{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:S5JBOLGC26ATFKN7F7FIN7LZDT","short_pith_number":"pith:S5JBOLGC","schema_version":"1.0","canonical_sha256":"9752172cc2d78132a9bf2fca86fd791cfe055c6825354e1f3673d32b46867b39","source":{"kind":"arxiv","id":"1001.0640","version":2},"attestation_state":"computed","paper":{"title":"Two exact sequences for lattice cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi","submitted_at":"2010-01-05T07:31:21Z","abstract_excerpt":"We establish two exact sequences for the lattice cohomology associated with non-degenerate plumbing graphs. The first is the analogue of the surgery exact triangle proved by Ozsvath and Szabo for the Heegaard-Floer invariant HF^+; for the lattice cohomology over Z_2-coefficients it was proved by J. Greene. Here we prove it over the integers, and we supplement it by some additional properties valid for negative definite graphs. The second exact sequence is an adapted version which does not mix the classes of the characteristic elements (spin^c-structures); it was partially motivated by the surg"},"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":"1001.0640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-01-05T07:31:21Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ecc8376f0e3c6208262d163e51e69536763964dea7a4258812963da9f8debfdb","abstract_canon_sha256":"9a0d449a1dbadc95d05382cdc15aa644f4f36faed5cf4543d42e14d7baaf7899"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:50.326955Z","signature_b64":"qdf6ltnXCoCn+zg4nw0p8rpOTT57FY9sgHHPOZSQcb3iaP5PL0DXvn9l6fXKJ7MpS8rdA+swAxn2pZIX1r8lAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9752172cc2d78132a9bf2fca86fd791cfe055c6825354e1f3673d32b46867b39","last_reissued_at":"2026-05-18T04:39:50.326438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:50.326438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two exact sequences for lattice cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi","submitted_at":"2010-01-05T07:31:21Z","abstract_excerpt":"We establish two exact sequences for the lattice cohomology associated with non-degenerate plumbing graphs. The first is the analogue of the surgery exact triangle proved by Ozsvath and Szabo for the Heegaard-Floer invariant HF^+; for the lattice cohomology over Z_2-coefficients it was proved by J. Greene. Here we prove it over the integers, and we supplement it by some additional properties valid for negative definite graphs. The second exact sequence is an adapted version which does not mix the classes of the characteristic elements (spin^c-structures); it was partially motivated by the surg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0640","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":"1001.0640","created_at":"2026-05-18T04:39:50.326521+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.0640v2","created_at":"2026-05-18T04:39:50.326521+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0640","created_at":"2026-05-18T04:39:50.326521+00:00"},{"alias_kind":"pith_short_12","alias_value":"S5JBOLGC26AT","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"S5JBOLGC26ATFKN7","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"S5JBOLGC","created_at":"2026-05-18T12:26:13.927090+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/S5JBOLGC26ATFKN7F7FIN7LZDT","json":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT.json","graph_json":"https://pith.science/api/pith-number/S5JBOLGC26ATFKN7F7FIN7LZDT/graph.json","events_json":"https://pith.science/api/pith-number/S5JBOLGC26ATFKN7F7FIN7LZDT/events.json","paper":"https://pith.science/paper/S5JBOLGC"},"agent_actions":{"view_html":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT","download_json":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT.json","view_paper":"https://pith.science/paper/S5JBOLGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.0640&json=true","fetch_graph":"https://pith.science/api/pith-number/S5JBOLGC26ATFKN7F7FIN7LZDT/graph.json","fetch_events":"https://pith.science/api/pith-number/S5JBOLGC26ATFKN7F7FIN7LZDT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT/action/storage_attestation","attest_author":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT/action/author_attestation","sign_citation":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT/action/citation_signature","submit_replication":"https://pith.science/pith/S5JBOLGC26ATFKN7F7FIN7LZDT/action/replication_record"}},"created_at":"2026-05-18T04:39:50.326521+00:00","updated_at":"2026-05-18T04:39:50.326521+00:00"}