{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:V75VXE6XQSJYPO5XQ7BXGE3ZH2","short_pith_number":"pith:V75VXE6X","schema_version":"1.0","canonical_sha256":"affb5b93d7849387bbb787c37313793e8e17a1d92d4dfc349e0473665ba02222","source":{"kind":"arxiv","id":"1508.01138","version":1},"attestation_state":"computed","paper":{"title":"Heegaard Floer correction terms of $(+1)$-surgeries along $(2,q)$-cablings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kouki Sato","submitted_at":"2015-08-05T17:23:06Z","abstract_excerpt":"The Heegaard Floer correction term ($d$-invariant) is an invariant of rational homology 3-spheres equipped with a Spin$^c$ structure. In particular, the correction term of 1-surgeries along knots in $S^3$ is a ($2\\mathbb{Z}$-valued) knot concordance invariant $d_1$. In this paper, we estimate $d_1$ for the $(2,q)$-cable of any knot $K$. This estimate does not depend on the knot type of $K$. If $K$ belongs to a certain class which contains all negative knots, then equality holds. As a corollary, we show that the relationship between $d_1$ and the Heegaard Floer $\\tau$-invariant is very weak in "},"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":"1508.01138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-08-05T17:23:06Z","cross_cats_sorted":[],"title_canon_sha256":"3c370c6b70ab66f277ddc7a9293636fe4e83408783df2a20f1123277628b2b1b","abstract_canon_sha256":"3bb5d332a7c59850087fd689f03a34712ea365833e59141a616f5ce487459089"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:00.940891Z","signature_b64":"TrYqeidPEVBs1YjCj97+la1FNsFlyAesndmMkgxRW9FJKgCfNGN0MnzwoeV+E9W7uOlBzagW9ZcOYCsid8L8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"affb5b93d7849387bbb787c37313793e8e17a1d92d4dfc349e0473665ba02222","last_reissued_at":"2026-05-17T23:56:00.940271Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:00.940271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heegaard Floer correction terms of $(+1)$-surgeries along $(2,q)$-cablings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kouki Sato","submitted_at":"2015-08-05T17:23:06Z","abstract_excerpt":"The Heegaard Floer correction term ($d$-invariant) is an invariant of rational homology 3-spheres equipped with a Spin$^c$ structure. In particular, the correction term of 1-surgeries along knots in $S^3$ is a ($2\\mathbb{Z}$-valued) knot concordance invariant $d_1$. In this paper, we estimate $d_1$ for the $(2,q)$-cable of any knot $K$. This estimate does not depend on the knot type of $K$. If $K$ belongs to a certain class which contains all negative knots, then equality holds. As a corollary, we show that the relationship between $d_1$ and the Heegaard Floer $\\tau$-invariant is very weak in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01138","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":"1508.01138","created_at":"2026-05-17T23:56:00.940408+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01138v1","created_at":"2026-05-17T23:56:00.940408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01138","created_at":"2026-05-17T23:56:00.940408+00:00"},{"alias_kind":"pith_short_12","alias_value":"V75VXE6XQSJY","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"V75VXE6XQSJYPO5X","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"V75VXE6X","created_at":"2026-05-18T12:29:44.643036+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/V75VXE6XQSJYPO5XQ7BXGE3ZH2","json":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2.json","graph_json":"https://pith.science/api/pith-number/V75VXE6XQSJYPO5XQ7BXGE3ZH2/graph.json","events_json":"https://pith.science/api/pith-number/V75VXE6XQSJYPO5XQ7BXGE3ZH2/events.json","paper":"https://pith.science/paper/V75VXE6X"},"agent_actions":{"view_html":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2","download_json":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2.json","view_paper":"https://pith.science/paper/V75VXE6X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01138&json=true","fetch_graph":"https://pith.science/api/pith-number/V75VXE6XQSJYPO5XQ7BXGE3ZH2/graph.json","fetch_events":"https://pith.science/api/pith-number/V75VXE6XQSJYPO5XQ7BXGE3ZH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2/action/storage_attestation","attest_author":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2/action/author_attestation","sign_citation":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2/action/citation_signature","submit_replication":"https://pith.science/pith/V75VXE6XQSJYPO5XQ7BXGE3ZH2/action/replication_record"}},"created_at":"2026-05-17T23:56:00.940408+00:00","updated_at":"2026-05-17T23:56:00.940408+00:00"}