{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GXG3A3DKYHV5RS6EC3U54HWPFR","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":"d57be02a8198aea183cc83fd4db588c97e5942bb3f68e8995df9d55c7a5b610b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-29T21:25:08Z","title_canon_sha256":"21fc825220d2cacda1b2efae03818f21ef11da19eca5015e59cbda52a3a1fd00"},"schema_version":"1.0","source":{"id":"2407.00532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.00532","created_at":"2026-07-05T08:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"2407.00532v1","created_at":"2026-07-05T08:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.00532","created_at":"2026-07-05T08:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"GXG3A3DKYHV5","created_at":"2026-07-05T08:38:21Z"},{"alias_kind":"pith_short_16","alias_value":"GXG3A3DKYHV5RS6E","created_at":"2026-07-05T08:38:21Z"},{"alias_kind":"pith_short_8","alias_value":"GXG3A3DK","created_at":"2026-07-05T08:38:21Z"}],"graph_snapshots":[{"event_id":"sha256:d92c76e99d5538d7d45137ac6e386130a66d81b8fdb7dad2d3923fec37a3ca2b","target":"graph","created_at":"2026-07-05T08:38:21Z","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/2407.00532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we construct explicit spanning sets for two spaces. One is the subspace generated by integral-weight Hecke eigenforms with nonvanishing quadratic twisted central $L$-values. The other is a subspace generated by half-integral weight Hecke eigenforms with certain nonvanishing Fourier coefficients. Along the way, we show that these subspaces are isomorphic via the Shimura lift.","authors_text":"Ben Neifeld, Connor Lane, Hui Xue, June Kayath, Tianyu Ni","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-29T21:25:08Z","title":"Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.00532","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":"sha256:12e9c1bdd6aefa40f826fc615581f2a100e294ec36050889bd9a181cb58ad973","target":"record","created_at":"2026-07-05T08:38:21Z","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":"d57be02a8198aea183cc83fd4db588c97e5942bb3f68e8995df9d55c7a5b610b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-29T21:25:08Z","title_canon_sha256":"21fc825220d2cacda1b2efae03818f21ef11da19eca5015e59cbda52a3a1fd00"},"schema_version":"1.0","source":{"id":"2407.00532","kind":"arxiv","version":1}},"canonical_sha256":"35cdb06c6ac1ebd8cbc416e9de1ecf2c4b2e95d4c30cd4f0ca42baf67fe5830a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35cdb06c6ac1ebd8cbc416e9de1ecf2c4b2e95d4c30cd4f0ca42baf67fe5830a","first_computed_at":"2026-07-05T08:38:21.003859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:38:21.003859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eXaIBNGmfYv6t2MCUL+yiauvo0TGLFrE6rRfmbzoShQmbgL/HXs1bt0Vvvt7WdyA54xWYqk5vFTmq/DhaUK1Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:38:21.004266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.00532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12e9c1bdd6aefa40f826fc615581f2a100e294ec36050889bd9a181cb58ad973","sha256:d92c76e99d5538d7d45137ac6e386130a66d81b8fdb7dad2d3923fec37a3ca2b"],"state_sha256":"d43fa7845d8395a3066cd85d5f6410d6dd59738b078e8037ffb8629ab9dddc2a"}