{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QDNGITV2XO6UQ7IATCUPUMPLUO","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":"9acd7f5cf36e8335fbb49ed7489f2d871df834b90d5b45da1e722c2fbeec98d3","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-30T20:32:20Z","title_canon_sha256":"0ae46469a37c805ab43250dcb68a4255f9c382dd196eb809f8a9ef78a299015c"},"schema_version":"1.0","source":{"id":"1211.7367","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7367","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7367v2","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7367","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"QDNGITV2XO6U","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QDNGITV2XO6UQ7IA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QDNGITV2","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:8c4b3a42f9ce521844fcc69a95bf9342f9b2a53a1da9f01a0a6c5fca13c41c63","target":"graph","created_at":"2026-05-18T02:56:11Z","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 paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology and it extends the well-known grading with values in a noncommutative group defined by Lipshitz-Ozsv\\'ath-Thurston.","authors_text":"Vinicius G. B. Ramos, Yang Huang","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-30T20:32:20Z","title":"A topological grading on bordered Heegaard Floer homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7367","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:b800e084186845c430d2be49df5f580d841646841baf3e38f8ccb30ed31f7877","target":"record","created_at":"2026-05-18T02:56:11Z","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":"9acd7f5cf36e8335fbb49ed7489f2d871df834b90d5b45da1e722c2fbeec98d3","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-30T20:32:20Z","title_canon_sha256":"0ae46469a37c805ab43250dcb68a4255f9c382dd196eb809f8a9ef78a299015c"},"schema_version":"1.0","source":{"id":"1211.7367","kind":"arxiv","version":2}},"canonical_sha256":"80da644ebabbbd487d0098a8fa31eba3ac4ee273926361e5d734a9de4814ec1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80da644ebabbbd487d0098a8fa31eba3ac4ee273926361e5d734a9de4814ec1f","first_computed_at":"2026-05-18T02:56:11.741271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:11.741271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/IWWELahMCqbj4ZN34lhy/n+ns/5dNZhDdj2/dqPgkxouvqjOckyVIvdW5Tcmkmtk/KWwNwvP2+UV1fIdnhaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:11.741697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7367","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b800e084186845c430d2be49df5f580d841646841baf3e38f8ccb30ed31f7877","sha256:8c4b3a42f9ce521844fcc69a95bf9342f9b2a53a1da9f01a0a6c5fca13c41c63"],"state_sha256":"1a3a54c06fe598f59e8cb50be65c890a8e53ec5b12426e26a40a85229fe3a0d3"}