{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HWDJ4S6HLRE3IN2OCJ4YKB222U","short_pith_number":"pith:HWDJ4S6H","canonical_record":{"source":{"id":"1802.00711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-02T14:57:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e97fa7094228465dc071e38c311c418614db13fd3ba884966d62529b1943337f","abstract_canon_sha256":"177ef7877e934d8e25e03bce36e7c323cf5757416863ac008d95d874d5a328cd"},"schema_version":"1.0"},"canonical_sha256":"3d869e4bc75c49b4374e127985075ad53dc550cc3ca5f64c27cf7c50a2b86589","source":{"kind":"arxiv","id":"1802.00711","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00711","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00711v1","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00711","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"HWDJ4S6HLRE3","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HWDJ4S6HLRE3IN2O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HWDJ4S6H","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HWDJ4S6HLRE3IN2OCJ4YKB222U","target":"record","payload":{"canonical_record":{"source":{"id":"1802.00711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-02T14:57:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e97fa7094228465dc071e38c311c418614db13fd3ba884966d62529b1943337f","abstract_canon_sha256":"177ef7877e934d8e25e03bce36e7c323cf5757416863ac008d95d874d5a328cd"},"schema_version":"1.0"},"canonical_sha256":"3d869e4bc75c49b4374e127985075ad53dc550cc3ca5f64c27cf7c50a2b86589","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:32.505274Z","signature_b64":"fm6Doyz+xFUs1UzrkjS9vtNmquE545uO6CvlaGrpdrMgA5vNMqlknO+3G3hy8SuiR4yIquoYr12dEna0uUP1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d869e4bc75c49b4374e127985075ad53dc550cc3ca5f64c27cf7c50a2b86589","last_reissued_at":"2026-05-18T00:24:32.504856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:32.504856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.00711","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":"2026-05-18T00:24:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+8YYQEPKaXAg5UrtSTwLOaU9lRHdP+lUyY6RmIkUpzmiKMdvoSuJhpZrpQaby7vJS9GfllUI0s6wLLpHmEZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:01:24.344471Z"},"content_sha256":"46781bb1e9681be3ca41eaca9ba09d919709f8465d7194ac4d2c5831304c6336","schema_version":"1.0","event_id":"sha256:46781bb1e9681be3ca41eaca9ba09d919709f8465d7194ac4d2c5831304c6336"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HWDJ4S6HLRE3IN2OCJ4YKB222U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gromov--Witten invariants of the Riemann sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Boris Dubrovin, Di Yang, Don Zagier","submitted_at":"2018-02-02T14:57:34Z","abstract_excerpt":"A conjectural formula for the $k$-point generating function of Gromov--Witten invariants of the Riemann sphere for all genera and all degrees was proposed in \\cite{DY2}. In this paper, we give a proof of this formula together with an explicit analytic (as opposed to formal) expression for the corresponding matrix resolvent. We also give a formula for the $k$-point function as a sum of $(k-1)!$ products of hypergeometric functions of one variable. We show that the $k$-point generating function coincides with the $\\epsilon\\rightarrow 0$ asymptotics of the analytic $k$-point function, and also co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00711","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":"2026-05-18T00:24:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PDIFSn8liFuaQAisQMI1FY+jbQtgsyz5Iba9nK8CEr4GPwrNoGps5g6YxlBr4ZHZynJpRtxNat9ZZGloAuEuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:01:24.345222Z"},"content_sha256":"ef955b6107519f466fe732daf904970a4b72e75b6535d6278a300399febcbfe0","schema_version":"1.0","event_id":"sha256:ef955b6107519f466fe732daf904970a4b72e75b6535d6278a300399febcbfe0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U/bundle.json","state_url":"https://pith.science/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U/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":"2026-06-09T03:01:24Z","links":{"resolver":"https://pith.science/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U","bundle":"https://pith.science/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U/bundle.json","state":"https://pith.science/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWDJ4S6HLRE3IN2OCJ4YKB222U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HWDJ4S6HLRE3IN2OCJ4YKB222U","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":"177ef7877e934d8e25e03bce36e7c323cf5757416863ac008d95d874d5a328cd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-02T14:57:34Z","title_canon_sha256":"e97fa7094228465dc071e38c311c418614db13fd3ba884966d62529b1943337f"},"schema_version":"1.0","source":{"id":"1802.00711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00711","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00711v1","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00711","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"HWDJ4S6HLRE3","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HWDJ4S6HLRE3IN2O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HWDJ4S6H","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:ef955b6107519f466fe732daf904970a4b72e75b6535d6278a300399febcbfe0","target":"graph","created_at":"2026-05-18T00:24:32Z","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":"A conjectural formula for the $k$-point generating function of Gromov--Witten invariants of the Riemann sphere for all genera and all degrees was proposed in \\cite{DY2}. In this paper, we give a proof of this formula together with an explicit analytic (as opposed to formal) expression for the corresponding matrix resolvent. We also give a formula for the $k$-point function as a sum of $(k-1)!$ products of hypergeometric functions of one variable. We show that the $k$-point generating function coincides with the $\\epsilon\\rightarrow 0$ asymptotics of the analytic $k$-point function, and also co","authors_text":"Boris Dubrovin, Di Yang, Don Zagier","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-02T14:57:34Z","title":"Gromov--Witten invariants of the Riemann sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00711","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":"sha256:46781bb1e9681be3ca41eaca9ba09d919709f8465d7194ac4d2c5831304c6336","target":"record","created_at":"2026-05-18T00:24:32Z","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":"177ef7877e934d8e25e03bce36e7c323cf5757416863ac008d95d874d5a328cd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-02T14:57:34Z","title_canon_sha256":"e97fa7094228465dc071e38c311c418614db13fd3ba884966d62529b1943337f"},"schema_version":"1.0","source":{"id":"1802.00711","kind":"arxiv","version":1}},"canonical_sha256":"3d869e4bc75c49b4374e127985075ad53dc550cc3ca5f64c27cf7c50a2b86589","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d869e4bc75c49b4374e127985075ad53dc550cc3ca5f64c27cf7c50a2b86589","first_computed_at":"2026-05-18T00:24:32.504856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:32.504856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fm6Doyz+xFUs1UzrkjS9vtNmquE545uO6CvlaGrpdrMgA5vNMqlknO+3G3hy8SuiR4yIquoYr12dEna0uUP1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:32.505274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46781bb1e9681be3ca41eaca9ba09d919709f8465d7194ac4d2c5831304c6336","sha256:ef955b6107519f466fe732daf904970a4b72e75b6535d6278a300399febcbfe0"],"state_sha256":"d90a9d66ae8f4352e4db3ea4d2da47be65088272e5a94da49178e95c3b761111"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yo87B2h/z/ljXM2bpf05pKYWIRC7qgcLgmcuOZAMxdctPbPvfJ0kVfo7CowQhCkEQzYHS5TcMJklAqB9ptBKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:01:24.349770Z","bundle_sha256":"ea80e5518c4cb4b07a300903f72b8dfec897112b495e51ac8d277e4733fe4b0a"}}