{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CYFS4GSLZAPLPPFJUQDOL6QTDL","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":"97f366d2e818b01eba255532bc992124799e49792293cf948c6151cb2a8cb216","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-20T12:07:37Z","title_canon_sha256":"e1d4a9732f8fa1dcbc994b5f58d377795073f67ff038f3e7753d6026d54d797c"},"schema_version":"1.0","source":{"id":"1610.06373","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06373","created_at":"2026-05-18T00:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06373v3","created_at":"2026-05-18T00:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06373","created_at":"2026-05-18T00:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"CYFS4GSLZAPL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYFS4GSLZAPLPPFJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYFS4GSL","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:4575c8984bcb8843fa6a1672dfd792e95473288a7debb677e74f9b43e15b228c","target":"graph","created_at":"2026-05-18T00:39:28Z","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":"We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in the form of a compact, oriented surface with boundary together with three tuples of simple closed curves, with possibly fewer curves than the genus of the surface, satisfying a pairwise standardness condition. This should be thought of as the $4$--dimensional analog of a sutured Heegaard diagram for a sutured $3$--manifold. We also give many foundational examples.","authors_text":"David T. Gay, Juanita Pinz\\'on-Caicedo, Nickolas A. Castro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-20T12:07:37Z","title":"Diagrams for Relative Trisections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06373","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:e9596fd15be64d88c1a6aa6831261f1b93e2b7f7e021f511e6184c35d8e881ce","target":"record","created_at":"2026-05-18T00:39:28Z","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":"97f366d2e818b01eba255532bc992124799e49792293cf948c6151cb2a8cb216","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-20T12:07:37Z","title_canon_sha256":"e1d4a9732f8fa1dcbc994b5f58d377795073f67ff038f3e7753d6026d54d797c"},"schema_version":"1.0","source":{"id":"1610.06373","kind":"arxiv","version":3}},"canonical_sha256":"160b2e1a4bc81eb7bca9a406e5fa131afa6d8db98519b8e2605019ea92a70dfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"160b2e1a4bc81eb7bca9a406e5fa131afa6d8db98519b8e2605019ea92a70dfd","first_computed_at":"2026-05-18T00:39:28.939370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:28.939370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RlBPHJsUM61yTa0iRf2dR6tWsI+ba9japr8grBt0nVUF4O2ztKl1Xs7mxgxFeVniPFyn5eQGvfyve2imKbXZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:28.939845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06373","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9596fd15be64d88c1a6aa6831261f1b93e2b7f7e021f511e6184c35d8e881ce","sha256:4575c8984bcb8843fa6a1672dfd792e95473288a7debb677e74f9b43e15b228c"],"state_sha256":"aa563d6f8ee94f455832e070f6cdc724281f816e9fa6e1a2382bedfe0595242f"}