{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZW6J3K73PEK3BIGOP7IZQWAP6G","short_pith_number":"pith:ZW6J3K73","schema_version":"1.0","canonical_sha256":"cdbc9dabfb7915b0a0ce7fd198580ff18bd3566b354791fbdc0acdfbd9547973","source":{"kind":"arxiv","id":"1908.08390","version":1},"attestation_state":"computed","paper":{"title":"Remarks on generating series for special cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Stephen Kudla","submitted_at":"2019-08-22T14:01:36Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.08390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-22T14:01:36Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"adfb30e65cc0d12d5bfd125a8d9bf7e1b75c3fd143deb9521d3f38c092afeb53","abstract_canon_sha256":"2afdbb8b79c76060cc905c4b58383acbb5efd1e8f093dcb2193d8472cc805453"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:54:53.385091Z","signature_b64":"pvQ2gXZO6rrmWfVLJMC6uJxtKRxqLzFE+wajh2MNQbp30WKCAUShOOEaI9l/nUYbJSqH3QlDFQm1h4NvHXwkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdbc9dabfb7915b0a0ce7fd198580ff18bd3566b354791fbdc0acdfbd9547973","last_reissued_at":"2026-07-05T03:54:53.384708Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:54:53.384708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on generating series for special cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Stephen Kudla","submitted_at":"2019-08-22T14:01:36Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08390","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08390/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.08390","created_at":"2026-07-05T03:54:53.384764+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08390v1","created_at":"2026-07-05T03:54:53.384764+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08390","created_at":"2026-07-05T03:54:53.384764+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZW6J3K73PEK3","created_at":"2026-07-05T03:54:53.384764+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZW6J3K73PEK3BIGO","created_at":"2026-07-05T03:54:53.384764+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZW6J3K73","created_at":"2026-07-05T03:54:53.384764+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08063","citing_title":"The modularity of special cycles on orthogonal Shimura varieties over totally real fields under the Beilinson-Bloch conjecture","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G","json":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G.json","graph_json":"https://pith.science/api/pith-number/ZW6J3K73PEK3BIGOP7IZQWAP6G/graph.json","events_json":"https://pith.science/api/pith-number/ZW6J3K73PEK3BIGOP7IZQWAP6G/events.json","paper":"https://pith.science/paper/ZW6J3K73"},"agent_actions":{"view_html":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G","download_json":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G.json","view_paper":"https://pith.science/paper/ZW6J3K73","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08390&json=true","fetch_graph":"https://pith.science/api/pith-number/ZW6J3K73PEK3BIGOP7IZQWAP6G/graph.json","fetch_events":"https://pith.science/api/pith-number/ZW6J3K73PEK3BIGOP7IZQWAP6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G/action/storage_attestation","attest_author":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G/action/author_attestation","sign_citation":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G/action/citation_signature","submit_replication":"https://pith.science/pith/ZW6J3K73PEK3BIGOP7IZQWAP6G/action/replication_record"}},"created_at":"2026-07-05T03:54:53.384764+00:00","updated_at":"2026-07-05T03:54:53.384764+00:00"}