{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:T6A3HUE5QYCXPYKZIC2XN5UHDZ","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":"553870881a59f43e5912317aeb306dcaf2097f159ba4898f760bc2363a926d24","cross_cats_sorted":["math-ph","math.AT","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2006-05-06T10:08:54Z","title_canon_sha256":"40673e88be2179007ad6774940e366f00c9200535ed4d1782da2d5b4a522aed8"},"schema_version":"1.0","source":{"id":"math/0605164","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605164","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605164v5","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605164","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"T6A3HUE5QYCX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"T6A3HUE5QYCXPYKZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"T6A3HUE5","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:3fa80706aa8307ec8ca13edc666ccc1fdc00ab8d8bc5d63077b860cb9d7ee7b8","target":"graph","created_at":"2026-05-18T02:37:52Z","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":"We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermionic topological quantum field theory.","authors_text":"Evgeniy V. Martyushev, Igor G. Korepanov, J\\'er\\^ome Dubois","cross_cats":["math-ph","math.AT","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2006-05-06T10:08:54Z","title":"A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605164","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:c886b5b8f53f23560a8532a3435a727c9ee18c9419491d978540d5e6153d90e9","target":"record","created_at":"2026-05-18T02:37:52Z","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":"553870881a59f43e5912317aeb306dcaf2097f159ba4898f760bc2363a926d24","cross_cats_sorted":["math-ph","math.AT","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2006-05-06T10:08:54Z","title_canon_sha256":"40673e88be2179007ad6774940e366f00c9200535ed4d1782da2d5b4a522aed8"},"schema_version":"1.0","source":{"id":"math/0605164","kind":"arxiv","version":5}},"canonical_sha256":"9f81b3d09d860577e15940b576f6871e5260535825d611addf4bec7ce0f6d8b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f81b3d09d860577e15940b576f6871e5260535825d611addf4bec7ce0f6d8b4","first_computed_at":"2026-05-18T02:37:52.508088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:52.508088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z4TutKoW/31BxZluPPuS/qUnnoPTn1y8kzVya5JReTRRRXJYgwMzjwRX7e5fkAeJmqFK96YjKP8WFAVEyl8iAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:52.508743Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605164","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c886b5b8f53f23560a8532a3435a727c9ee18c9419491d978540d5e6153d90e9","sha256:3fa80706aa8307ec8ca13edc666ccc1fdc00ab8d8bc5d63077b860cb9d7ee7b8"],"state_sha256":"e6d3d890ce54bcdefc5071938173342d4bc9a418dd933dcff6e0d21c20edd107"}