{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I76WQ2MULKGTJ4PXAN6VXNNAVH","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":"a696e335ca2903a202d174f71e459e79040094d3f496f23de02b207bfbe8f78e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-17T10:02:17Z","title_canon_sha256":"5c594d4d789a04a7a33dd89b2cbff991b7286622709c668d9a13e567b4362eed"},"schema_version":"1.0","source":{"id":"1403.4050","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4050","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4050v2","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4050","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"pith_short_12","alias_value":"I76WQ2MULKGT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I76WQ2MULKGTJ4PX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I76WQ2MU","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:2f13ceb10068ce7971fd7fe87c11ceda38f75931d7cf97acb27d17d031af31d6","target":"graph","created_at":"2026-05-18T01:22:52Z","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":"Let $\\mathbb{F}$ be a field and let $G\\subset \\mathbb{F}\\setminus \\{0\\}$ be a multiplicative subgroup. We consider the category $\\mathcal{Cob}_G$ of $3$-dimensional cobordisms equipped with a representation of their fundamental group in $G$, and the category ${Vect}_{\\mathbb{F},\\pm G}$ of $\\mathbb{F}$-linear maps defined up to multiplication by an element of $\\pm G$. Using the elementary theory of Reidemeister torsions, we construct a \"Reidemeister functor\" from $Cob_G$ to ${Vect}_{\\mathbb{F},\\pm G}$. In particular, when the group $G$ is free abelian and $\\mathbb{F}$ is the field of fractions ","authors_text":"Gwenael Massuyeau, Vincent Florens","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-17T10:02:17Z","title":"A functorial extension of the abelian Reidemeister torsions of three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4050","kind":"arxiv","version":2},"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:a8e986ba4954e00e5eeee107e3c6458b3b00a7f8924ca0feb8f9b5b0db695b89","target":"record","created_at":"2026-05-18T01:22:52Z","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":"a696e335ca2903a202d174f71e459e79040094d3f496f23de02b207bfbe8f78e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-17T10:02:17Z","title_canon_sha256":"5c594d4d789a04a7a33dd89b2cbff991b7286622709c668d9a13e567b4362eed"},"schema_version":"1.0","source":{"id":"1403.4050","kind":"arxiv","version":2}},"canonical_sha256":"47fd6869945a8d34f1f7037d5bb5a0a9faf943816e82e428169c0d401a1b9614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47fd6869945a8d34f1f7037d5bb5a0a9faf943816e82e428169c0d401a1b9614","first_computed_at":"2026-05-18T01:22:52.505371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:52.505371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lPPH6lwTkMtRr3PrNPtfGrNTEHn0E5qSj0AEgzpt3Xcj/w0964vLpmSlDYkA0EwnC2nAk973Sad8TdwaC87VCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:52.505868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4050","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8e986ba4954e00e5eeee107e3c6458b3b00a7f8924ca0feb8f9b5b0db695b89","sha256:2f13ceb10068ce7971fd7fe87c11ceda38f75931d7cf97acb27d17d031af31d6"],"state_sha256":"06af4f35892c7511ff5028021ea948810faa4e937e45775780098bafccd29783"}