{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:Y7CKIFC5Q5AOOOAJRT7HSJTAO3","short_pith_number":"pith:Y7CKIFC5","schema_version":"1.0","canonical_sha256":"c7c4a4145d8740e738098cfe79266076f54f5e2de4d3a6ac8459d567c9196de6","source":{"kind":"arxiv","id":"2211.08917","version":3},"attestation_state":"computed","paper":{"title":"A simple formula for the $x$-$y$ symplectic transformation in topological recursion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP","math.OA","math.PR"],"primary_cat":"math-ph","authors_text":"Alexander Hock","submitted_at":"2022-11-16T13:55:46Z","abstract_excerpt":"Let $W_{g,n}$ be the correlators computed by Topological Recursion for some given spectral curve $(x,y)$ and $W^\\vee_{g,n}$ for $(y,x)$, where the role of $x,y$ is inverted. These two sets of correlators $W_{g,n}$ and $W^\\vee_{g,n}$ are related by the $x$-$y$ symplectic transformation. Bychkov, Dunin-Barkowski, Kazarian and Shadrin computed a functional relation between two slightly different sets of correlators. Together with Alexandrov, they proved that their functional relation is indeed the $x$-$y$ symplectic transformation in Topological Recursion. This article provides a fairly simple fo"},"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":"2211.08917","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T13:55:46Z","cross_cats_sorted":["hep-th","math.CO","math.MP","math.OA","math.PR"],"title_canon_sha256":"e104ab3e8b510c608da40debe5ebddf2760deea4871c4b53165b33c90adcd07e","abstract_canon_sha256":"d4d5aed513d0ce135100022643b810067e922c393a94ed8acbb56fe3a00d88bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:09:44.527572Z","signature_b64":"1BRl5RFZ5scZa4XvBufipFFilaOE35xQweTkLxhjlnwblPHL8QlXT974OW+gyTxkuy7Xrhq+yLeeGjAzzh8ODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7c4a4145d8740e738098cfe79266076f54f5e2de4d3a6ac8459d567c9196de6","last_reissued_at":"2026-07-05T07:09:44.526918Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:09:44.526918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simple formula for the $x$-$y$ symplectic transformation in topological recursion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP","math.OA","math.PR"],"primary_cat":"math-ph","authors_text":"Alexander Hock","submitted_at":"2022-11-16T13:55:46Z","abstract_excerpt":"Let $W_{g,n}$ be the correlators computed by Topological Recursion for some given spectral curve $(x,y)$ and $W^\\vee_{g,n}$ for $(y,x)$, where the role of $x,y$ is inverted. These two sets of correlators $W_{g,n}$ and $W^\\vee_{g,n}$ are related by the $x$-$y$ symplectic transformation. Bychkov, Dunin-Barkowski, Kazarian and Shadrin computed a functional relation between two slightly different sets of correlators. Together with Alexandrov, they proved that their functional relation is indeed the $x$-$y$ symplectic transformation in Topological Recursion. This article provides a fairly simple fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08917","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/2211.08917/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":"2211.08917","created_at":"2026-07-05T07:09:44.527001+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.08917v3","created_at":"2026-07-05T07:09:44.527001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08917","created_at":"2026-07-05T07:09:44.527001+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y7CKIFC5Q5AO","created_at":"2026-07-05T07:09:44.527001+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y7CKIFC5Q5AOOOAJ","created_at":"2026-07-05T07:09:44.527001+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y7CKIFC5","created_at":"2026-07-05T07:09:44.527001+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"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":53,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3","json":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3.json","graph_json":"https://pith.science/api/pith-number/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/graph.json","events_json":"https://pith.science/api/pith-number/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/events.json","paper":"https://pith.science/paper/Y7CKIFC5"},"agent_actions":{"view_html":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3","download_json":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3.json","view_paper":"https://pith.science/paper/Y7CKIFC5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.08917&json=true","fetch_graph":"https://pith.science/api/pith-number/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/graph.json","fetch_events":"https://pith.science/api/pith-number/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/action/storage_attestation","attest_author":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/action/author_attestation","sign_citation":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/action/citation_signature","submit_replication":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/action/replication_record"}},"created_at":"2026-07-05T07:09:44.527001+00:00","updated_at":"2026-07-05T07:09:44.527001+00:00"}