tensor_convention":"N[i][j][k] is the coefficient of X_k in X_i * X_j. Indices are zero-based; X_0 is the unit. The supplied source basis is preserved.","hash_convention":"SHA-256 of UTF-8 compact JSON, without a trailing newline.","invariants":{"dual_indices":[0,2,1,4,3,6,5,8,7,9],"invertible_indices":[0,1,2,7,8],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,0.9999999999999963,0.9999999999999997,5.1925824035672505,5.1925824035672505,5.1925824035672505,5.1925824035672505,0.9999999999999993,0.9999999999999993,5.192582403567251],"global_fp_dimension_approx":139.8145600891812,"central_casimir_polynomial":"(t - 10)**8*(t**2 - 145*t + 725)","dimensions_method":"Numerical Frobenius–Perron dimensions from the audited input tensor; approximate values.","character_method":"Exact character calculations and certificates are retained in the linked research package.","formal_codegree_polynomial":"(t - 10)**8*(t**2 - 145*t + 725)"},"research":[{"title":"Current accepted case decision","source":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","source_sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82","data":{"id":"R10_1_190","rank":10,"input_line":190,"status":"excluded","tensor_sha256_compact_json":"e1c150784ecb829ebafceae6f182d955372064b7921645f4e0d93e0c1c2bc375","tensor_sha256_uint8_flattened":"37ccd42fdd5af6820550f0831d3c6e72bb362a8471c3b868384fca4eed5ec341","commutative":true,"dual":[0,2,1,4,3,6,5,8,7,9],"fp_dimensions_approx":[1.0,0.9999999999999963,0.9999999999999997,5.1925824035672505,5.1925824035672505,5.1925824035672505,5.1925824035672505,0.9999999999999993,0.9999999999999993,5.192582403567251],"fp_dimension_approx":139.8145600891812,"exclusions":[{"criterion":"two_dimension_induction","scope":"no fusion category over C","proof":"deliverable/report.pdf","certificate":"work/obstructions/two_dimension_induction.json","verifier":"python work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/two_dimension_induction.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/two_dimension_induction.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/two_dimension_induction.json","sha256":"c3a5b36e87cb6fc329332ff6bd58689da3d7937793c3aaa08cf26b70681706b0"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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work/root_audit/verify_baseline.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank9_rank10_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/README.md","sha256":"87ac9998204939c41dffae17781b6429fbbc41847d1e9e71abfe3685b454fcf7"},{"label":"deliverable/case_notes.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/case_notes.json","sha256":"ff5a4b5910611d75211a3e1f51d7bfea5cad68e3eb55935efeb53721ba40c491"},{"label":"deliverable/ledger.json","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"},{"label":"deliverable/report.pdf","path":"evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/report.pdf","sha256":"43fba73129136ae9b90abf0218909c5c3150c4308bd468f3ac9f2ecf05e84899"},{"label":"manifest.json","path":"evidence/rank9_rank10_m1_20261023/manifest.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/manifest.json","sha256":"559312062f717a16c8d438b71b1fdc11f6e32233158e2395326b59376f452fe6"},{"label":"verification_report.json","path":"evidence/rank9_rank10_m1_20261023/verification_report.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verification_report.json","sha256":"f82e34902eec1b5214b13449baaa3d8041280506eccd191e5297acc309d09a92"},{"label":"verify.py","path":"evidence/rank9_rank10_m1_20261023/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/verify.py","sha256":"f42036fb2c42568abf1f4c8aab7b7e93c70e27b088f4922f0f5c595b378dd49e"},{"label":"work/input_audit/tensors.json","path":"evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/input_audit/tensors.json","sha256":"7b6c0c20142acb7f087d01eb6f261bbb6c7716ddcf14a9f2eddaa39a0b308229"},{"label":"work/obstructions/arithmetic.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/arithmetic.json","sha256":"9424428d89b9035e9cea723dc1f3c702eeb1cd677353c506893ba9d5dfc7cfdf"},{"label":"work/obstructions/gng.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/gng.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/gng.json","sha256":"b651b8027cb0071bb9c9f113d6a52a558d2195c4b512e6bb2eaa92172d4d44f0"},{"label":"work/obstructions/two_dimension_induction.json","path":"evidence/rank9_rank10_m1_20261023/work/obstructions/two_dimension_induction.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/obstructions/two_dimension_induction.json","sha256":"c3a5b36e87cb6fc329332ff6bd58689da3d7937793c3aaa08cf26b70681706b0"},{"label":"work/root_audit/verify_baseline.py","path":"evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/work/root_audit/verify_baseline.py","sha256":"73396b709034c3caef45141d04251e6b0901ecabb535fa00a373da31bfd85c25"}],"categorification_scope":{"general_status":"excluded","level_status":{"general":"excluded","pivotal":"excluded","spherical":"excluded","pseudo_unitary":"excluded","unitary":"excluded"},"strongest_excluded":"general","same_category_implications":[],"existence_implications":[],"notes":["General fusion categorification over the complex numbers is excluded by the cited proof and exact certificates."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank9_rank10_m1_20261023/deliverable/ledger.json","sha256":"39fac448316e892ce9e95a69c00e14930e4a558258af2bc544b7358b7850bc82"}],"braided":{"status":"excluded","explanation":"The general nonexistence result also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate 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