{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZD7FHNX2ZBRPONUBFCPHOKVM2F","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":"b5e6aec744dc901ff43849dc7dd210263f33b5b262d8bc3b2f2ea49352a3c3e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-07-01T11:51:28Z","title_canon_sha256":"4c20b0bc202a672c7f77cfdb9d5f3006c3a7f06532213925f8138af55e94841f"},"schema_version":"1.0","source":{"id":"2407.01205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.01205","created_at":"2026-07-05T09:23:07Z"},{"alias_kind":"arxiv_version","alias_value":"2407.01205v2","created_at":"2026-07-05T09:23:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01205","created_at":"2026-07-05T09:23:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZD7FHNX2ZBRP","created_at":"2026-07-05T09:23:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZD7FHNX2ZBRPONUB","created_at":"2026-07-05T09:23:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZD7FHNX2","created_at":"2026-07-05T09:23:07Z"}],"graph_snapshots":[{"event_id":"sha256:1017bca71eed0f0a6313247461052897019ededd69c8bb647d2656010c748d6c","target":"graph","created_at":"2026-07-05T09:23:07Z","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/2407.01205/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The vector valued theta series of a positive-definite even lattice is a modular form for the Weil representation of $\\mathrm{SL}_2(\\mathbb{Z})$. We show that the space of cusp forms for the Weil representation is generated by such functions. This gives a positive answer to Eichler's basis problem in this case. As applications we derive Waldspurger's result on the basis problem for scalar valued modular forms and give a new proof of the surjectivity of the Borcherds lift based on the analysis of local Picard groups.","authors_text":"Manuel K.-H. M\\\"uller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-07-01T11:51:28Z","title":"The basis problem for modular forms for the Weil representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01205","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":"sha256:582b85fb83786d6284432ac4377f6a460a8d1c02c2be1c2a6a6ac38eb23cfcd6","target":"record","created_at":"2026-07-05T09:23:07Z","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":"b5e6aec744dc901ff43849dc7dd210263f33b5b262d8bc3b2f2ea49352a3c3e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-07-01T11:51:28Z","title_canon_sha256":"4c20b0bc202a672c7f77cfdb9d5f3006c3a7f06532213925f8138af55e94841f"},"schema_version":"1.0","source":{"id":"2407.01205","kind":"arxiv","version":2}},"canonical_sha256":"c8fe53b6fac862f73681289e772aacd167cc440b4ca73b3778486887c17a6db4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8fe53b6fac862f73681289e772aacd167cc440b4ca73b3778486887c17a6db4","first_computed_at":"2026-07-05T09:23:07.744444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:23:07.744444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JyInil0f3NJ0bFVQVXE7iYJhE5UFRxDL+GfweYDBOXxgod6+pt8JIpk/s1kWqRL91psfVGUQ0JpYeFJHz2YkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:23:07.744918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.01205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:582b85fb83786d6284432ac4377f6a460a8d1c02c2be1c2a6a6ac38eb23cfcd6","sha256:1017bca71eed0f0a6313247461052897019ededd69c8bb647d2656010c748d6c"],"state_sha256":"7bbe63c0a4505d2c2cccdb150981a3066df67f5497d69a6dc96303283d23a338"}