{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CUZ35VEC7OBNPNZVRLBES7RFDG","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":"62749c4edf78939caf27a23a355043fcd4c3ebd96687ac311d4609558a7ce6f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-01T11:26:30Z","title_canon_sha256":"af0fb1788969148c4ba39501cb3943d24090ab4258ff5e72220c0f3724b4d732"},"schema_version":"1.0","source":{"id":"2509.01378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.01378","created_at":"2026-07-05T12:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"2509.01378v1","created_at":"2026-07-05T12:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01378","created_at":"2026-07-05T12:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"CUZ35VEC7OBN","created_at":"2026-07-05T12:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"CUZ35VEC7OBNPNZV","created_at":"2026-07-05T12:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"CUZ35VEC","created_at":"2026-07-05T12:02:59Z"}],"graph_snapshots":[{"event_id":"sha256:d53ef7801cc21b2c032474bf9445d1e165c323e7ac8b8c5e005eb3dfcb12f67b","target":"graph","created_at":"2026-07-05T12:02:59Z","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/2509.01378/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1975, Zagier introduced the highly influential hyperbolic Poincar\\'e series $f_{k,D}$. We connect the divisor modular form of $f_{k,D}$ to a new weak Maass form $\\omega_{k+1,D}$. Furthermore, we show that the generating function of $\\omega_{k+1,D}$ has the same modularity properties as Kohnen and Zagier's fruitful theta kernel generating the $f_{k,D}$'s. This yields a new theta lift.","authors_text":"Andreas Mono, Johann Stumpenhusen, Larry Rolen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-01T11:26:30Z","title":"On a Divisor Modular Form and a Theta Lift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01378","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":"sha256:6e89b7fd3a862ba8a7279cd414716ec783c3cc085874af548407ddfa0fb6e84d","target":"record","created_at":"2026-07-05T12:02:59Z","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":"62749c4edf78939caf27a23a355043fcd4c3ebd96687ac311d4609558a7ce6f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-01T11:26:30Z","title_canon_sha256":"af0fb1788969148c4ba39501cb3943d24090ab4258ff5e72220c0f3724b4d732"},"schema_version":"1.0","source":{"id":"2509.01378","kind":"arxiv","version":1}},"canonical_sha256":"1533bed482fb82d7b7358ac2497e2519b17fbc622d4951e8f0d4cb72665f3239","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1533bed482fb82d7b7358ac2497e2519b17fbc622d4951e8f0d4cb72665f3239","first_computed_at":"2026-07-05T12:02:59.460347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:02:59.460347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"22FyTrp+uH/JG8Y8bhhrZEHXlFD6BYSAY9D7lJiLaXwTgLTrau+7BreKyFj9Y6sOuyk6yxu+VVxZ88IudVNBDw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:02:59.460884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.01378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e89b7fd3a862ba8a7279cd414716ec783c3cc085874af548407ddfa0fb6e84d","sha256:d53ef7801cc21b2c032474bf9445d1e165c323e7ac8b8c5e005eb3dfcb12f67b"],"state_sha256":"7b22c6df0e342c6cba1342adddb5bfe7b081d8dfb005f68b5ab54aecc1999593"}