{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:C6Q4RNQR4YXBSY7GGTWTSEFJQ6","short_pith_number":"pith:C6Q4RNQR","schema_version":"1.0","canonical_sha256":"17a1c8b611e62e1963e634ed3910a98782dd60d549112071607d4c8a2eacb96f","source":{"kind":"arxiv","id":"0905.2574","version":1},"attestation_state":"computed","paper":{"title":"On reciprocality of twisted Alexander invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniel S. Silver (University of South Alabama), Jonathan A. Hillman (University of Sydney), Susan G. Williams (University of South Alabama)","submitted_at":"2009-05-15T15:59:33Z","abstract_excerpt":"Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0905.2574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-05-15T15:59:33Z","cross_cats_sorted":[],"title_canon_sha256":"6a882c8a7ae872ca4f9e4024d29d74516f664ee4080ab9a73e76f54c154079e8","abstract_canon_sha256":"cf47e0934702d2682fa99cfa8d804573f60c3f881ed479af73812d1602481b29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.262704Z","signature_b64":"GDd2u9+aTv15DADx5lz1fOUwqA0s/uBk3aVAj5jlTBeDrra7f0HhvFqcCvRE/HvOcUis1helYQNZSC7r5zxgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a1c8b611e62e1963e634ed3910a98782dd60d549112071607d4c8a2eacb96f","last_reissued_at":"2026-05-18T02:41:51.262229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.262229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On reciprocality of twisted Alexander invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniel S. Silver (University of South Alabama), Jonathan A. Hillman (University of Sydney), Susan G. Williams (University of South Alabama)","submitted_at":"2009-05-15T15:59:33Z","abstract_excerpt":"Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2574","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0905.2574","created_at":"2026-05-18T02:41:51.262303+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.2574v1","created_at":"2026-05-18T02:41:51.262303+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2574","created_at":"2026-05-18T02:41:51.262303+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6Q4RNQR4YXB","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6Q4RNQR4YXBSY7G","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6Q4RNQR","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6","json":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6.json","graph_json":"https://pith.science/api/pith-number/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/graph.json","events_json":"https://pith.science/api/pith-number/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/events.json","paper":"https://pith.science/paper/C6Q4RNQR"},"agent_actions":{"view_html":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6","download_json":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6.json","view_paper":"https://pith.science/paper/C6Q4RNQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.2574&json=true","fetch_graph":"https://pith.science/api/pith-number/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/graph.json","fetch_events":"https://pith.science/api/pith-number/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/action/storage_attestation","attest_author":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/action/author_attestation","sign_citation":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/action/citation_signature","submit_replication":"https://pith.science/pith/C6Q4RNQR4YXBSY7GGTWTSEFJQ6/action/replication_record"}},"created_at":"2026-05-18T02:41:51.262303+00:00","updated_at":"2026-05-18T02:41:51.262303+00:00"}