{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5OPJ77ECUY56S3VFOIUYONZL4I","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":"e5fe48f663d7bdade9fc37934796d2649ee0f182599d454ba4d9567c3d50b852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-08T07:43:38Z","title_canon_sha256":"92631e0d2a1406bac60e8765aa88c210ba7d08431abd99890e55015040fe4f02"},"schema_version":"1.0","source":{"id":"1905.02946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02946","created_at":"2026-05-17T23:46:44Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02946v1","created_at":"2026-05-17T23:46:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02946","created_at":"2026-05-17T23:46:44Z"},{"alias_kind":"pith_short_12","alias_value":"5OPJ77ECUY56","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5OPJ77ECUY56S3VF","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5OPJ77EC","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:ac04677822f93a375960446dd80d87af6fe5aa132e9bb3be989473e6805c36af","target":"graph","created_at":"2026-05-17T23:46:44Z","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":"This was originally an appendix to our paper `Fourier expansions at cusps'  [arXiv:1807.00391]. The purpose of this note is to give a proof of a theorem of Shimura on the action of $\\mathrm{Aut}(\\mathbb{C})$ on modular forms for $\\Gamma(N)$ from the perspective of algebraic modular forms. As the theorem is well-known, we do not intend to publish this note but want to keep it available as a preprint.","authors_text":"Fran\\c{c}ois Brunault, Michael Neururer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-08T07:43:38Z","title":"Note on Fourier expansions at cusps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02946","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":"sha256:7fc0d78bec21f1b97e8e3b53c885f4de0ca4277dea89510b92fcdaeed3c88314","target":"record","created_at":"2026-05-17T23:46:44Z","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":"e5fe48f663d7bdade9fc37934796d2649ee0f182599d454ba4d9567c3d50b852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-08T07:43:38Z","title_canon_sha256":"92631e0d2a1406bac60e8765aa88c210ba7d08431abd99890e55015040fe4f02"},"schema_version":"1.0","source":{"id":"1905.02946","kind":"arxiv","version":1}},"canonical_sha256":"eb9e9ffc82a63be96ea5722987372be213f45cc76cecee1e177335e2a399c3ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb9e9ffc82a63be96ea5722987372be213f45cc76cecee1e177335e2a399c3ae","first_computed_at":"2026-05-17T23:46:44.948990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:44.948990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qEqfw0xevKHi0BZ+E5+kSRuEtHnIJRDN2azqq6LUMKF9+hYVUIf8aA02iF9U7zD/8VSkIYy3TSpQVLr10YmHDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:44.949466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fc0d78bec21f1b97e8e3b53c885f4de0ca4277dea89510b92fcdaeed3c88314","sha256:ac04677822f93a375960446dd80d87af6fe5aa132e9bb3be989473e6805c36af"],"state_sha256":"813e66d3eb4dc16f4a403a7ffc8fcf0221475c30e3c115f1fbb20194263e329d"}