{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:32L6NSMUCCBTNTUCIP6MVLHE5O","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":"00f8a939619cc806354d5e863be879ef60e3453cea9eed6d592238db303e73ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-03T12:54:08Z","title_canon_sha256":"ae5899d5ad22ff4eef5cdb291964ba124009a02264e6251a5fb866a17c6ea3ad"},"schema_version":"1.0","source":{"id":"1004.0440","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0440","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0440v2","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0440","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"32L6NSMUCCBT","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"32L6NSMUCCBTNTUC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"32L6NSMU","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:67454d3a4712635897aa6ec784fe4ed6ca0b739374b0c5c3b54e55a3873f11f7","target":"graph","created_at":"2026-05-18T04:15:28Z","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":"This survey paper contains an elementary exposition of Casson and Rivin's technique for finding the hyperbolic metric on a 3-manifold M with toroidal boundary. We also survey a number of applications of this technique.\n  The method involves subdividing M into ideal tetrahedra and solving a system of gluing equations to find hyperbolic shapes for the tetrahedra. The gluing equations decompose into a linear and non-linear part. The solutions to the linear equations form a convex polytope A. The solution to the non-linear part (unique if it exists) is a critical point of a certain volume function","authors_text":"David Futer, Fran\\c{c}ois Gu\\'eritaud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-03T12:54:08Z","title":"From angled triangulations to hyperbolic structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0440","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":"sha256:7faa541768b030f41985fba44447e638d5f5daf7318994446cfa91cd41fa63d6","target":"record","created_at":"2026-05-18T04:15:28Z","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":"00f8a939619cc806354d5e863be879ef60e3453cea9eed6d592238db303e73ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-03T12:54:08Z","title_canon_sha256":"ae5899d5ad22ff4eef5cdb291964ba124009a02264e6251a5fb866a17c6ea3ad"},"schema_version":"1.0","source":{"id":"1004.0440","kind":"arxiv","version":2}},"canonical_sha256":"de97e6c994108336ce8243fccaace4eb8464bd334df567cfc95ffcc6dd1cb502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de97e6c994108336ce8243fccaace4eb8464bd334df567cfc95ffcc6dd1cb502","first_computed_at":"2026-05-18T04:15:28.524142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:28.524142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UiMSNnlJLvN40zD0aEM66pyZO3XHRxeoodb0zpi7WMkZbubZniUn4SSUTTaALCf9Qgz/07DAv0+pDuYhfPJRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:28.524587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0440","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7faa541768b030f41985fba44447e638d5f5daf7318994446cfa91cd41fa63d6","sha256:67454d3a4712635897aa6ec784fe4ed6ca0b739374b0c5c3b54e55a3873f11f7"],"state_sha256":"dd94965c5ac46ee58f93d6491720b53ecdb7b46b97a9226b79280a21f395ff0c"}