{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NUN6FAANKVHTHTNP45MR2YTWUJ","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":"27ed195d981517b8f929320cdde9f744ecdad034047ab04b89e9caa623c0bb39","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-07-16T14:20:01Z","title_canon_sha256":"6a04512987d232e2b373bb51754da82cb2d0f5e342c0ee838b2082ff76ef75d4"},"schema_version":"1.0","source":{"id":"2407.11759","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.11759","created_at":"2026-07-05T09:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"2407.11759v3","created_at":"2026-07-05T09:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.11759","created_at":"2026-07-05T09:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"NUN6FAANKVHT","created_at":"2026-07-05T09:44:13Z"},{"alias_kind":"pith_short_16","alias_value":"NUN6FAANKVHTHTNP","created_at":"2026-07-05T09:44:13Z"},{"alias_kind":"pith_short_8","alias_value":"NUN6FAAN","created_at":"2026-07-05T09:44:13Z"}],"graph_snapshots":[{"event_id":"sha256:1e6701b349aa938d2b02baecb8c03a0e70d830f1f8c8976c96d408ea060e2861","target":"graph","created_at":"2026-07-05T09:44:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.11759/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Thurston norm is a seminorm on the second real homology group of a compact orientable 3-manifold. The unit ball of this norm is a convex polyhedron, whose shape's data (e.g. number of vertices, regularity) measures the complexity of the surfaces sitting in the ambient 3-manifold.\n  Unfortunately, the Thurston norm is generally quite hard to compute, and a long-standing problem is to understand which polyhedra are realised as the unit balls of the Thurston norms of $3$-manifolds. We show that, when $M$ is the complement of a $2$-bridge link $L$ with components $\\ell_1$ and $\\ell_2$, the Thu","authors_text":"Alessandro V. Cigna","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-07-16T14:20:01Z","title":"The Thurston norm of 2-bridge link complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.11759","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:d5ff076a14753d769e9fb8f5b6bd83fd40af24f5a7ea1e8240a9edd508747561","target":"record","created_at":"2026-07-05T09:44:13Z","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":"27ed195d981517b8f929320cdde9f744ecdad034047ab04b89e9caa623c0bb39","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-07-16T14:20:01Z","title_canon_sha256":"6a04512987d232e2b373bb51754da82cb2d0f5e342c0ee838b2082ff76ef75d4"},"schema_version":"1.0","source":{"id":"2407.11759","kind":"arxiv","version":3}},"canonical_sha256":"6d1be2800d554f33cdafe7591d6276a273b588cf5efb6db49a2879190c5600c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d1be2800d554f33cdafe7591d6276a273b588cf5efb6db49a2879190c5600c3","first_computed_at":"2026-07-05T09:44:13.141817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:44:13.141817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GEAbPihJ+bSt0Wdf/Y8S5I8UxJb7QH/8EqiGq0ZEIBowKNMdhr5umroBUEz1sDz8AffNXbUwF4Q5nWju34Y3Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:44:13.142376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.11759","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5ff076a14753d769e9fb8f5b6bd83fd40af24f5a7ea1e8240a9edd508747561","sha256:1e6701b349aa938d2b02baecb8c03a0e70d830f1f8c8976c96d408ea060e2861"],"state_sha256":"3fb78747e5ca2521c3a40f29b01f2aac151201d7571b6322f19506ee571c76eb"}