{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GID6ENL6VR4HBJ4AN3GJWRFID3","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":"adf69663826e99948e409d0506d5f829db8df7f3fb01243f7a4d0cca5565a34f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-25T01:00:46Z","title_canon_sha256":"1ae1247e8ced3d8da8ce478761c53e1fee49adf169603f87fcb2849ce9a43430"},"schema_version":"1.0","source":{"id":"1503.07251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07251","created_at":"2026-05-18T02:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07251v1","created_at":"2026-05-18T02:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07251","created_at":"2026-05-18T02:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"GID6ENL6VR4H","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GID6ENL6VR4HBJ4A","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GID6ENL6","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:450dadd05f9bd40ba9764391e4bfc1f1cca0370b843a45c270fd240d4c35f6c6","target":"graph","created_at":"2026-05-18T02:20:27Z","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 show that the Thurston norm of any irreducible 3-manifold can be detected using twisted Reidemeister torsions corresponding to integral representations and also corresponding to representations over finite fields. In particular our result holds for all graph manifolds, these are not covered by the earlier work of the first author and Vidussi.","authors_text":"Matthias Nagel, Stefan Friedl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-25T01:00:46Z","title":"Twisted Reidemeister torsion and the Thurston norm: graph manifolds and finite representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07251","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:bfd27461d876aa281c636b286aeb654ca1525dcc13756586693b9b4c4e08d0f0","target":"record","created_at":"2026-05-18T02:20:27Z","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":"adf69663826e99948e409d0506d5f829db8df7f3fb01243f7a4d0cca5565a34f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-25T01:00:46Z","title_canon_sha256":"1ae1247e8ced3d8da8ce478761c53e1fee49adf169603f87fcb2849ce9a43430"},"schema_version":"1.0","source":{"id":"1503.07251","kind":"arxiv","version":1}},"canonical_sha256":"3207e2357eac7870a7806ecc9b44a81ec1ca0ba80fbe619e79e49a8e8f29f410","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3207e2357eac7870a7806ecc9b44a81ec1ca0ba80fbe619e79e49a8e8f29f410","first_computed_at":"2026-05-18T02:20:27.913639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:27.913639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mpug7r2IC2pymgLpJbmB2AOhXbyZsotCGrKJ//e1+iQl0lsGd4lt9CRlPJfU9+bce1c0sbhI/DnQ/jElySwzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:27.914293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfd27461d876aa281c636b286aeb654ca1525dcc13756586693b9b4c4e08d0f0","sha256:450dadd05f9bd40ba9764391e4bfc1f1cca0370b843a45c270fd240d4c35f6c6"],"state_sha256":"caf55fc780acf5286a01092baa9a70bba17a37e2967cd499e3680de246d7eb07"}