{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EQI7RVZFZXTKDWRUK6ZLDZGN5O","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":"6f60c2c0f97bacd5ce00a674a0627a90513668e2416402aa580717f35227f7b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-30T13:07:07Z","title_canon_sha256":"4b7369e7cc13257d278cb89057dc73aa2944524e7ecab618ff6d3381ad45d67d"},"schema_version":"1.0","source":{"id":"1207.6930","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6930","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6930v3","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6930","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"EQI7RVZFZXTK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EQI7RVZFZXTKDWRU","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EQI7RVZF","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:3bfc645ca5d1d82d0b47704c1293c99ab426141787a1a5ae17797d7b03d2452b","target":"graph","created_at":"2026-05-18T03:38:23Z","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 article is a research exposition based on the author's talk at the International Colloquium on Automorphic Representations and L-Functions, 2012, held at TIFR, Mumbai. We consider some special cases of the following question: when is a natural subset of the Fourier coefficients sufficient to uniquely determine a \"modular form\"? Two kinds of modular forms are considered in this article: a) classical modular forms of half-integral weight, and b) Siegel modular forms of genus 2 and integral weight. These two apparently different scenarios turn out to be closely related. Our results were moti","authors_text":"Abhishek Saha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-30T13:07:07Z","title":"Determination of modular forms by fundamental Fourier coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6930","kind":"arxiv","version":3},"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":"sha256:04a64315816efacfbaab1dc02d42b949becb55dd3c3a0da76d64f072075e177a","target":"record","created_at":"2026-05-18T03:38:23Z","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":"6f60c2c0f97bacd5ce00a674a0627a90513668e2416402aa580717f35227f7b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-30T13:07:07Z","title_canon_sha256":"4b7369e7cc13257d278cb89057dc73aa2944524e7ecab618ff6d3381ad45d67d"},"schema_version":"1.0","source":{"id":"1207.6930","kind":"arxiv","version":3}},"canonical_sha256":"2411f8d725cde6a1da3457b2b1e4cdeb984d8794d51b0cfb0e3b2f1d4a8b26fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2411f8d725cde6a1da3457b2b1e4cdeb984d8794d51b0cfb0e3b2f1d4a8b26fb","first_computed_at":"2026-05-18T03:38:23.328457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:23.328457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wwmk51Mr0it8TpkzxxdlWKFSJaIPovTkyq9IM+P3zRujW6ogexEKPksDoEYD1ckoe+gZHq1K1xtBalB8pJ8ECg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:23.329025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6930","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04a64315816efacfbaab1dc02d42b949becb55dd3c3a0da76d64f072075e177a","sha256:3bfc645ca5d1d82d0b47704c1293c99ab426141787a1a5ae17797d7b03d2452b"],"state_sha256":"846e6dd66bdace8ec18fa7f34567ac7042407e45fe69014f52c13c62fd29ff18"}