{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZW6J3K73PEK3BIGOP7IZQWAP6G","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":"2afdbb8b79c76060cc905c4b58383acbb5efd1e8f093dcb2193d8472cc805453","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-22T14:01:36Z","title_canon_sha256":"adfb30e65cc0d12d5bfd125a8d9bf7e1b75c3fd143deb9521d3f38c092afeb53"},"schema_version":"1.0","source":{"id":"1908.08390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08390","created_at":"2026-07-05T03:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08390v1","created_at":"2026-07-05T03:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08390","created_at":"2026-07-05T03:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZW6J3K73PEK3","created_at":"2026-07-05T03:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZW6J3K73PEK3BIGO","created_at":"2026-07-05T03:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZW6J3K73","created_at":"2026-07-05T03:54:53Z"}],"graph_snapshots":[{"event_id":"sha256:ed11394df787555bc4a5be4116164a47d39580274accde80e47bb0333781424e","target":"graph","created_at":"2026-07-05T03:54:53Z","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/1908.08390/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we consider special algebraic cycles on the Shimura variety S associated to a quadratic space V over a totally real field F, |F:\\Q|=d, of signature ((m,2)^{d_+},(m+2,0)^{d-d_+}), 1\\le d_+<d. For each n, 1\\le n\\le m, there are special cycles Z(T) in S, of codimension nd_+, indexed by totally positive semi-definite matrices with coefficients in the ring of integers O_F. The generating series for the classes of these cycles in the cohomology group H^{2nd_+}(S) are Hilbert-Siegel modular forms of parallel weight m/2+1. One can form analogous generating series for the classes of the s","authors_text":"Stephen Kudla","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-22T14:01:36Z","title":"Remarks on generating series for special cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08390","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":"sha256:4ffdd3eff636d8863126beb01eddb885e4d20ca22312115d286950fc1888b66e","target":"record","created_at":"2026-07-05T03:54:53Z","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":"2afdbb8b79c76060cc905c4b58383acbb5efd1e8f093dcb2193d8472cc805453","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-22T14:01:36Z","title_canon_sha256":"adfb30e65cc0d12d5bfd125a8d9bf7e1b75c3fd143deb9521d3f38c092afeb53"},"schema_version":"1.0","source":{"id":"1908.08390","kind":"arxiv","version":1}},"canonical_sha256":"cdbc9dabfb7915b0a0ce7fd198580ff18bd3566b354791fbdc0acdfbd9547973","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdbc9dabfb7915b0a0ce7fd198580ff18bd3566b354791fbdc0acdfbd9547973","first_computed_at":"2026-07-05T03:54:53.384708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:53.384708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pvQ2gXZO6rrmWfVLJMC6uJxtKRxqLzFE+wajh2MNQbp30WKCAUShOOEaI9l/nUYbJSqH3QlDFQm1h4NvHXwkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:53.385091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ffdd3eff636d8863126beb01eddb885e4d20ca22312115d286950fc1888b66e","sha256:ed11394df787555bc4a5be4116164a47d39580274accde80e47bb0333781424e"],"state_sha256":"eb724a3ae5d6c61352782df7485ec6aea2d3280c8b73d008fa719331ae5bc4a8"}