{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5CAD7TFS7RDZMP7W4UPAONV65W","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":"fb4a24bd1356755dcd4cc3c83a18aee49cb859fd09da127e283db81327dea37e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-04T16:24:03Z","title_canon_sha256":"dacb54bdd2029d770fb7afc8784801fce856c3a1ff405673c02f618c3bcd775b"},"schema_version":"1.0","source":{"id":"1202.0905","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0905","created_at":"2026-05-18T02:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0905v3","created_at":"2026-05-18T02:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0905","created_at":"2026-05-18T02:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"5CAD7TFS7RDZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5CAD7TFS7RDZMP7W","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5CAD7TFS","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:117b5ee04be10c269654bec23b611817e0b4039c0f6ba236bb2718f022f8c904","target":"graph","created_at":"2026-05-18T02:17:12Z","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":"In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyperbolic structures on the surface or 3-manifold completely determines the curve. For an orientable surface $S$ of negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case on closed surfaces of genus two that we describe completely), while for hyperbolizable 3-manifolds, we show that curves freely homotopic to","authors_text":"James W. Anderson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-04T16:24:03Z","title":"Prising apart geodesics by length in hyperbolic 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0905","kind":"arxiv","version":3},"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":"sha256:5aef1844019482079f9c0ee4554218f3cdce3daa6b78115fbcd27e576973509c","target":"record","created_at":"2026-05-18T02:17:12Z","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":"fb4a24bd1356755dcd4cc3c83a18aee49cb859fd09da127e283db81327dea37e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-04T16:24:03Z","title_canon_sha256":"dacb54bdd2029d770fb7afc8784801fce856c3a1ff405673c02f618c3bcd775b"},"schema_version":"1.0","source":{"id":"1202.0905","kind":"arxiv","version":3}},"canonical_sha256":"e8803fccb2fc47963ff6e51e0736beeda82c78953f76260f72841ed7eab01f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8803fccb2fc47963ff6e51e0736beeda82c78953f76260f72841ed7eab01f4d","first_computed_at":"2026-05-18T02:17:12.738477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:12.738477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vsKmTz4l9PRXXjnmC2OY7VJW/ISE0xqo6r/B1a1fSRBZgK6CeQFkrsFTgeB4NUgV8vpoZiRj3dOtz9sg2HxCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:12.739147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0905","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aef1844019482079f9c0ee4554218f3cdce3daa6b78115fbcd27e576973509c","sha256:117b5ee04be10c269654bec23b611817e0b4039c0f6ba236bb2718f022f8c904"],"state_sha256":"fb19df3a3e8f992b2571ac8ce7b15323f6b36f855286036b3d592ddf84ab72aa"}