{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7ROUG6UOMRPAJ4ODTFZ73X7OSQ","short_pith_number":"pith:7ROUG6UO","canonical_record":{"source":{"id":"1806.09738","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-26T00:23:56Z","cross_cats_sorted":["hep-th","math.AG","math.CO","math.MP","nlin.SI"],"title_canon_sha256":"118954934600ee214b2363f1947add1a9c2f86f40f94bfba839da411c277881f","abstract_canon_sha256":"3760534eb785801887969f0fcc49e552daa7bbae0cf1bc163694b9f7661ac287"},"schema_version":"1.0"},"canonical_sha256":"fc5d437a8e645e04f1c39973fddfee94256a93a561c26c03459c24c8a40c385f","source":{"kind":"arxiv","id":"1806.09738","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09738","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09738v7","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09738","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"7ROUG6UOMRPA","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"7ROUG6UOMRPAJ4OD","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"7ROUG6UO","created_at":"2026-07-05T02:19:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7ROUG6UOMRPAJ4ODTFZ73X7OSQ","target":"record","payload":{"canonical_record":{"source":{"id":"1806.09738","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-26T00:23:56Z","cross_cats_sorted":["hep-th","math.AG","math.CO","math.MP","nlin.SI"],"title_canon_sha256":"118954934600ee214b2363f1947add1a9c2f86f40f94bfba839da411c277881f","abstract_canon_sha256":"3760534eb785801887969f0fcc49e552daa7bbae0cf1bc163694b9f7661ac287"},"schema_version":"1.0"},"canonical_sha256":"fc5d437a8e645e04f1c39973fddfee94256a93a561c26c03459c24c8a40c385f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:19:52.700206Z","signature_b64":"61HjyRm3HP2K5GOGUEkfb/CyLZ00gSg/grMpPQS2iwRrd8S81RV8SORDcuODzS/7AQieyMPVkZ49rp/I7kSsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5d437a8e645e04f1c39973fddfee94256a93a561c26c03459c24c8a40c385f","last_reissued_at":"2026-07-05T02:19:52.699745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:19:52.699745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.09738","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aSXwDHO0dCpRL+IHjijBart3tJVwc9vCCnONiqgVYja180hOhCxM+MJtXtNk0XK4COpo3xiCGim67RpWYd5pBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:22:30.947113Z"},"content_sha256":"3d27f4422c7252d42ffa0313a9ee46f2d6bf96ac39acf9373abf993af68082e7","schema_version":"1.0","event_id":"sha256:3d27f4422c7252d42ffa0313a9ee46f2d6bf96ac39acf9373abf993af68082e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7ROUG6UOMRPAJ4ODTFZ73X7OSQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Hurwitz numbers and topological recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.CO","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"A. Alexandrov, B. Eynard, G. Chapuy, J. Harnad","submitted_at":"2018-06-26T00:23:56Z","abstract_excerpt":"The KP and 2D Toda tau-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme. A graphical representation of such weighted Hurwitz numbers is given in terms of weighted constellations. The associated classical and quantum spectral spectral curves are derived, and these are interpreted combinatorially in terms of the graphical model. The pair correlators are given a finite Christoffel-Darboux representation and determinantal expressions are obtained for the multipair correlators. The g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09738","kind":"arxiv","version":7},"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/1806.09738/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":"2026-07-05T02:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/hmS/nL7XARS+DgNjZCDt0n1ZqqRLfmkMOpQc8DuDVBzB1Di1PNzEmquDUW9KmBqijpiJe73IGL33OWS0x0dBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:22:30.948082Z"},"content_sha256":"4e42c17135b00d0304da145ae5619508b6926c9e4cf9a1046e1aca66e2271ada","schema_version":"1.0","event_id":"sha256:4e42c17135b00d0304da145ae5619508b6926c9e4cf9a1046e1aca66e2271ada"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ/bundle.json","state_url":"https://pith.science/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ/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":"2026-08-16T14:22:30Z","links":{"resolver":"https://pith.science/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ","bundle":"https://pith.science/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ/bundle.json","state":"https://pith.science/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ROUG6UOMRPAJ4ODTFZ73X7OSQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7ROUG6UOMRPAJ4ODTFZ73X7OSQ","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":"3760534eb785801887969f0fcc49e552daa7bbae0cf1bc163694b9f7661ac287","cross_cats_sorted":["hep-th","math.AG","math.CO","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-26T00:23:56Z","title_canon_sha256":"118954934600ee214b2363f1947add1a9c2f86f40f94bfba839da411c277881f"},"schema_version":"1.0","source":{"id":"1806.09738","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09738","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09738v7","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09738","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"7ROUG6UOMRPA","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"7ROUG6UOMRPAJ4OD","created_at":"2026-07-05T02:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"7ROUG6UO","created_at":"2026-07-05T02:19:52Z"}],"graph_snapshots":[{"event_id":"sha256:4e42c17135b00d0304da145ae5619508b6926c9e4cf9a1046e1aca66e2271ada","target":"graph","created_at":"2026-07-05T02:19:52Z","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/1806.09738/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The KP and 2D Toda tau-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme. A graphical representation of such weighted Hurwitz numbers is given in terms of weighted constellations. The associated classical and quantum spectral spectral curves are derived, and these are interpreted combinatorially in terms of the graphical model. The pair correlators are given a finite Christoffel-Darboux representation and determinantal expressions are obtained for the multipair correlators. The g","authors_text":"A. Alexandrov, B. Eynard, G. Chapuy, J. Harnad","cross_cats":["hep-th","math.AG","math.CO","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-26T00:23:56Z","title":"Weighted Hurwitz numbers and topological recursion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09738","kind":"arxiv","version":7},"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":"sha256:3d27f4422c7252d42ffa0313a9ee46f2d6bf96ac39acf9373abf993af68082e7","target":"record","created_at":"2026-07-05T02:19:52Z","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":"3760534eb785801887969f0fcc49e552daa7bbae0cf1bc163694b9f7661ac287","cross_cats_sorted":["hep-th","math.AG","math.CO","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-26T00:23:56Z","title_canon_sha256":"118954934600ee214b2363f1947add1a9c2f86f40f94bfba839da411c277881f"},"schema_version":"1.0","source":{"id":"1806.09738","kind":"arxiv","version":7}},"canonical_sha256":"fc5d437a8e645e04f1c39973fddfee94256a93a561c26c03459c24c8a40c385f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc5d437a8e645e04f1c39973fddfee94256a93a561c26c03459c24c8a40c385f","first_computed_at":"2026-07-05T02:19:52.699745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:52.699745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61HjyRm3HP2K5GOGUEkfb/CyLZ00gSg/grMpPQS2iwRrd8S81RV8SORDcuODzS/7AQieyMPVkZ49rp/I7kSsDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:52.700206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09738","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d27f4422c7252d42ffa0313a9ee46f2d6bf96ac39acf9373abf993af68082e7","sha256:4e42c17135b00d0304da145ae5619508b6926c9e4cf9a1046e1aca66e2271ada"],"state_sha256":"2a709ac23f6da8494faf83f85532585de51472ec2b8721ccbedf061b116d3a8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"69a7vH028Rl1/KLtyUhul1sYJgkXsC5Rq9tAkQ9Q7wAIE0xmi47O9+kj25+erILFyEl4e5XfYGEoHvzs0ATTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:22:30.953399Z","bundle_sha256":"8d4e3354ca159a28fe8648da4eddf5a5bbec8ab4bdb3cdb1ab61f48b7159d534"}}