{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:7RBVDTRW2WL3MDDEOP7XPB6RUS","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":"8cc5ecc15ecae54415c6d5b22ee129645c878be943404678bade73de205122b0","cross_cats_sorted":["hep-th","math.AG","math.QA","q-alg"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-11-24T13:06:45Z","title_canon_sha256":"4fa7eb5ba705c9c6bae512a2ab877dda8778d2614d0ea0c76552249f4683c100"},"schema_version":"1.0","source":{"id":"alg-geom/9611028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9611028","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9611028v2","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9611028","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"7RBVDTRW2WL3","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7RBVDTRW2WL3MDDE","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7RBVDTRW","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:cff91ea4e2cb34e9e47c816af3f5447be14723467e7241bed8c5afd4a54d33f5","target":"graph","created_at":"2026-05-18T01:07:47Z","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 variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary polarization). The data for these liftings are Jacobi forms of integral and half-integral indices. In particular, we get modular forms which are generalizations of the Dedekind eta-function. Some of these forms define automorphic corrections of Lorentzian Kac-Moody algebras with hyperbolic generalized Cartan matrices of rank three classified in Part I of this pape","authors_text":"Valeri A. Gritsenko, Viacheslav V. Nikulin","cross_cats":["hep-th","math.AG","math.QA","q-alg"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1996-11-24T13:06:45Z","title":"Automorphic Forms and Lorentzian Kac-Moody Algebras. Part II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9611028","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:c9affba85f8c03048e4d9f6679e6057f63e749753c348d09400750fcce76073f","target":"record","created_at":"2026-05-18T01:07:47Z","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":"8cc5ecc15ecae54415c6d5b22ee129645c878be943404678bade73de205122b0","cross_cats_sorted":["hep-th","math.AG","math.QA","q-alg"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-11-24T13:06:45Z","title_canon_sha256":"4fa7eb5ba705c9c6bae512a2ab877dda8778d2614d0ea0c76552249f4683c100"},"schema_version":"1.0","source":{"id":"alg-geom/9611028","kind":"arxiv","version":2}},"canonical_sha256":"fc4351ce36d597b60c6473ff7787d1a49f17177165dad243c8169730c2e1fc59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4351ce36d597b60c6473ff7787d1a49f17177165dad243c8169730c2e1fc59","first_computed_at":"2026-05-18T01:07:47.136091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:47.136091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8s+yjzufSg9ihXZgq+k50t//kNKggns++GeLih3+G8/QYVJkX1QkJNj4Hs87Uepqz2IY1ghWG8iO6jX+ogSoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:47.136589Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9611028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9affba85f8c03048e4d9f6679e6057f63e749753c348d09400750fcce76073f","sha256:cff91ea4e2cb34e9e47c816af3f5447be14723467e7241bed8c5afd4a54d33f5"],"state_sha256":"fec22814c4712c6cdf09283de3158a72e3d33a4cfac34f813f35faedb61dec6d"}