{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YANHDYNPF6CCQDF6R5NQ6C4QTI","short_pith_number":"pith:YANHDYNP","canonical_record":{"source":{"id":"0908.2267","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-17T00:05:43Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"6e91f98410ad7f837b60cd94d633dfec28ba7c3af59571dabd3e93395a820a5d","abstract_canon_sha256":"bac5a9ffb90065cb52011c3857b8c217043dbb98269be406c33afe845baa5548"},"schema_version":"1.0"},"canonical_sha256":"c01a71e1af2f84280cbe8f5b0f0b909a15cfd63a945fc9eaed704e1275dcdfb8","source":{"kind":"arxiv","id":"0908.2267","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2267","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2267v4","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2267","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"YANHDYNPF6CC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YANHDYNPF6CCQDF6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YANHDYNP","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YANHDYNPF6CCQDF6R5NQ6C4QTI","target":"record","payload":{"canonical_record":{"source":{"id":"0908.2267","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-17T00:05:43Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"6e91f98410ad7f837b60cd94d633dfec28ba7c3af59571dabd3e93395a820a5d","abstract_canon_sha256":"bac5a9ffb90065cb52011c3857b8c217043dbb98269be406c33afe845baa5548"},"schema_version":"1.0"},"canonical_sha256":"c01a71e1af2f84280cbe8f5b0f0b909a15cfd63a945fc9eaed704e1275dcdfb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:59.553336Z","signature_b64":"tIGbM1BRmf++eqGb1rapJU7iXHeVps81u0Ehbnw8yrX0oLEP/OnfvZJyBSKhb1UE1f9vOlSTGpV05nxLMOSSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c01a71e1af2f84280cbe8f5b0f0b909a15cfd63a945fc9eaed704e1275dcdfb8","last_reissued_at":"2026-05-18T04:39:59.552698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:59.552698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.2267","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90JBIG2Imga6HlNQrEmYuxWj4Rnid3k5dmyz8nNbvly2Sc9LiGGCNl3N2LMW3Quic41USftudMbRvre3mKBqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:21:31.899572Z"},"content_sha256":"20e9888284a4c50eb7c011da45927c408fdc763ffc78ec76807fa7d3d739fbd5","schema_version":"1.0","event_id":"sha256:20e9888284a4c50eb7c011da45927c408fdc763ffc78ec76807fa7d3d739fbd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YANHDYNPF6CCQDF6R5NQ6C4QTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial recursion formula for linear Hodge integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.AG","authors_text":"Motohico Mulase, Naizhen Zhang","submitted_at":"2009-08-17T00:05:43Z","abstract_excerpt":"We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion recovers the Witten-Kontsevich theorem when restricted to the top degree terms, and also the combinatorial factor of the lambda_g formula as the lowest degree terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2267","kind":"arxiv","version":4},"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":"2026-05-18T04:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlSy/YhG313tThhIQM5zB/JBptZHCqGR+wl31R3mC52s0k65QvyS/kNfLUxMpbNpSm2QHYLTZHU8bc36PolVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:21:31.900266Z"},"content_sha256":"51e663e625a01ca4c8c5835ad477f49618be62fef99d5c44a858128f976cba02","schema_version":"1.0","event_id":"sha256:51e663e625a01ca4c8c5835ad477f49618be62fef99d5c44a858128f976cba02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI/bundle.json","state_url":"https://pith.science/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI/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":"2026-05-31T18:21:31Z","links":{"resolver":"https://pith.science/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI","bundle":"https://pith.science/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI/bundle.json","state":"https://pith.science/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YANHDYNPF6CCQDF6R5NQ6C4QTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YANHDYNPF6CCQDF6R5NQ6C4QTI","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":"bac5a9ffb90065cb52011c3857b8c217043dbb98269be406c33afe845baa5548","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-17T00:05:43Z","title_canon_sha256":"6e91f98410ad7f837b60cd94d633dfec28ba7c3af59571dabd3e93395a820a5d"},"schema_version":"1.0","source":{"id":"0908.2267","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2267","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2267v4","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2267","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"YANHDYNPF6CC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YANHDYNPF6CCQDF6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YANHDYNP","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:51e663e625a01ca4c8c5835ad477f49618be62fef99d5c44a858128f976cba02","target":"graph","created_at":"2026-05-18T04:39:59Z","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 establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion recovers the Witten-Kontsevich theorem when restricted to the top degree terms, and also the combinatorial factor of the lambda_g formula as the lowest degree terms.","authors_text":"Motohico Mulase, Naizhen Zhang","cross_cats":["math.CO","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-17T00:05:43Z","title":"Polynomial recursion formula for linear Hodge integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2267","kind":"arxiv","version":4},"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":"sha256:20e9888284a4c50eb7c011da45927c408fdc763ffc78ec76807fa7d3d739fbd5","target":"record","created_at":"2026-05-18T04:39:59Z","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":"bac5a9ffb90065cb52011c3857b8c217043dbb98269be406c33afe845baa5548","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-17T00:05:43Z","title_canon_sha256":"6e91f98410ad7f837b60cd94d633dfec28ba7c3af59571dabd3e93395a820a5d"},"schema_version":"1.0","source":{"id":"0908.2267","kind":"arxiv","version":4}},"canonical_sha256":"c01a71e1af2f84280cbe8f5b0f0b909a15cfd63a945fc9eaed704e1275dcdfb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c01a71e1af2f84280cbe8f5b0f0b909a15cfd63a945fc9eaed704e1275dcdfb8","first_computed_at":"2026-05-18T04:39:59.552698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.552698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tIGbM1BRmf++eqGb1rapJU7iXHeVps81u0Ehbnw8yrX0oLEP/OnfvZJyBSKhb1UE1f9vOlSTGpV05nxLMOSSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.553336Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.2267","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20e9888284a4c50eb7c011da45927c408fdc763ffc78ec76807fa7d3d739fbd5","sha256:51e663e625a01ca4c8c5835ad477f49618be62fef99d5c44a858128f976cba02"],"state_sha256":"e866fcfb82f450f9dafbb586d8b9c5a5bd781e0286004664befa0839bcb7f058"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CdAvEa49yIuCF/NWx0CV2f5UzVQA0HenpxP2yU3JXURoUitNi9YdO14BWCa4VnfUH9BFCnrNUhYXFmdoPkbvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:21:31.904539Z","bundle_sha256":"9e241ddc16a548648e841944d55e6a6f3c54811572bd4d15a4c3f985c809f3fd"}}