{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:2PIX5NXSGJ5ZUDGRX3X6KY6HA2","short_pith_number":"pith:2PIX5NXS","canonical_record":{"source":{"id":"0709.1458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-10T18:52:34Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"038e13b2a2e032e6d27c836507ff6156c42ee04b3f3ad8d09fdbe771c96706d4","abstract_canon_sha256":"7bd8e63a516e26a23603b5b86d0a48df6f63a471b3a478db204fe90558b918dd"},"schema_version":"1.0"},"canonical_sha256":"d3d17eb6f2327b9a0cd1beefe563c7069b742022d138c1d5fe7b57768219d11c","source":{"kind":"arxiv","id":"0709.1458","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1458","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1458v2","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1458","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"pith_short_12","alias_value":"2PIX5NXSGJ5Z","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"pith_short_16","alias_value":"2PIX5NXSGJ5ZUDGR","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"pith_short_8","alias_value":"2PIX5NXS","created_at":"2026-07-04T15:33:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:2PIX5NXSGJ5ZUDGRX3X6KY6HA2","target":"record","payload":{"canonical_record":{"source":{"id":"0709.1458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-10T18:52:34Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"038e13b2a2e032e6d27c836507ff6156c42ee04b3f3ad8d09fdbe771c96706d4","abstract_canon_sha256":"7bd8e63a516e26a23603b5b86d0a48df6f63a471b3a478db204fe90558b918dd"},"schema_version":"1.0"},"canonical_sha256":"d3d17eb6f2327b9a0cd1beefe563c7069b742022d138c1d5fe7b57768219d11c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:33:20.017901Z","signature_b64":"Qq3iFDyZju6Xi8V5DnlqDk9PXpQaouGwllH59uH321pts+7Ym2aVoqMMpOER/KpDDzPauyd4IjI6PMsJ4grxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3d17eb6f2327b9a0cd1beefe563c7069b742022d138c1d5fe7b57768219d11c","last_reissued_at":"2026-07-04T15:33:20.017504Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:33:20.017504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.1458","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:33:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ByIGCMhI4Bb9GHHqK73hp7JusRC9KGWiw2JCC5OEwFJTg5SQchmTx976YDEzBJ2/CtmouY6Aqnu87tIL/71ACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:48:05.227624Z"},"content_sha256":"8fd33929ab31817e33a6ba0b8d4176cc353100803e624ca7196b57c7f29d1fa3","schema_version":"1.0","event_id":"sha256:8fd33929ab31817e33a6ba0b8d4176cc353100803e624ca7196b57c7f29d1fa3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:2PIX5NXSGJ5ZUDGRX3X6KY6HA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hurwitz numbers, matrix models and enumerative geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Marcos Marino, Vincent Bouchard","submitted_at":"2007-09-10T18:52:34Z","abstract_excerpt":"We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topological vertex, leads to a recursion relation for Hodge integrals with three Hodge class insertions. Our conjecture in Hurwitz theory follows from this recursion for the framed vertex in the limit of infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1458","kind":"arxiv","version":2},"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/0709.1458/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":"2026-07-04T15:33:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GGRy3BtupciUTR6JVtR4PtxRZEgsdwHsOL1c18K5Iek/7k0hP9/ctq16F2PrHrJTW8my9Ei3y4pryHGSqusCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:48:05.227970Z"},"content_sha256":"f9333cb75a9b2fc899a520912d7a2fdf5f65cbc599ae1aaca4ad31fffc9af3a1","schema_version":"1.0","event_id":"sha256:f9333cb75a9b2fc899a520912d7a2fdf5f65cbc599ae1aaca4ad31fffc9af3a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2/bundle.json","state_url":"https://pith.science/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2/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":"2026-08-18T18:48:05Z","links":{"resolver":"https://pith.science/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2","bundle":"https://pith.science/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2/bundle.json","state":"https://pith.science/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2PIX5NXSGJ5ZUDGRX3X6KY6HA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:2PIX5NXSGJ5ZUDGRX3X6KY6HA2","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":"7bd8e63a516e26a23603b5b86d0a48df6f63a471b3a478db204fe90558b918dd","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-10T18:52:34Z","title_canon_sha256":"038e13b2a2e032e6d27c836507ff6156c42ee04b3f3ad8d09fdbe771c96706d4"},"schema_version":"1.0","source":{"id":"0709.1458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1458","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1458v2","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1458","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"pith_short_12","alias_value":"2PIX5NXSGJ5Z","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"pith_short_16","alias_value":"2PIX5NXSGJ5ZUDGR","created_at":"2026-07-04T15:33:20Z"},{"alias_kind":"pith_short_8","alias_value":"2PIX5NXS","created_at":"2026-07-04T15:33:20Z"}],"graph_snapshots":[{"event_id":"sha256:f9333cb75a9b2fc899a520912d7a2fdf5f65cbc599ae1aaca4ad31fffc9af3a1","target":"graph","created_at":"2026-07-04T15:33:20Z","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/0709.1458/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topological vertex, leads to a recursion relation for Hodge integrals with three Hodge class insertions. Our conjecture in Hurwitz theory follows from this recursion for the framed vertex in the limit of infi","authors_text":"Marcos Marino, Vincent Bouchard","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-10T18:52:34Z","title":"Hurwitz numbers, matrix models and enumerative geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1458","kind":"arxiv","version":2},"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":"sha256:8fd33929ab31817e33a6ba0b8d4176cc353100803e624ca7196b57c7f29d1fa3","target":"record","created_at":"2026-07-04T15:33:20Z","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":"7bd8e63a516e26a23603b5b86d0a48df6f63a471b3a478db204fe90558b918dd","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-10T18:52:34Z","title_canon_sha256":"038e13b2a2e032e6d27c836507ff6156c42ee04b3f3ad8d09fdbe771c96706d4"},"schema_version":"1.0","source":{"id":"0709.1458","kind":"arxiv","version":2}},"canonical_sha256":"d3d17eb6f2327b9a0cd1beefe563c7069b742022d138c1d5fe7b57768219d11c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3d17eb6f2327b9a0cd1beefe563c7069b742022d138c1d5fe7b57768219d11c","first_computed_at":"2026-07-04T15:33:20.017504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:33:20.017504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qq3iFDyZju6Xi8V5DnlqDk9PXpQaouGwllH59uH321pts+7Ym2aVoqMMpOER/KpDDzPauyd4IjI6PMsJ4grxCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:33:20.017901Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.1458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fd33929ab31817e33a6ba0b8d4176cc353100803e624ca7196b57c7f29d1fa3","sha256:f9333cb75a9b2fc899a520912d7a2fdf5f65cbc599ae1aaca4ad31fffc9af3a1"],"state_sha256":"9b0631d0cf2feff16f341c21cfe0e909da46806dc8298f5594f5c914c94797b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dBK/c4W2IT11p9xkU9W8in447yQXvOx70tJLUQLjGt2Ck4nDQISGyFZxr/XQ4vBcuWxtR2vaZPr1VIJW0Bd7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:48:05.231162Z","bundle_sha256":"256bba0d3b51dbf30bbd86c5ec5d39de13a2740a837bfacc45d1c728a6f6cb1b"}}