{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:MH5C65OG53OOHJCYJ77IYMGKPH","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":"9765f2e9274e1ea30e3db96a97c6ccb970daeab5b66efbdc526ce346bee70e4a","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DG","submitted_at":"2007-12-24T18:11:43Z","title_canon_sha256":"d7e39d48f1f662ac745dcb6381b5202ab9aee9e073ef3c1ad615f243dbfca1df"},"schema_version":"1.0","source":{"id":"0712.4016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4016","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4016v1","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4016","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"MH5C65OG53OO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"MH5C65OG53OOHJCY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"MH5C65OG","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:bc7568c9e761c72822cc50f85e7458a5a5a3c3322d062f929feb09edc85b5a44","target":"graph","created_at":"2026-05-18T03:42:56Z","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":"The Kodaira--Thurston M manifold is a compact, 4-dimensional nilmanifold which is symplectic and complex but not Kaehler. We describe a construction of theta-functions associated to M which parallels the classical theory of theta-functions associated to the torus (from the point of view of representation theory and geometry), and yields pseudoperiodic complex-valued functions on R^4.\n  There exists a three-step nilpotent Lie group G which acts transitively on the Kodaira--Thurston manifold M in a Hamiltonian fashion. The theta-functions discussed in this paper are intimately related to the rep","authors_text":"Alejandro Uribe, William D. Kirwin","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-12-24T18:11:43Z","title":"Theta-functions on the Kodaira-Thurston manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4016","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:c6d7c97a5b262f232dd1e2247e2aaf74341373de2453233c97095049662bef7e","target":"record","created_at":"2026-05-18T03:42:56Z","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":"9765f2e9274e1ea30e3db96a97c6ccb970daeab5b66efbdc526ce346bee70e4a","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DG","submitted_at":"2007-12-24T18:11:43Z","title_canon_sha256":"d7e39d48f1f662ac745dcb6381b5202ab9aee9e073ef3c1ad615f243dbfca1df"},"schema_version":"1.0","source":{"id":"0712.4016","kind":"arxiv","version":1}},"canonical_sha256":"61fa2f75c6eedce3a4584ffe8c30ca79c966833e6425a6c36f0c481da2c8d807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61fa2f75c6eedce3a4584ffe8c30ca79c966833e6425a6c36f0c481da2c8d807","first_computed_at":"2026-05-18T03:42:56.041461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:56.041461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tSrPFnYX9XuUajx0wseoP/EUuIYLKJqCsJJ5ZvMW1te5QgHcc5X/X6mjWhC0gtmqz3tO6ugFwRXa1LE369oCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:56.041955Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6d7c97a5b262f232dd1e2247e2aaf74341373de2453233c97095049662bef7e","sha256:bc7568c9e761c72822cc50f85e7458a5a5a3c3322d062f929feb09edc85b5a44"],"state_sha256":"aa239c28dfd4d40262f486dcaefd18bb340bc7789d4d393cd7723640a7e1244f"}