{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6P55335X55VFWRKFIWZZWBWSVD","short_pith_number":"pith:6P55335X","schema_version":"1.0","canonical_sha256":"f3fbddefb7ef6a5b454545b39b06d2a8c8289c0b7257f8087164b96767bce730","source":{"kind":"arxiv","id":"1505.06672","version":2},"attestation_state":"computed","paper":{"title":"The Upsilon function of L-space knots is a Legendre transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maciej Borodzik, Matthew Hedden","submitted_at":"2015-05-25T15:54:18Z","abstract_excerpt":"Given an L-space knot we show that its Upsilon function is the Legendre transform of a counting function equivalent to the d-invariants of its large surgeries. The unknotting obstruction obtained for the Upsilon function is, in the case of L-space knots, contained in the d-invariants of large surgeries. Generalizations apply for connected sums of L-space knots, which imply that the slice obstruction provided by Upsilon on the subgroup of concordance generated by L-space knots is no finer than that provided by the d-invariants."},"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":"1505.06672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-25T15:54:18Z","cross_cats_sorted":[],"title_canon_sha256":"e49c6aa1f3418da0f96458b77949a5ebd20a6a5529c758008539e9926f656ea3","abstract_canon_sha256":"245a76f88503ea1bc6b71dc20e5ed6a8ff96d0078a50e5579ec1057d95d42d84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:54.728076Z","signature_b64":"OfipaHOmlDrgDfdEjBIfeuXcMqLth0DLWgNZPjRUsIOoXtZw+B/+YE8Gd5gED4vUebwRdSYEAjx0Q1l8UFM0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3fbddefb7ef6a5b454545b39b06d2a8c8289c0b7257f8087164b96767bce730","last_reissued_at":"2026-05-18T01:39:54.727583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:54.727583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Upsilon function of L-space knots is a Legendre transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maciej Borodzik, Matthew Hedden","submitted_at":"2015-05-25T15:54:18Z","abstract_excerpt":"Given an L-space knot we show that its Upsilon function is the Legendre transform of a counting function equivalent to the d-invariants of its large surgeries. The unknotting obstruction obtained for the Upsilon function is, in the case of L-space knots, contained in the d-invariants of large surgeries. Generalizations apply for connected sums of L-space knots, which imply that the slice obstruction provided by Upsilon on the subgroup of concordance generated by L-space knots is no finer than that provided by the d-invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06672","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":"1505.06672","created_at":"2026-05-18T01:39:54.727647+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06672v2","created_at":"2026-05-18T01:39:54.727647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06672","created_at":"2026-05-18T01:39:54.727647+00:00"},{"alias_kind":"pith_short_12","alias_value":"6P55335X55VF","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6P55335X55VFWRKF","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6P55335X","created_at":"2026-05-18T12:29:07.941421+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/6P55335X55VFWRKFIWZZWBWSVD","json":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD.json","graph_json":"https://pith.science/api/pith-number/6P55335X55VFWRKFIWZZWBWSVD/graph.json","events_json":"https://pith.science/api/pith-number/6P55335X55VFWRKFIWZZWBWSVD/events.json","paper":"https://pith.science/paper/6P55335X"},"agent_actions":{"view_html":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD","download_json":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD.json","view_paper":"https://pith.science/paper/6P55335X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06672&json=true","fetch_graph":"https://pith.science/api/pith-number/6P55335X55VFWRKFIWZZWBWSVD/graph.json","fetch_events":"https://pith.science/api/pith-number/6P55335X55VFWRKFIWZZWBWSVD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD/action/storage_attestation","attest_author":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD/action/author_attestation","sign_citation":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD/action/citation_signature","submit_replication":"https://pith.science/pith/6P55335X55VFWRKFIWZZWBWSVD/action/replication_record"}},"created_at":"2026-05-18T01:39:54.727647+00:00","updated_at":"2026-05-18T01:39:54.727647+00:00"}