{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QXG3FUDS4VPWQJ66KVTNMW2WWU","short_pith_number":"pith:QXG3FUDS","canonical_record":{"source":{"id":"1905.11270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-27T14:40:28Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"9783af01789534e7cc8451a1c75073a145ebc6c3b6479223db45b392264ec278","abstract_canon_sha256":"52d3660990cb29b6a3ebdd0c68306f26ec6746800f13e86edc33c40c12ca020c"},"schema_version":"1.0"},"canonical_sha256":"85cdb2d072e55f6827de5566d65b56b503806c7993bb2e952e074a978c53dd7e","source":{"kind":"arxiv","id":"1905.11270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11270","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11270v1","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11270","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"QXG3FUDS4VPW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QXG3FUDS4VPWQJ66","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QXG3FUDS","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QXG3FUDS4VPWQJ66KVTNMW2WWU","target":"record","payload":{"canonical_record":{"source":{"id":"1905.11270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-27T14:40:28Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"9783af01789534e7cc8451a1c75073a145ebc6c3b6479223db45b392264ec278","abstract_canon_sha256":"52d3660990cb29b6a3ebdd0c68306f26ec6746800f13e86edc33c40c12ca020c"},"schema_version":"1.0"},"canonical_sha256":"85cdb2d072e55f6827de5566d65b56b503806c7993bb2e952e074a978c53dd7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.790009Z","signature_b64":"cw4b9ZrhWm7d68Amxf+cCmogFMDWhpom8ToW53Sl0O3HUG5A9ldsuFMtAnvjG12k90cPaSYLxGzR04wbxH8NDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85cdb2d072e55f6827de5566d65b56b503806c7993bb2e952e074a978c53dd7e","last_reissued_at":"2026-05-17T23:45:00.789382Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.789382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.11270","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yHv/ZAsgKoj26AmA4ShHd7XSskN6IkFZvpnZjzsnJ4H5AQT4IrOVlgczmgIRgqDYgs26M7we4WKQq3IJEw37DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:42:38.396340Z"},"content_sha256":"fb2f56c74cad7f968dfdd9bdfb99237f34ed340168107660f0dd5e7144479768","schema_version":"1.0","event_id":"sha256:fb2f56c74cad7f968dfdd9bdfb99237f34ed340168107660f0dd5e7144479768"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QXG3FUDS4VPWQJ66KVTNMW2WWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large genus behavior of topological recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Bertrand Eynard","submitted_at":"2019-05-27T14:40:28Z","abstract_excerpt":"We show that for a rather generic set of regular spectral curves, the Topological-Recursion invariants F_g grow at most like $O((\\beta g)! r^{-g}) $ with some $r>0$ and $\\beta\\leq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11270","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DegsmW55Rj/FOhFNbe1cvM7LiMuk58sn5M4Tf/lSI9z8rIrUU2qFp3EktNTDpijXlpeKRe0xJO+HUc7Uu5pLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:42:38.396682Z"},"content_sha256":"9e748adbdad3ddf12522aa1d5e934617fea4b21fc3cb01fa84f7a5b57f280b81","schema_version":"1.0","event_id":"sha256:9e748adbdad3ddf12522aa1d5e934617fea4b21fc3cb01fa84f7a5b57f280b81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU/bundle.json","state_url":"https://pith.science/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU/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":"2026-05-28T09:42:38Z","links":{"resolver":"https://pith.science/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU","bundle":"https://pith.science/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU/bundle.json","state":"https://pith.science/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXG3FUDS4VPWQJ66KVTNMW2WWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QXG3FUDS4VPWQJ66KVTNMW2WWU","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":"52d3660990cb29b6a3ebdd0c68306f26ec6746800f13e86edc33c40c12ca020c","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-27T14:40:28Z","title_canon_sha256":"9783af01789534e7cc8451a1c75073a145ebc6c3b6479223db45b392264ec278"},"schema_version":"1.0","source":{"id":"1905.11270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11270","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11270v1","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11270","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"QXG3FUDS4VPW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QXG3FUDS4VPWQJ66","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QXG3FUDS","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:9e748adbdad3ddf12522aa1d5e934617fea4b21fc3cb01fa84f7a5b57f280b81","target":"graph","created_at":"2026-05-17T23:45:00Z","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"},"paper":{"abstract_excerpt":"We show that for a rather generic set of regular spectral curves, the Topological-Recursion invariants F_g grow at most like $O((\\beta g)! r^{-g}) $ with some $r>0$ and $\\beta\\leq 5$.","authors_text":"Bertrand Eynard","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-27T14:40:28Z","title":"Large genus behavior of topological recursion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11270","kind":"arxiv","version":1},"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:fb2f56c74cad7f968dfdd9bdfb99237f34ed340168107660f0dd5e7144479768","target":"record","created_at":"2026-05-17T23:45:00Z","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":"52d3660990cb29b6a3ebdd0c68306f26ec6746800f13e86edc33c40c12ca020c","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-27T14:40:28Z","title_canon_sha256":"9783af01789534e7cc8451a1c75073a145ebc6c3b6479223db45b392264ec278"},"schema_version":"1.0","source":{"id":"1905.11270","kind":"arxiv","version":1}},"canonical_sha256":"85cdb2d072e55f6827de5566d65b56b503806c7993bb2e952e074a978c53dd7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85cdb2d072e55f6827de5566d65b56b503806c7993bb2e952e074a978c53dd7e","first_computed_at":"2026-05-17T23:45:00.789382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:00.789382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cw4b9ZrhWm7d68Amxf+cCmogFMDWhpom8ToW53Sl0O3HUG5A9ldsuFMtAnvjG12k90cPaSYLxGzR04wbxH8NDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:00.790009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb2f56c74cad7f968dfdd9bdfb99237f34ed340168107660f0dd5e7144479768","sha256:9e748adbdad3ddf12522aa1d5e934617fea4b21fc3cb01fa84f7a5b57f280b81"],"state_sha256":"7ae6576295f0f764ee789e6f4a1ed8fe57bc33ccc221b0cf39afb384c212f3d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uRydnCsWtQf2EwH0zhSoZ4vbby+Vpn9UeKRDMRD/3AeJvYUtRhocsflokUJCXW1B55Nqm+GdCOMsieczFG/8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:42:38.398594Z","bundle_sha256":"1ffe65ea9f7d70abe51e49b37dfb9a867df0b90a55b27137b63b775d3dfba23c"}}