{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ROI5HONIGIMBZDZRJO6HUB75YO","short_pith_number":"pith:ROI5HONI","schema_version":"1.0","canonical_sha256":"8b91d3b9a832181c8f314bbc7a07fdc3b732e5e2bbbb83cd6ecc3dcb9ad56010","source":{"kind":"arxiv","id":"1610.03353","version":2},"attestation_state":"computed","paper":{"title":"Heegaard Floer invariants in codimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Daniel Ruberman","submitted_at":"2016-10-11T14:16:07Z","abstract_excerpt":"Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \\times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. We show how this invariant can be used to obstruct embeddings of certain types of $3$-manifolds, including those obtained as a connected sum of a rational homology $3$-sphere and any number of copies of $S^1 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.03353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-11T14:16:07Z","cross_cats_sorted":[],"title_canon_sha256":"74e0f654450064724c0732145fa28fbae1d26eb23971f2671e55a29c9d29989b","abstract_canon_sha256":"7a6b709e985c6ad4e03e68242da89b350edf4987bc18dd7818e4236e0d2aeeb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:40.018775Z","signature_b64":"uneXTXct0WWWLMAl5vVHN/uLXnscF+EQ6AFxIXx6Lgdzdl28MeZhXVYyynEGhId1rKgDs1Jw9dEkaTE+PPXUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b91d3b9a832181c8f314bbc7a07fdc3b732e5e2bbbb83cd6ecc3dcb9ad56010","last_reissued_at":"2026-05-18T00:39:40.018122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:40.018122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heegaard Floer invariants in codimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Daniel Ruberman","submitted_at":"2016-10-11T14:16:07Z","abstract_excerpt":"Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \\times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. We show how this invariant can be used to obstruct embeddings of certain types of $3$-manifolds, including those obtained as a connected sum of a rational homology $3$-sphere and any number of copies of $S^1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03353","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.03353","created_at":"2026-05-18T00:39:40.018217+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.03353v2","created_at":"2026-05-18T00:39:40.018217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03353","created_at":"2026-05-18T00:39:40.018217+00:00"},{"alias_kind":"pith_short_12","alias_value":"ROI5HONIGIMB","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"ROI5HONIGIMBZDZR","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"ROI5HONI","created_at":"2026-05-18T12:30:41.710351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO","json":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO.json","graph_json":"https://pith.science/api/pith-number/ROI5HONIGIMBZDZRJO6HUB75YO/graph.json","events_json":"https://pith.science/api/pith-number/ROI5HONIGIMBZDZRJO6HUB75YO/events.json","paper":"https://pith.science/paper/ROI5HONI"},"agent_actions":{"view_html":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO","download_json":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO.json","view_paper":"https://pith.science/paper/ROI5HONI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.03353&json=true","fetch_graph":"https://pith.science/api/pith-number/ROI5HONIGIMBZDZRJO6HUB75YO/graph.json","fetch_events":"https://pith.science/api/pith-number/ROI5HONIGIMBZDZRJO6HUB75YO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO/action/storage_attestation","attest_author":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO/action/author_attestation","sign_citation":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO/action/citation_signature","submit_replication":"https://pith.science/pith/ROI5HONIGIMBZDZRJO6HUB75YO/action/replication_record"}},"created_at":"2026-05-18T00:39:40.018217+00:00","updated_at":"2026-05-18T00:39:40.018217+00:00"}