{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:O5GTEWE3D5MSFDCKKJ7SM5JE6U","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":"b04e69ce2512175830b4f538660e289062abfb8527507f04b4e4a1a705c12a48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-05-16T18:41:53Z","title_canon_sha256":"a394a8e402554dce8ced27a663e97a3b3af60824607742b3fdb63451daf6fe27"},"schema_version":"1.0","source":{"id":"0705.2371","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.2371","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"0705.2371v5","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2371","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"O5GTEWE3D5MS","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"O5GTEWE3D5MSFDCK","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"O5GTEWE3","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:0fe2715f5dc6113aa3f02450291ad723716eb2301df10d4aa875083479262cbc","target":"graph","created_at":"2026-05-18T01:37:22Z","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":"Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We then show that the invariants coincide with sign-determined Reidemeister torsion in a normalized setting, and refine the duality theorem. We further obtain necessary conditions on the invariants for a knot to be fibered, and study behavior of the highest degrees of the invariants.","authors_text":"Takahiro Kitayama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-05-16T18:41:53Z","title":"Normalization of twisted Alexander invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2371","kind":"arxiv","version":5},"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:d889c01d4411bfe275f3d25ae4a6869b7c71b795be0ba7132fd19b95e08bff61","target":"record","created_at":"2026-05-18T01:37:22Z","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":"b04e69ce2512175830b4f538660e289062abfb8527507f04b4e4a1a705c12a48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-05-16T18:41:53Z","title_canon_sha256":"a394a8e402554dce8ced27a663e97a3b3af60824607742b3fdb63451daf6fe27"},"schema_version":"1.0","source":{"id":"0705.2371","kind":"arxiv","version":5}},"canonical_sha256":"774d32589b1f59228c4a527f267524f52085bdaa3e85e8d357d9644313663de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774d32589b1f59228c4a527f267524f52085bdaa3e85e8d357d9644313663de1","first_computed_at":"2026-05-18T01:37:22.023212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:22.023212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHs8lyZWtVNR9oTW8PIYCkqZpGx+xqmulcYEjdrgO73Dn9QlZv70Ut+PvjA9jD39d8hpdiNu5tRhm20ZPSCkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:22.023989Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.2371","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d889c01d4411bfe275f3d25ae4a6869b7c71b795be0ba7132fd19b95e08bff61","sha256:0fe2715f5dc6113aa3f02450291ad723716eb2301df10d4aa875083479262cbc"],"state_sha256":"6f742cd58ceb4f5ebc28a3d76e982bcb4e3900d43d719472fc4e6fc420d5d057"}