{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MYWXSCHZXXUBLY6R37MZ5QHU7K","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":"73e16e5444f52d3f1cf71b9907b050669fa8fa3ecf37f4ec66c84067126193b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-03T13:05:39Z","title_canon_sha256":"356c2cda2f506e9d04045d3b5de89da0232886188080d8f61e4e08cbfd06b2f4"},"schema_version":"1.0","source":{"id":"1508.00406","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00406","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00406v2","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00406","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"pith_short_12","alias_value":"MYWXSCHZXXUB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MYWXSCHZXXUBLY6R","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MYWXSCHZ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:003dd30e58f1124b7f449d2d07bd6c0f7293703e505194fc51f9213c453020b0","target":"graph","created_at":"2026-05-18T01:35:43Z","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 give a new geometrical interpretation of the local analytic solutions to a differential system, which we call a tautological system $\\tau$, arising from the universal family of Calabi-Yau hypersurfaces $Y_a$ in a $G$-variety $X$ of dimension $n$. First, we construct a natural topological correspondence between relative cycles in $H_n(X-Y_a,\\cup D-Y_a)$ bounded by the union of $G$-invariant divisors $\\cup D$ in $X$ to the solution sheaf of $\\tau$, in the form of chain integrals. Applying this to a toric variety with torus action, we show that in addition to the period integrals over cycles i","authors_text":"An Huang, Bong H. Lian, Shing-Tung Yau, Xinwen Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-03T13:05:39Z","title":"Chain Integral Solutions to Tautological Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00406","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":"sha256:1824171c6c90957a954f561a135a9c1cc480b39fc27c8293e691c9d477a59a8b","target":"record","created_at":"2026-05-18T01:35:43Z","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":"73e16e5444f52d3f1cf71b9907b050669fa8fa3ecf37f4ec66c84067126193b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-03T13:05:39Z","title_canon_sha256":"356c2cda2f506e9d04045d3b5de89da0232886188080d8f61e4e08cbfd06b2f4"},"schema_version":"1.0","source":{"id":"1508.00406","kind":"arxiv","version":2}},"canonical_sha256":"662d7908f9bde815e3d1dfd99ec0f4fa97ad2c7c131c540687c8793cd28f671c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"662d7908f9bde815e3d1dfd99ec0f4fa97ad2c7c131c540687c8793cd28f671c","first_computed_at":"2026-05-18T01:35:43.187993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:43.187993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vwEczb7IfMd6ByhyxW5IPYWHNN0wjaah0wqe69O9BNIqVM3j4YwoZinFI9yoHNPMqZR89Inmk7iYg30Q3jN+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:43.188513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00406","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1824171c6c90957a954f561a135a9c1cc480b39fc27c8293e691c9d477a59a8b","sha256:003dd30e58f1124b7f449d2d07bd6c0f7293703e505194fc51f9213c453020b0"],"state_sha256":"8fb6185d9822e380b393c6b36b383ba32d622faac36f611eeb2414fb829e70c7"}