{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G4PVEKIBDIHVNM6M7RHVOU7VY5","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":"f10824d36b3379d7774c9be62a54f51c0de8729e2f5c04c73250cad845e1951f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T21:18:36Z","title_canon_sha256":"2228b4a17f71636dceb61c89c829922bfed09367a9055972b19a781b9ef9685d"},"schema_version":"1.0","source":{"id":"0910.2997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2997","created_at":"2026-05-18T03:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2997v1","created_at":"2026-05-18T03:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2997","created_at":"2026-05-18T03:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"G4PVEKIBDIHV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G4PVEKIBDIHVNM6M","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G4PVEKIB","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:f2b21e0794c68fb933f251110ff70b6747cc72ff5ecd9f49c5bcfa6ed6a0554a","target":"graph","created_at":"2026-05-18T03:25:46Z","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 examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.","authors_text":"Darrin Doud, Paul Jenkins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T21:18:36Z","title":"$p$-adic properties of coefficients of weakly holomorphic modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2997","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:bb1045542a3279dbdd1928daff0686f1c5e3c1daf6528024efef5409b6dda9bb","target":"record","created_at":"2026-05-18T03:25:46Z","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":"f10824d36b3379d7774c9be62a54f51c0de8729e2f5c04c73250cad845e1951f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T21:18:36Z","title_canon_sha256":"2228b4a17f71636dceb61c89c829922bfed09367a9055972b19a781b9ef9685d"},"schema_version":"1.0","source":{"id":"0910.2997","kind":"arxiv","version":1}},"canonical_sha256":"371f5229011a0f56b3ccfc4f5753f5c74be7e52683a80e1face2b6b0280b92c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"371f5229011a0f56b3ccfc4f5753f5c74be7e52683a80e1face2b6b0280b92c7","first_computed_at":"2026-05-18T03:25:46.865757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:46.865757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hSdYMOnGneXMxpxnPNbkHYsSWRXpdoiiOciheMh7fqkba0TmwL/xQXibkDnMuAoef7jfZ5RL5JTG0H+xKLOmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:46.866623Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb1045542a3279dbdd1928daff0686f1c5e3c1daf6528024efef5409b6dda9bb","sha256:f2b21e0794c68fb933f251110ff70b6747cc72ff5ecd9f49c5bcfa6ed6a0554a"],"state_sha256":"2dafbfdc3ce6782c21b5456e429ba6c67c43ec6f12b5485a6a9bbff97a98dc5a"}