{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NU44BOLQ6GBDXPM4KVK2ZAZJSY","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":"e2f9ff64572c620b66edcf77a1bfc300914b79ccd04d80efbc06d5246e0271ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2016-12-30T10:00:24Z","title_canon_sha256":"8b8e1c4d07492d91f2a61333c6d2fe8dee6fd003499832427bf05d18db89dbec"},"schema_version":"1.0","source":{"id":"1612.09439","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09439","created_at":"2026-05-18T00:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09439v2","created_at":"2026-05-18T00:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09439","created_at":"2026-05-18T00:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"NU44BOLQ6GBD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NU44BOLQ6GBDXPM4","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NU44BOLQ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:13d15b1f61cbad9c2a5ea751a72aa3d27a546c184d9b8b3d204721965945d626","target":"graph","created_at":"2026-05-18T00:42:12Z","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":"Given a variation of Hodge structure over $\\mathbb{P}^1$ with Hodge numbers $(1,1,\\dots,1)$, we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-M\\\"oller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi-Yau threefolds.","authors_text":"Alan Thompson, Andrew Harder, Charles F. Doran","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2016-12-30T10:00:24Z","title":"Hodge Numbers from Picard-Fuchs Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09439","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":"sha256:18c66979bc7793c29be9bb6bf4e5139a3d475413c41c1386f87534692f6b9e2f","target":"record","created_at":"2026-05-18T00:42:12Z","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":"e2f9ff64572c620b66edcf77a1bfc300914b79ccd04d80efbc06d5246e0271ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2016-12-30T10:00:24Z","title_canon_sha256":"8b8e1c4d07492d91f2a61333c6d2fe8dee6fd003499832427bf05d18db89dbec"},"schema_version":"1.0","source":{"id":"1612.09439","kind":"arxiv","version":2}},"canonical_sha256":"6d39c0b970f1823bbd9c5555ac8329963b730cb3f9db64c948005f45e18558b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d39c0b970f1823bbd9c5555ac8329963b730cb3f9db64c948005f45e18558b4","first_computed_at":"2026-05-18T00:42:12.523690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:12.523690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TgdHiSfUpBML0C2XGIfKbe2NMfWT/L+gFw0eusNGew17yDGux2wQEJOJ21/vP0Ac4uQwVya5UUdovEeAX0gWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:12.524203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09439","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18c66979bc7793c29be9bb6bf4e5139a3d475413c41c1386f87534692f6b9e2f","sha256:13d15b1f61cbad9c2a5ea751a72aa3d27a546c184d9b8b3d204721965945d626"],"state_sha256":"db354760b4062f4c6a9f20d9d988b44092b408e423594cb00191bf5921f30bab"}