{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WO52OUCLRREZ63IVQN7OS2VJT4","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":"56e5ae4e6bba8c27fb4c1f4cde6dfc72fdc3e21af0dab9ed75b97d9c04a04687","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-08T12:33:00Z","title_canon_sha256":"e4b2d0d33ae692c751741e2c7334646d5ef8d3b853714a564280d6ba1f9111a8"},"schema_version":"1.0","source":{"id":"2506.07107","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07107","created_at":"2026-07-05T11:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07107v2","created_at":"2026-07-05T11:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07107","created_at":"2026-07-05T11:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"WO52OUCLRREZ","created_at":"2026-07-05T11:46:43Z"},{"alias_kind":"pith_short_16","alias_value":"WO52OUCLRREZ63IV","created_at":"2026-07-05T11:46:43Z"},{"alias_kind":"pith_short_8","alias_value":"WO52OUCL","created_at":"2026-07-05T11:46:43Z"}],"graph_snapshots":[{"event_id":"sha256:15259f39ee7c016a7f7444a30e6d879260535051681be9fc5921ca9385a37a7b","target":"graph","created_at":"2026-07-05T11:46:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07107/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Several authors have recently proved results which express a cusp form as a $p$-adic limit of weakly holomorphic modular forms under repeated application of Atkin's $U$-operator. Initially, these results had a deficiency: one could not rule out the possibility when a certain quantity vanishes and the final result fails to be true. Later on, Ahlgren and Samart \\cite{AS} found a method to prove that no exceptions happen in the specific case considered by El-Guindy and Ono, Hanson and Jameson, and (independently) Dicks. generalized this method to finitely many other cases.\n  In this paper, we pre","authors_text":"Pavel Guerzhoy","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-08T12:33:00Z","title":"Cusp forms as $p$-adic limits circumventing $p$-adic version of the Legendre period relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07107","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":"sha256:31b40c376549d2c2052d6e1eb3009431724bb65231ee788809a95c8ff566ebdc","target":"record","created_at":"2026-07-05T11:46:43Z","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":"56e5ae4e6bba8c27fb4c1f4cde6dfc72fdc3e21af0dab9ed75b97d9c04a04687","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-08T12:33:00Z","title_canon_sha256":"e4b2d0d33ae692c751741e2c7334646d5ef8d3b853714a564280d6ba1f9111a8"},"schema_version":"1.0","source":{"id":"2506.07107","kind":"arxiv","version":2}},"canonical_sha256":"b3bba7504b8c499f6d15837ee96aa99f05603ae7b85ba72e8e9e2281cacb11ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3bba7504b8c499f6d15837ee96aa99f05603ae7b85ba72e8e9e2281cacb11ca","first_computed_at":"2026-07-05T11:46:43.986887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:43.986887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dbRbul3ansLZv0GLipY9+RoqkjRKSVUSQQ9giUbAum1MuE0LDtJGFH8iPYnYI1ZNK6k0P4YNly7OAA06hILAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:43.987358Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07107","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31b40c376549d2c2052d6e1eb3009431724bb65231ee788809a95c8ff566ebdc","sha256:15259f39ee7c016a7f7444a30e6d879260535051681be9fc5921ca9385a37a7b"],"state_sha256":"465d965f243bb409883a1ec8e4fb1eb56111a3a18601ba20dec658fa1a671f03"}