{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:73ANXPE6AFODX3NOFCEIR63MT3","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":"194a55bfd162cca4e2b2c5d0a8d1bdc8128c9bdd5eb299e29a67575b67f14653","cross_cats_sorted":["hep-th","math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-29T10:22:07Z","title_canon_sha256":"32ef4a3a952645f1ef30c994bcb9b298dc4de19fc16cdbb42e30ff57f8ee1e5a"},"schema_version":"1.0","source":{"id":"1601.08029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08029","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08029v1","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08029","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"73ANXPE6AFOD","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"73ANXPE6AFODX3NO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"73ANXPE6","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:1cec8cc0b73785d77ff8ddfee21b21201cc7ec8806b4e10ec9ea20331afbe599","target":"graph","created_at":"2026-05-18T01:21:41Z","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":"Associated Legendre functions of the first kind give a family of BCOV rings on elliptic curves. We prove that the family is parametrized by $q$-exponents of the eta function $\\eta(q^{24})$. Our method involves a classification of rational solutions of a Riccati equation under some constraints.","authors_text":"So Okada","cross_cats":["hep-th","math.CA","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-29T10:22:07Z","title":"BCOV rings on elliptic curves and eta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08029","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":"sha256:5e05d4feff2e0a83aaac41969cb209a04eb0b1b9d2bff88448501775f9c5beb6","target":"record","created_at":"2026-05-18T01:21:41Z","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":"194a55bfd162cca4e2b2c5d0a8d1bdc8128c9bdd5eb299e29a67575b67f14653","cross_cats_sorted":["hep-th","math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-29T10:22:07Z","title_canon_sha256":"32ef4a3a952645f1ef30c994bcb9b298dc4de19fc16cdbb42e30ff57f8ee1e5a"},"schema_version":"1.0","source":{"id":"1601.08029","kind":"arxiv","version":1}},"canonical_sha256":"fec0dbbc9e015c3bedae288888fb6c9ec0d0df3017b1d858a25f318d3b6afd55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fec0dbbc9e015c3bedae288888fb6c9ec0d0df3017b1d858a25f318d3b6afd55","first_computed_at":"2026-05-18T01:21:41.174838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:41.174838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jani/op2KxnKVo2VEtt7iNz4YMzZeKbxUI1vs6cUAwYHnmmp4fYXzjIqhRK/mGqt++1stlPuXjhxJIhA1ibcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:41.175360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e05d4feff2e0a83aaac41969cb209a04eb0b1b9d2bff88448501775f9c5beb6","sha256:1cec8cc0b73785d77ff8ddfee21b21201cc7ec8806b4e10ec9ea20331afbe599"],"state_sha256":"8e70e2d9c6d6b56ee65a46b6ea2d910bce89c86429eb1eda2d03d79d242b06e1"}