{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3GL42JKNJRMR4U7FDMUVCZQW25","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fef1b34d0b98b40bb6c40506318c97be2242ee074bfcb5d76616a4996a9dce20","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-10T10:08:01Z","title_canon_sha256":"bdc10d6f42ee274dc556bfec69e87653eed0fc6b2b7386ee3e45ce2b63b24200"},"schema_version":"1.0","source":{"id":"1506.03243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03243","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03243v1","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03243","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"pith_short_12","alias_value":"3GL42JKNJRMR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3GL42JKNJRMR4U7F","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3GL42JKN","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:a1b17825ceeccd9ee40b8d81d37b8eecabe84092c1e35d307b2b675f34333908","target":"graph","created_at":"2026-05-18T01:55:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\mathscr{C}$ be a modular tensor category over an algebraically closed field $k$ of characteristic 0. Then there is the ubiquitous notion of the S-matrix $S(\\mathscr{C})$ associated with the modular category. The matrix $S(\\mathscr{C})$ is a symmetric matrix, its entries are cyclotomic integers and the matrix $(\\dim \\mathscr{C})^{-\\frac{1}{2}}\\cdot S(\\mathscr{C})$ is a unitary matrix. Here $\\dim \\mathscr{C}\\in k$ denotes the categorical dimension of $\\mathscr{C}$ and it is a totally positive cyclotomic integer. Now suppose that we also have a modular autoequivalence $F:\\mathscr{C}\\to \\mat","authors_text":"Tanmay Deshpande","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-10T10:08:01Z","title":"Modular categories, crossed S-matrices and Shintani descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03243","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:29c8e46a9bb21f37239356324be1301f55321cc459f2a943559b3548a91e0efa","target":"record","created_at":"2026-05-18T01:55:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fef1b34d0b98b40bb6c40506318c97be2242ee074bfcb5d76616a4996a9dce20","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-10T10:08:01Z","title_canon_sha256":"bdc10d6f42ee274dc556bfec69e87653eed0fc6b2b7386ee3e45ce2b63b24200"},"schema_version":"1.0","source":{"id":"1506.03243","kind":"arxiv","version":1}},"canonical_sha256":"d997cd254d4c591e53e51b29516616d754ff41a33ae6a36b431d77ba38e50acf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d997cd254d4c591e53e51b29516616d754ff41a33ae6a36b431d77ba38e50acf","first_computed_at":"2026-05-18T01:55:31.167566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:31.167566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhQ57D+UCNs0OZySaZTHGd7hT6oEPaEbQzgw5oZaiE9PT6gXKkM8ylgceanWtZoUbNV2aeK/uPeTtPGevjvHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:31.168219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29c8e46a9bb21f37239356324be1301f55321cc459f2a943559b3548a91e0efa","sha256:a1b17825ceeccd9ee40b8d81d37b8eecabe84092c1e35d307b2b675f34333908"],"state_sha256":"ca40a12bd9b7676856454a7e8dbcc9cbd3c6ee7344e2723d6730c212427ee3c1"}