{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:T54GPBJDXF3R3FD43ZN3VB2FHW","short_pith_number":"pith:T54GPBJD","schema_version":"1.0","canonical_sha256":"9f78678523b9771d947cde5bba87453d8204103912f95b30d61e51704ef3aae2","source":{"kind":"arxiv","id":"2212.00320","version":3},"attestation_state":"computed","paper":{"title":"A universal formula for the $x-y$ swap in topological recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Alexandrov, Boris Bychkov, Maxim Kazarian, Petr Dunin-Barkowski, Sergey Shadrin","submitted_at":"2022-12-01T07:11:05Z","abstract_excerpt":"We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock).\n  As an application of this general $x-y$ swap result, we prove an explicit closed formula for the topological recursion differentials for the case of any spectral curve with unramified $y$ and arbitrary rational $x$."},"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":"2212.00320","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-12-01T07:11:05Z","cross_cats_sorted":["hep-th","math.AG","math.CO","math.MP"],"title_canon_sha256":"41670dfcc7cfe8376becebd3a76f0f6d8a034bfbced352d4aaeb4b849f6c09ca","abstract_canon_sha256":"42d07442e2f86a0b7fc9cda3f9c1dab38e06ef51d2fa194406d8dbe8e907ddb2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:56.543403Z","signature_b64":"Z9Xcek46xSCWMpEltzu+ND8hbPz/HmQ98VTiuEflhGk4O4P7rgAOpY621s2bcRLyHzunzzjisVCiNEuU8llHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f78678523b9771d947cde5bba87453d8204103912f95b30d61e51704ef3aae2","last_reissued_at":"2026-07-05T11:09:56.542834Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:56.542834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A universal formula for the $x-y$ swap in topological recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Alexandrov, Boris Bychkov, Maxim Kazarian, Petr Dunin-Barkowski, Sergey Shadrin","submitted_at":"2022-12-01T07:11:05Z","abstract_excerpt":"We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock).\n  As an application of this general $x-y$ swap result, we prove an explicit closed formula for the topological recursion differentials for the case of any spectral curve with unramified $y$ and arbitrary rational $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.00320","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.00320/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2212.00320","created_at":"2026-07-05T11:09:56.542904+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.00320v3","created_at":"2026-07-05T11:09:56.542904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.00320","created_at":"2026-07-05T11:09:56.542904+00:00"},{"alias_kind":"pith_short_12","alias_value":"T54GPBJDXF3R","created_at":"2026-07-05T11:09:56.542904+00:00"},{"alias_kind":"pith_short_16","alias_value":"T54GPBJDXF3R3FD4","created_at":"2026-07-05T11:09:56.542904+00:00"},{"alias_kind":"pith_short_8","alias_value":"T54GPBJD","created_at":"2026-07-05T11:09:56.542904+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.04854","citing_title":"Resonance transformations for the $(2,2p+1)$ minimal string via $x-y$ swap: a proof of Artemev's conjecture","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.00584","citing_title":"A new family of weighted double Hurwitz numbers and a new ELSV-type formula with $\\Omega$-classes","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW","json":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW.json","graph_json":"https://pith.science/api/pith-number/T54GPBJDXF3R3FD43ZN3VB2FHW/graph.json","events_json":"https://pith.science/api/pith-number/T54GPBJDXF3R3FD43ZN3VB2FHW/events.json","paper":"https://pith.science/paper/T54GPBJD"},"agent_actions":{"view_html":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW","download_json":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW.json","view_paper":"https://pith.science/paper/T54GPBJD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.00320&json=true","fetch_graph":"https://pith.science/api/pith-number/T54GPBJDXF3R3FD43ZN3VB2FHW/graph.json","fetch_events":"https://pith.science/api/pith-number/T54GPBJDXF3R3FD43ZN3VB2FHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW/action/storage_attestation","attest_author":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW/action/author_attestation","sign_citation":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW/action/citation_signature","submit_replication":"https://pith.science/pith/T54GPBJDXF3R3FD43ZN3VB2FHW/action/replication_record"}},"created_at":"2026-07-05T11:09:56.542904+00:00","updated_at":"2026-07-05T11:09:56.542904+00:00"}