{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NGY34EHC2PPZ5DFZU7HMNQZWBM","short_pith_number":"pith:NGY34EHC","schema_version":"1.0","canonical_sha256":"69b1be10e2d3df9e8cb9a7cec6c3360b26df89fd2f225294bb822b2ca19cd28a","source":{"kind":"arxiv","id":"1105.5508","version":1},"attestation_state":"computed","paper":{"title":"Heegaard Floer homologies for (+1) surgeries on torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andr\\'as N\\'emethi, Maciej Borodzik","submitted_at":"2011-05-27T09:45:28Z","abstract_excerpt":"We compute the Heegaard Floer homology of $S^3_1(K)$ (the (+1) surgery on the torus knot $T_{p,q}$) in terms of the semigroup generated by $p$ and $q$, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsvath--Szabo d-invariant. We relate the result to known knot invariants of $T_{p,q}$ as the genus and the Levine--Tristram signatures. Furthermore, we emphasize the striking resemblance between Heegaard Floer homologies of (+1) and (-1) surgeries on torus knots. This relation is best seen at the level of $\\tau$ functions."},"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":"1105.5508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-27T09:45:28Z","cross_cats_sorted":[],"title_canon_sha256":"b144061a9d0085c435691bc600461ef8e2c08db78ba736f443e5211d3b5a56b7","abstract_canon_sha256":"cd88eca9b21b52de6c30363e7636b25083c0d0ce35a3c3c87779ad4de77c92c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:11.515058Z","signature_b64":"Djf7bvolHdk7JSt0ly8O3X0Gwd072EC3PUoMHgjIpvaB7rzfuHDW/Fka4uLd14tDRmgq3S3lNCfKqUyd0wPQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69b1be10e2d3df9e8cb9a7cec6c3360b26df89fd2f225294bb822b2ca19cd28a","last_reissued_at":"2026-05-18T04:21:11.514563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:11.514563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heegaard Floer homologies for (+1) surgeries on torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andr\\'as N\\'emethi, Maciej Borodzik","submitted_at":"2011-05-27T09:45:28Z","abstract_excerpt":"We compute the Heegaard Floer homology of $S^3_1(K)$ (the (+1) surgery on the torus knot $T_{p,q}$) in terms of the semigroup generated by $p$ and $q$, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsvath--Szabo d-invariant. We relate the result to known knot invariants of $T_{p,q}$ as the genus and the Levine--Tristram signatures. Furthermore, we emphasize the striking resemblance between Heegaard Floer homologies of (+1) and (-1) surgeries on torus knots. This relation is best seen at the level of $\\tau$ functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5508","kind":"arxiv","version":1},"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":"1105.5508","created_at":"2026-05-18T04:21:11.514648+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.5508v1","created_at":"2026-05-18T04:21:11.514648+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5508","created_at":"2026-05-18T04:21:11.514648+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGY34EHC2PPZ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGY34EHC2PPZ5DFZ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGY34EHC","created_at":"2026-05-18T12:26:37.096874+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/NGY34EHC2PPZ5DFZU7HMNQZWBM","json":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM.json","graph_json":"https://pith.science/api/pith-number/NGY34EHC2PPZ5DFZU7HMNQZWBM/graph.json","events_json":"https://pith.science/api/pith-number/NGY34EHC2PPZ5DFZU7HMNQZWBM/events.json","paper":"https://pith.science/paper/NGY34EHC"},"agent_actions":{"view_html":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM","download_json":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM.json","view_paper":"https://pith.science/paper/NGY34EHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.5508&json=true","fetch_graph":"https://pith.science/api/pith-number/NGY34EHC2PPZ5DFZU7HMNQZWBM/graph.json","fetch_events":"https://pith.science/api/pith-number/NGY34EHC2PPZ5DFZU7HMNQZWBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM/action/storage_attestation","attest_author":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM/action/author_attestation","sign_citation":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM/action/citation_signature","submit_replication":"https://pith.science/pith/NGY34EHC2PPZ5DFZU7HMNQZWBM/action/replication_record"}},"created_at":"2026-05-18T04:21:11.514648+00:00","updated_at":"2026-05-18T04:21:11.514648+00:00"}