{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:Y7CKIFC5Q5AOOOAJRT7HSJTAO3","short_pith_number":"pith:Y7CKIFC5","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"},"canonical_sha256":"c7c4a4145d8740e738098cfe79266076f54f5e2de4d3a6ac8459d567c9196de6","source":{"kind":"arxiv","id":"2211.08917","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.08917","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"2211.08917v3","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08917","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"Y7CKIFC5Q5AO","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"Y7CKIFC5Q5AOOOAJ","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"Y7CKIFC5","created_at":"2026-07-05T07:09:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:Y7CKIFC5Q5AOOOAJRT7HSJTAO3","target":"record","payload":{"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"},"canonical_sha256":"c7c4a4145d8740e738098cfe79266076f54f5e2de4d3a6ac8459d567c9196de6","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"},"source_kind":"arxiv","source_id":"2211.08917","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wqoJtLZzetx4B7qggBFxJQjrwV0NnK4aVg0Mk+NK2oGrj4410A/H179Sw7lLZvRDiwcQ3o36bAaNvQDgBRfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:24:17.519815Z"},"content_sha256":"9df0fabcede10d2c1a3447072ad73b8833d69a60e0efef5b35718bb2977b7732","schema_version":"1.0","event_id":"sha256:9df0fabcede10d2c1a3447072ad73b8833d69a60e0efef5b35718bb2977b7732"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:Y7CKIFC5Q5AOOOAJRT7HSJTAO3","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4qYWiqBVDBuxnJM/w7DXdTApio8ihCMxEf1Lh0H3atXtKzM6Vcb4x8ppTZefvR55BjUdLIIBLYv+AD59YUmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:24:17.520320Z"},"content_sha256":"fda54dd2df2456345cd850a3ab23f997e1394ed9079fce37cfe1ad0707aa3741","schema_version":"1.0","event_id":"sha256:fda54dd2df2456345cd850a3ab23f997e1394ed9079fce37cfe1ad0707aa3741"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/bundle.json","state_url":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T11:24:17Z","links":{"resolver":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3","bundle":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/bundle.json","state":"https://pith.science/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y7CKIFC5Q5AOOOAJRT7HSJTAO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Y7CKIFC5Q5AOOOAJRT7HSJTAO3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d4d5aed513d0ce135100022643b810067e922c393a94ed8acbb56fe3a00d88bb","cross_cats_sorted":["hep-th","math.CO","math.MP","math.OA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T13:55:46Z","title_canon_sha256":"e104ab3e8b510c608da40debe5ebddf2760deea4871c4b53165b33c90adcd07e"},"schema_version":"1.0","source":{"id":"2211.08917","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.08917","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"2211.08917v3","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08917","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"Y7CKIFC5Q5AO","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"Y7CKIFC5Q5AOOOAJ","created_at":"2026-07-05T07:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"Y7CKIFC5","created_at":"2026-07-05T07:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:fda54dd2df2456345cd850a3ab23f997e1394ed9079fce37cfe1ad0707aa3741","target":"graph","created_at":"2026-07-05T07:09:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.08917/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Alexander Hock","cross_cats":["hep-th","math.CO","math.MP","math.OA","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T13:55:46Z","title":"A simple formula for the $x$-$y$ symplectic transformation in topological recursion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08917","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9df0fabcede10d2c1a3447072ad73b8833d69a60e0efef5b35718bb2977b7732","target":"record","created_at":"2026-07-05T07:09:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d4d5aed513d0ce135100022643b810067e922c393a94ed8acbb56fe3a00d88bb","cross_cats_sorted":["hep-th","math.CO","math.MP","math.OA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T13:55:46Z","title_canon_sha256":"e104ab3e8b510c608da40debe5ebddf2760deea4871c4b53165b33c90adcd07e"},"schema_version":"1.0","source":{"id":"2211.08917","kind":"arxiv","version":3}},"canonical_sha256":"c7c4a4145d8740e738098cfe79266076f54f5e2de4d3a6ac8459d567c9196de6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7c4a4145d8740e738098cfe79266076f54f5e2de4d3a6ac8459d567c9196de6","first_computed_at":"2026-07-05T07:09:44.526918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:09:44.526918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1BRl5RFZ5scZa4XvBufipFFilaOE35xQweTkLxhjlnwblPHL8QlXT974OW+gyTxkuy7Xrhq+yLeeGjAzzh8ODQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:09:44.527572Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.08917","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df0fabcede10d2c1a3447072ad73b8833d69a60e0efef5b35718bb2977b7732","sha256:fda54dd2df2456345cd850a3ab23f997e1394ed9079fce37cfe1ad0707aa3741"],"state_sha256":"cdc7e87104bd7a8483e626c9b1622c85cf40c817c04c05a23d423be79d76140f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RxMnQRvtFuitzHupsg5DL6sOXVxS3BwVnLtTy3FFpDLnANBSqRfQi5PQ0i6t2dkW43DcHnV1F8nSzjbt3ZVlDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T11:24:17.523891Z","bundle_sha256":"f37c72fbacb9a47d6b1ceee96c63522c2cd264b848440a04f488919e4a2b9b26"}}