{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W7622GXLEQZPL5YXS3LJD4L2P5","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":"10a8a56d484ee48b632562407e306b69cca7b4c92d9b21671caab870e100efaf","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-16T13:02:02Z","title_canon_sha256":"a0c4e079be568878a80ba53ab8379060c20a33777754a13b5993f1ae674c68a0"},"schema_version":"1.0","source":{"id":"1409.4616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4616","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4616v1","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4616","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"W7622GXLEQZP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W7622GXLEQZPL5YX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W7622GXL","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:27ae9f30a74d711a45fddf061908cd407b851220be3fefbd3a35525635f85fd4","target":"graph","created_at":"2026-05-18T02:42:45Z","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":"For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the intersection numbers of the Gromov--Witten classes and their descendents along with the characteristic classes of Hodge bundles on the moduli spaces of stable maps. For the one-dimensional Frobenius manifold the Hodge hierarchy is a deformation of the Korteweg--de Vries hierarchy depending on an infinite number of parameters. Conjecturally this hierarchy is","authors_text":"Boris Dubrovin, Di Yang, Si-Qi Liu, Youjin Zhang","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-16T13:02:02Z","title":"Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4616","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":"sha256:485f0316e2fe312cfb2a747c65c543f5a00bb03cacf3ca24130d3bb7bc4b0311","target":"record","created_at":"2026-05-18T02:42:45Z","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":"10a8a56d484ee48b632562407e306b69cca7b4c92d9b21671caab870e100efaf","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-16T13:02:02Z","title_canon_sha256":"a0c4e079be568878a80ba53ab8379060c20a33777754a13b5993f1ae674c68a0"},"schema_version":"1.0","source":{"id":"1409.4616","kind":"arxiv","version":1}},"canonical_sha256":"b7fdad1aeb2432f5f71796d691f17a7f458efc5c69d80925148c9ad9e6fef003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7fdad1aeb2432f5f71796d691f17a7f458efc5c69d80925148c9ad9e6fef003","first_computed_at":"2026-05-18T02:42:45.224151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:45.224151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PAbkFrFb+CyiavyXlDgi1Z4qMZjCl4vB0ydf1FJ5drSvfTce4Wf+2HfYHjrSSMrSmLLGDifClb2ARkAUT2KwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:45.224782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:485f0316e2fe312cfb2a747c65c543f5a00bb03cacf3ca24130d3bb7bc4b0311","sha256:27ae9f30a74d711a45fddf061908cd407b851220be3fefbd3a35525635f85fd4"],"state_sha256":"62e8d547322b594d88ce482ac6989bac5faa8c9f62cdc9f9b9d2451ff68b52dd"}