{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SZYH4D7CP3FDPX7GCGNXUVGUBE","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":"51d0d37e25739211865bd95c46878242d88fe29b8f3bf9a3e0ef960626c1bbea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-11-29T21:15:12Z","title_canon_sha256":"23a2971075faf21536eafdc554d8abc87bd436e47b5d0ae7496e871fda4adbe3"},"schema_version":"1.0","source":{"id":"2111.14962","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.14962","created_at":"2026-07-05T08:45:19Z"},{"alias_kind":"arxiv_version","alias_value":"2111.14962v4","created_at":"2026-07-05T08:45:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.14962","created_at":"2026-07-05T08:45:19Z"},{"alias_kind":"pith_short_12","alias_value":"SZYH4D7CP3FD","created_at":"2026-07-05T08:45:19Z"},{"alias_kind":"pith_short_16","alias_value":"SZYH4D7CP3FDPX7G","created_at":"2026-07-05T08:45:19Z"},{"alias_kind":"pith_short_8","alias_value":"SZYH4D7C","created_at":"2026-07-05T08:45:19Z"}],"graph_snapshots":[{"event_id":"sha256:c19b9a228457b48b636479653da61e7c50c9fceec200a4d3d02d66017df0da40","target":"graph","created_at":"2026-07-05T08:45:19Z","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/2111.14962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove N\\'{e}methi's conjecture: if $Y$ is a 3-manifold which is the boundary of a plumbing of a tree of disk bundles over $S^2$, then the lattice homology of $Y$ coincides with the Heegaard Floer homology of $Y$. We also give a conjectural description of the $H_1(Y)/\\mathrm{Tors}$ action when $b_1(Y)>0$.","authors_text":"Ian Zemke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-11-29T21:15:12Z","title":"The equivalence of lattice and Heegaard Floer homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14962","kind":"arxiv","version":4},"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":"sha256:5551718550cae685446a88c6d28eeea78087d15145dd1766fbd5976b1476a297","target":"record","created_at":"2026-07-05T08:45:19Z","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":"51d0d37e25739211865bd95c46878242d88fe29b8f3bf9a3e0ef960626c1bbea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-11-29T21:15:12Z","title_canon_sha256":"23a2971075faf21536eafdc554d8abc87bd436e47b5d0ae7496e871fda4adbe3"},"schema_version":"1.0","source":{"id":"2111.14962","kind":"arxiv","version":4}},"canonical_sha256":"96707e0fe27eca37dfe6119b7a54d4092504e3532157b005357523e075c184ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96707e0fe27eca37dfe6119b7a54d4092504e3532157b005357523e075c184ed","first_computed_at":"2026-07-05T08:45:19.305885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:45:19.305885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aUTStgxLjeK5XA3nWp135Y8NhY0O5nDeciaXh9v51Je2wI/HX5GzA2IfzWAQhJ87tV3abDUJkXnVTX50DVo0AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:45:19.306362Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.14962","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5551718550cae685446a88c6d28eeea78087d15145dd1766fbd5976b1476a297","sha256:c19b9a228457b48b636479653da61e7c50c9fceec200a4d3d02d66017df0da40"],"state_sha256":"927a4e455dc76aac02d9b1e5a5b9646e9a1a143bd636bec01ffcf65056deff60"}