{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FGZRHMNI3BPO2NA5ZULUHKJOQY","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":"aec83e324d5270180b30f5574cb2076df10eca5eb0014263d35f75d200083233","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-15T01:10:02Z","title_canon_sha256":"96b161e1240ccc7f7728f5c17a2365012a3563c7b35dbb8ea4136a8b00c1e2b4"},"schema_version":"1.0","source":{"id":"1609.04486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04486","created_at":"2026-05-18T01:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04486v1","created_at":"2026-05-18T01:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04486","created_at":"2026-05-18T01:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"FGZRHMNI3BPO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGZRHMNI3BPO2NA5","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGZRHMNI","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:3022ab8e4f2fed6a29b1c00663067415eb851eb9b79e5d1e6bdc19ad3560331c","target":"graph","created_at":"2026-05-18T01:04:36Z","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":"We give a comprehensive treatment of the transformation laws of theta functions from an algebro-geometric perspective, that is, in terms of moduli of abelian schemes. This is accomplished by introducing geometric notions of theta-descent structures, metaplectic stacks, and bundles of half-forms, whose analytic incarnations underlie different aspects of the classical transformation laws. As an application, we lay the foundations for a geometric theory of modular forms of half-integral weight and, more generally, for modular forms taking values in the Weil representation. We discuss further appl","authors_text":"Luca Candelori","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-15T01:10:02Z","title":"The transformation laws of algebraic theta functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04486","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:ba686d2d474deb17dbf8795ae4533f4cf8bcafa9bb6b8ebd5d750781e62c5b9e","target":"record","created_at":"2026-05-18T01:04:36Z","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":"aec83e324d5270180b30f5574cb2076df10eca5eb0014263d35f75d200083233","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-15T01:10:02Z","title_canon_sha256":"96b161e1240ccc7f7728f5c17a2365012a3563c7b35dbb8ea4136a8b00c1e2b4"},"schema_version":"1.0","source":{"id":"1609.04486","kind":"arxiv","version":1}},"canonical_sha256":"29b313b1a8d85eed341dcd1743a92e8622b1ffce6398553b1ff2c447fd784c53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29b313b1a8d85eed341dcd1743a92e8622b1ffce6398553b1ff2c447fd784c53","first_computed_at":"2026-05-18T01:04:36.598067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:36.598067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dEBQDnXBJBdR83sl8Rov7L1tWEbTIXIHlwlYYJBwSwk4ufeDDpd7neqEbn7jCnEusd1Rx8sDxhWDom00a/RDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:36.598824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba686d2d474deb17dbf8795ae4533f4cf8bcafa9bb6b8ebd5d750781e62c5b9e","sha256:3022ab8e4f2fed6a29b1c00663067415eb851eb9b79e5d1e6bdc19ad3560331c"],"state_sha256":"de9380228632137c0f1060f9367d9abfae0ec3fe439f68ee739cad967bc3423a"}