{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QKPZLQ2GBQHAK7IX43LLMXPVAV","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":"ae188d2784455dc609f2ee943ad09c1498d1c611c5faec409478189bf15d06b1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-29T00:46:08Z","title_canon_sha256":"0549e950c3aa364d450986762f2fcd2320fbac4d1f4a2c71c9895ba0d6216ad6"},"schema_version":"1.0","source":{"id":"1009.5725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5725","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5725v2","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5725","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"QKPZLQ2GBQHA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QKPZLQ2GBQHAK7IX","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QKPZLQ2G","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:f957bc8aa669a624142bd0b51f2b1a3ca3ae34876d0c7b25659f6a697f273741","target":"graph","created_at":"2026-05-18T01:18:10Z","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":"In this article we study the period map for a family of $K3$ surfaces which is given by the anticanonial divisor of a toric variety. We determine the period differential equation and its monodromy group. Moreover we show the exact relation between our period differential equation and the unifomizing differential equation of the Hilbert modular orbifold for the field $\\mathbb{Q}(\\sqrt{5})$.","authors_text":"Atsuhira Nagano","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-29T00:46:08Z","title":"A period differential equation for a family of $K3$ surfaces and the Hilbert modular orbifold for the field $\\mathbb{Q}(\\sqrt{5})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5725","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:b09bcfe6ce7e17a70673dc3dd5952a9a6b70dbcda8937b33277354d827aa9915","target":"record","created_at":"2026-05-18T01:18:10Z","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":"ae188d2784455dc609f2ee943ad09c1498d1c611c5faec409478189bf15d06b1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-29T00:46:08Z","title_canon_sha256":"0549e950c3aa364d450986762f2fcd2320fbac4d1f4a2c71c9895ba0d6216ad6"},"schema_version":"1.0","source":{"id":"1009.5725","kind":"arxiv","version":2}},"canonical_sha256":"829f95c3460c0e057d17e6d6b65df505495540478256876c46039125637a6a8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"829f95c3460c0e057d17e6d6b65df505495540478256876c46039125637a6a8f","first_computed_at":"2026-05-18T01:18:10.521062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:10.521062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"urD1vc88rXGxQRU4z3/EKZNAlOP+qvs/iP0RCH3K+A9RoQJ1fl3N4Ixt7akJnOZtgh1K79kUTlKNDUGcPaPbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:10.521568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b09bcfe6ce7e17a70673dc3dd5952a9a6b70dbcda8937b33277354d827aa9915","sha256:f957bc8aa669a624142bd0b51f2b1a3ca3ae34876d0c7b25659f6a697f273741"],"state_sha256":"cbad5e749a3cc7a9091ef93b3798ac1d14be5a4530843953bc798ac80a741723"}