{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PWWYKWWDSYK6DNQYCVEOL2WQJ2","short_pith_number":"pith:PWWYKWWD","schema_version":"1.0","canonical_sha256":"7dad855ac39615e1b6181548e5ead04e96ddf908f7d6108125f1177aff493f94","source":{"kind":"arxiv","id":"1805.03457","version":2},"attestation_state":"computed","paper":{"title":"Combinatorial duality for Poincar\\'e series, polytopes and invariants of plumbed 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi, J\\'anos Nagy, Tam\\'as L\\'aszl\\'o","submitted_at":"2018-05-09T11:14:29Z","abstract_excerpt":"Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the `periodic constant' of the topological multivariable Poincar\\'e series (zeta function). This involves a complicated regularization procedure (via quasipolynomials measuring the asymptotic behaviour of the coefficients).\n  We show that the (a Gorenstein type) symmetry of the zeta function combined with Ehrhart-Macdonald-Stanley reciprocity (of Ehrhart theory of polytopes) provide a simple expression for the periodic constant. Using these dualities "},"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":"1805.03457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-09T11:14:29Z","cross_cats_sorted":[],"title_canon_sha256":"471cdfe6c67fcb62b680c6679c969cb2fd430b590b78b0deffdc0195af86cf13","abstract_canon_sha256":"4b977b165a1f1ec63ca803f779f47021477ebbbab1e50dd8c20059059e4d30ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:24.280206Z","signature_b64":"Y2n7sFIyZBCMLiZgCGWKvSSZuGEDG3npYUVV8xe4/KAMM6gYwX1x4cjMf08xcQgs413Y6QefIU2Yn5oS3iBlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dad855ac39615e1b6181548e5ead04e96ddf908f7d6108125f1177aff493f94","last_reissued_at":"2026-05-18T00:12:24.279494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:24.279494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial duality for Poincar\\'e series, polytopes and invariants of plumbed 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi, J\\'anos Nagy, Tam\\'as L\\'aszl\\'o","submitted_at":"2018-05-09T11:14:29Z","abstract_excerpt":"Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the `periodic constant' of the topological multivariable Poincar\\'e series (zeta function). This involves a complicated regularization procedure (via quasipolynomials measuring the asymptotic behaviour of the coefficients).\n  We show that the (a Gorenstein type) symmetry of the zeta function combined with Ehrhart-Macdonald-Stanley reciprocity (of Ehrhart theory of polytopes) provide a simple expression for the periodic constant. Using these dualities "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03457","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":"1805.03457","created_at":"2026-05-18T00:12:24.279606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.03457v2","created_at":"2026-05-18T00:12:24.279606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03457","created_at":"2026-05-18T00:12:24.279606+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWWYKWWDSYK6","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWWYKWWDSYK6DNQY","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWWYKWWD","created_at":"2026-05-18T12:32:46.962924+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/PWWYKWWDSYK6DNQYCVEOL2WQJ2","json":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2.json","graph_json":"https://pith.science/api/pith-number/PWWYKWWDSYK6DNQYCVEOL2WQJ2/graph.json","events_json":"https://pith.science/api/pith-number/PWWYKWWDSYK6DNQYCVEOL2WQJ2/events.json","paper":"https://pith.science/paper/PWWYKWWD"},"agent_actions":{"view_html":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2","download_json":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2.json","view_paper":"https://pith.science/paper/PWWYKWWD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.03457&json=true","fetch_graph":"https://pith.science/api/pith-number/PWWYKWWDSYK6DNQYCVEOL2WQJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/PWWYKWWDSYK6DNQYCVEOL2WQJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2/action/storage_attestation","attest_author":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2/action/author_attestation","sign_citation":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2/action/citation_signature","submit_replication":"https://pith.science/pith/PWWYKWWDSYK6DNQYCVEOL2WQJ2/action/replication_record"}},"created_at":"2026-05-18T00:12:24.279606+00:00","updated_at":"2026-05-18T00:12:24.279606+00:00"}