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work/rank11/nonintegral/verify_spherical_lattice.py"}],"models":[]}}],"evidence":[{"label":"README.md","path":"evidence/rank11_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/README.md","sha256":"28c78f307ac89b81de61e7fbf8e1c7e5ed257af495af050ae0c4a2bf73758c48"},{"label":"RESULTS.json","path":"evidence/rank11_m1_20261023/RESULTS.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/RESULTS.json","sha256":"066dde699882b0424261fc5a44d591d63c03ea66f1ea74f4a6e3b8de06fc68da"},{"label":"SHA256SUMS","path":"evidence/rank11_m1_20261023/SHA256SUMS","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/SHA256SUMS","sha256":"7f3ee6c29a3e64cc26dd32a7df1e7758f85dbcee36e76020b542521adca706f5"},{"label":"VERIFICATION.md","path":"evidence/rank11_m1_20261023/VERIFICATION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/VERIFICATION.md","sha256":"0fca6a73c79bce430d4eaa246246dab739d81b4136fad2d51f791bf0e583a68d"},{"label":"work/rank11/criteria_audit/CRITERIA_AUDIT.md","path":"evidence/rank11_m1_20261023/work/rank11/criteria_audit/CRITERIA_AUDIT.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/criteria_audit/CRITERIA_AUDIT.md","sha256":"a98076b9dd6e9e9eea64ffbc8b83da7d2c4dbb88762b579a5e163d9cc0b4200e"},{"label":"work/rank11/ledger.json","path":"evidence/rank11_m1_20261023/work/rank11/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/ledger.json","sha256":"2e6f3513a373fafdbdfad36c9eab75b946d3fc557d070660f73c78315cf67a29"},{"label":"work/rank11/nonintegral/THEORY.md","path":"evidence/rank11_m1_20261023/work/rank11/nonintegral/THEORY.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/nonintegral/THEORY.md","sha256":"513c007e70069845aefffff70e2d91c1846c77e9935a2378038f1da1b17b23b4"},{"label":"work/rank11/nonintegral/spherical_lattice.json","path":"evidence/rank11_m1_20261023/work/rank11/nonintegral/spherical_lattice.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/nonintegral/spherical_lattice.json","sha256":"553450a0b3edc0afffc52fa11e40e901e0c3a8c3fa53374a752187aa1fb960ea"},{"label":"work/rank11/nonintegral/verify_reduction.py","path":"evidence/rank11_m1_20261023/work/rank11/nonintegral/verify_reduction.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/nonintegral/verify_reduction.py","sha256":"f0d79a7820604d3220cb42f42368c2d6e64bfcb43262bf1eeb45a583547674d8"},{"label":"work/rank11/nonintegral/verify_spherical_lattice.py","path":"evidence/rank11_m1_20261023/work/rank11/nonintegral/verify_spherical_lattice.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/nonintegral/verify_spherical_lattice.py","sha256":"5d51bcb6d3b1911e1762e690870a95da685746b244ea4f7d2afd4d60694de47b"},{"label":"work/rank11/replay_all.py","path":"evidence/rank11_m1_20261023/work/rank11/replay_all.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/replay_all.py","sha256":"b5220a3425c05b442ef37c72160d647f7a2f26e41f3fd3ac931fdd22361bc648"},{"label":"work/rank11/structural/THEORY.md","path":"evidence/rank11_m1_20261023/work/rank11/structural/THEORY.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/structural/THEORY.md","sha256":"2fe9b073062cab72bbf0bd2f9a113e06d850e6406302c34301276304933b40c6"},{"label":"work/rank11/structural/one_spectrum.json","path":"evidence/rank11_m1_20261023/work/rank11/structural/one_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/structural/one_spectrum.json","sha256":"cf443edea7be488bf7b16622362df77c6f3015422cf29c4cd3f6f8ed9e5aea5b"},{"label":"work/rank11/structural/verify_baseline.py","path":"evidence/rank11_m1_20261023/work/rank11/structural/verify_baseline.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/structural/verify_baseline.py","sha256":"ec04324a31ccf50697d4e7e71ecde924b1e9c87d26ead4720c2498c2eae520e2"},{"label":"work/rank11/structural/zero_spectrum.json","path":"evidence/rank11_m1_20261023/work/rank11/structural/zero_spectrum.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_2026102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from fusion categorification over ℂ by zero spectrum. The proof covers general complex fusion categories."],"audit_sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank11_m1_20261023/work/rank11/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/ledger.json","sha256":"2e6f3513a373fafdbdfad36c9eab75b946d3fc557d070660f73c78315cf67a29"}],"braided":{"status":"excluded","explanation":"General nonexistence also excludes a braided categorification.","sources":[{"label":"Accepted case proof and certificate record","path":"evidence/rank11_m1_20261023/work/rank11/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/ledger.json","sha256":"2e6f3513a373fafdbdfad36c9eab75b946d3fc557d070660f73c78315cf67a29"}]}},"download_url":"./downloads/fusion-tensors/R11_1_2.txt","investigation_deferred":false},{"id":"R11_1_3","rank":11,"multiplicity":1,"status":"excluded","summary":"Excluded from fusion categorification over ℂ by two-character central-restriction obstruction. 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from fusion categorification over ℂ by casimir dnumber, cyclotomic. 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from fusion categorification over ℂ by central dihedral and Brauer-Picard grading obstruction in dimension 120. 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C","certificate":"arithmetic/arithmetic.json","proof":"arithmetic/THEORY.md","verifier":"python work/rank11/arithmetic/run.py 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from fusion categorification over ℂ by casimir dnumber, cyclotomic, primitive codegree. 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unitary realization exists: Rep(D38). 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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":[0,1,2,3,4,5,6,7,8,9,10],"invertible_indices":[0],"commutative":true,"frobenius_perron_dimensions_approx":[1.0,1.981371892072657,3.8157944950835656,7.190336945064109,5.367217076492404,6.5205777207221365,5.999779670225879,6.919909745688184,4.634673383788572,7.326821771793451,2.9258345746955965],"global_fp_dimension_approx":310.117550133364,"central_casimir_polynomial":"t**11 - 506*t**10 + 75647*t**9 - 5219643*t**8 + 200086315*t**7 - 4685657704*t**6 + 70465083164*t**5 - 694584391188*t**4 + 4463726161017*t**3 - 18011526614630*t**2 + 41426511213649*t - 41426511213649","dimensions_method":"Numerical Frobenius–Perron dimensions from the original tensor; displayed values are approximate.","character_method":"Exact character calculations and certificates are included in the linked verification package.","formal_codegree_polynomial":"t**11 - 506*t**10 + 75647*t**9 - 5219643*t**8 + 200086315*t**7 - 4685657704*t**6 + 70465083164*t**5 - 694584391188*t**4 + 4463726161017*t**3 - 18011526614630*t**2 + 41426511213649*t - 41426511213649"},"research":[{"title":"Current accepted case 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unitary realization exists: V4 zest of SO(8)2, parameters (0,0,0,2). 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unitary realization exists: TY(C3 × C2²) equivariantized by C2, positive parity. 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unitary realization exists: C2 zest of SU(2)10. 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work/rank11/nonintegral/audit104/verify.py"}]}}],"evidence":[{"label":"README.md","path":"evidence/rank11_m1_20261023/README.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/README.md","sha256":"28c78f307ac89b81de61e7fbf8e1c7e5ed257af495af050ae0c4a2bf73758c48"},{"label":"RESULTS.json","path":"evidence/rank11_m1_20261023/RESULTS.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/RESULTS.json","sha256":"066dde699882b0424261fc5a44d591d63c03ea66f1ea74f4a6e3b8de06fc68da"},{"label":"SHA256SUMS","path":"evidence/rank11_m1_20261023/SHA256SUMS","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/SHA256SUMS","sha256":"7f3ee6c29a3e64cc26dd32a7df1e7758f85dbcee36e76020b542521adca706f5"},{"label":"VERIFICATION.md","path":"evidence/rank11_m1_20261023/VERIFICATION.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/VERIFICATION.md","sha256":"0fca6a73c79bce430d4eaa246246dab739d81b4136fad2d51f791bf0e583a68d"},{"label":"work/rank11/criteria_audit/CRITERIA_AUDIT.md","path":"evidence/rank11_m1_20261023/work/rank11/criteria_audit/CRITERIA_AUDIT.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/criteria_audit/CRITERIA_AUDIT.md","sha256":"a98076b9dd6e9e9eea64ffbc8b83da7d2c4dbb88762b579a5e163d9cc0b4200e"},{"label":"work/rank11/known_models/PROOF_JORDAN32.md","path":"evidence/rank11_m1_20261023/work/rank11/known_models/PROOF_JORDAN32.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/known_models/PROOF_JORDAN32.md","sha256":"a06bfbe409a420e2853af2c44a366a5b22e7ea06e77d9b14e11ff7565c0037cb"},{"label":"work/rank11/known_models/jordan_gt_model.json","path":"evidence/rank11_m1_20261023/work/rank11/known_models/jordan_gt_model.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/known_models/jordan_gt_model.json","sha256":"feda0a41c3a0e149b8e40ff78f9ae9c52d6fad5d49dafd5d3d98a619d8c58233"},{"label":"work/rank11/known_models/jordan_verify.py","path":"evidence/rank11_m1_20261023/work/rank11/known_models/jordan_verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/known_models/jordan_verify.py","sha256":"d5292996a6cc8fbe157ea81aa555a3414c4fdd98160f9b3670b02875604c186f"},{"label":"work/rank11/ledger.json","path":"evidence/rank11_m1_20261023/work/rank11/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/ledger.json","sha256":"2e6f3513a373fafdbdfad36c9eab75b946d3fc557d070660f73c78315cf67a29"},{"label":"work/rank11/nonintegral/audit104/THEORY.md","path":"evidence/rank11_m1_20261023/work/rank11/nonintegral/audit104/THEORY.md","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/nonintegral/audit104/THEORY.md","sha256":"fb3f6a110428d552d84c071e6aae5efdeeba339c00390a074331cd0b354062dd"},{"label":"work/rank11/nonintegral/audit104/verify.py","path":"evidence/rank11_m1_20261023/work/rank11/nonintegral/audit104/verify.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/nonintegral/audit104/verify.py","sha256":"9584fa6af56000c1f32a0ee99179767067a46e4659c261b020a73c4c9558f8f5"},{"label":"work/rank11/replay_all.py","path":"evidence/rank11_m1_20261023/work/rank11/replay_all.py","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/replay_all.py","sha256":"b5220a3425c05b442ef37c72160d647f7a2f26e41f3fd3ac931fdd22361bc648"},{"label":"work/rank11/tensors.json","path":"evidence/rank11_m1_20261023/work/rank11/tensors.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/tensors.json","sha256":"e3e27c43f31bb54fc152a93d0f793504a53bd5b11659930764f96ed951eb519f"}],"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 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unitary realization exists: V4 zest of SO(8)2, parameters (0,0,0,1). 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unitary realization exists: Vec(C16) equivariantized by multiplication by 7. 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accepted case decision","source":"evidence/rank11_m1_20261023/work/rank11/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/ledger.json","source_sha256":"2e6f3513a373fafdbdfad36c9eab75b946d3fc557d070660f73c78315cf67a29","data":{"id":"R11_1_162","input_line":162,"rank":11,"multiplicity":1,"status":"excluded","tensor_sha256_compact_json":"23ee8a704a5904485baf04384cd39caf24e0ec3f6f6d6434499b31e6abf0363a","tensor_sha256_uint8_flattened":"0c902087152c1ec973d51c6535c0d26002c57d3f4562abf1c1c665dfa0b77fa2","commutative":true,"dual":[0,2,1,4,3,6,5,7,8,9,10],"fp_dimensions_approx":[1.0,0.9999999999999996,0.9999999999999986,4.672823701000946,4.672823701000946,0.9999999999999992,0.9999999999999996,5.24481696931715,5.24481696931715,0.9999999999999996,4.672823701000946],"fp_dimension_approx":126.52205410518282,"exclusions":[{"criterion":"casimir_dnumber, cyclotomic","scope":"no fusion category over 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accepted case decision","source":"evidence/rank11_m1_20261023/work/rank11/ledger.json","url":"https://github.com/sebastienpalcoux/grothendieck-ring-classification/blob/main/evidence/rank11_m1_20261023/work/rank11/ledger.json","source_sha256":"2e6f3513a373fafdbdfad36c9eab75b946d3fc557d070660f73c78315cf67a29","data":{"id":"R11_1_180","input_line":180,"rank":11,"multiplicity":1,"status":"excluded","tensor_sha256_compact_json":"bb008d43866960a02286ba28812f3fc103ff2f50c3a4b9877ed61375a117fa20","tensor_sha256_uint8_flattened":"c5a6380fcbddf6223b8e93de2a2a74d8d8636d8956702adc641767c9308bb5f4","commutative":true,"dual":[0,2,1,4,3,6,5,8,7,9,10],"fp_dimensions_approx":[1.0,0.9999999999999984,0.9999999999999997,4.672823701000947,4.672823701000947,5.24481696931715,5.24481696931715,0.9999999999999993,0.9999999999999993,0.9999999999999993,4.672823701000946],"fp_dimension_approx":126.52205410518285,"exclusions":[{"criterion":"casimir_dnumber, cyclotomic","scope":"no fusion category over 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