{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:7KAFAFLA6YLSZ3X4HBHSGPDWKN","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":"dc7fa5af47732f292652f2b286ff077ef173c82cf2174902ad8360a63646360c","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.QA","submitted_at":"2005-07-05T20:08:35Z","title_canon_sha256":"65fab4c9820e39828ec07f63025d3aae52c07695689e6212b74e427017775c5d"},"schema_version":"1.0","source":{"id":"math/0507106","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0507106","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0507106v2","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507106","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"7KAFAFLA6YLS","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7KAFAFLA6YLSZ3X4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7KAFAFLA","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:50580e552948d79952edb33ed37656afa47c097661b681a261dfe45fa722e1d6","target":"graph","created_at":"2026-05-18T00:10:32Z","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":"We study the genus expansion of Barannikov-Kontsevich solutions of the WDVV equation. In terms of the related graph calculus we give a definition of descendants at one point and prove that this definition satisfies the topological recursion relations in genera 0, 1, and 2, string and dilaton equations, and the pull-back formula.","authors_text":"Sergei Shadrin","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2005-07-05T20:08:35Z","title":"A definition of descendants at one point in graph calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507106","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":"sha256:31a62f32a2b926990f92d8299ea48f9038d69234ab99350be9e8ae1a0a003e25","target":"record","created_at":"2026-05-18T00:10:32Z","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":"dc7fa5af47732f292652f2b286ff077ef173c82cf2174902ad8360a63646360c","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.QA","submitted_at":"2005-07-05T20:08:35Z","title_canon_sha256":"65fab4c9820e39828ec07f63025d3aae52c07695689e6212b74e427017775c5d"},"schema_version":"1.0","source":{"id":"math/0507106","kind":"arxiv","version":2}},"canonical_sha256":"fa80501560f6172ceefc384f233c76537cfcb7d719f91eaae6276ac364a92970","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa80501560f6172ceefc384f233c76537cfcb7d719f91eaae6276ac364a92970","first_computed_at":"2026-05-18T00:10:32.592771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:32.592771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zTpr/UqhO1WCLrs4S/6ObpmrBNrKHpgqfynPD53IuRfljSbP3gM8TVXhFAogQ2Tc8oK7YLj9FqgTMzttjN+WDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:32.593328Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0507106","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31a62f32a2b926990f92d8299ea48f9038d69234ab99350be9e8ae1a0a003e25","sha256:50580e552948d79952edb33ed37656afa47c097661b681a261dfe45fa722e1d6"],"state_sha256":"8700518e13df6cbb88c2cbbe80fabf6a9940ed28f80550632dd8033374f36277"}