{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:446VBW6UIFL3TGB2EYL6PN2EQO","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":"75568eb8b986899f4b422e6c469636cafefe0cb19ec89f281ceb0c039eadf553","cross_cats_sorted":["math.AG","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-17T18:31:13Z","title_canon_sha256":"7a79ead9f56cb58f89f913b3b6967130477b4819420ebfc700ccb12e4257dfe3"},"schema_version":"1.0","source":{"id":"2507.13473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13473","created_at":"2026-07-05T11:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13473v1","created_at":"2026-07-05T11:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13473","created_at":"2026-07-05T11:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"446VBW6UIFL3","created_at":"2026-07-05T11:39:17Z"},{"alias_kind":"pith_short_16","alias_value":"446VBW6UIFL3TGB2","created_at":"2026-07-05T11:39:17Z"},{"alias_kind":"pith_short_8","alias_value":"446VBW6U","created_at":"2026-07-05T11:39:17Z"}],"graph_snapshots":[{"event_id":"sha256:2e4c7e6055d69b771ad791bb0494b3dd30d9899308811b9c75d344761b6ceb9a","target":"graph","created_at":"2026-07-05T11:39:17Z","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/2507.13473/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the higher Siegel--Weil formula for \\emph{corank one} terms, relating (1) the $r^{\\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual dimension 0 on the moduli stack of Hermitian shtukas with $r$ legs. Notably, the formula holds for all $r$, regardless of the order of vanishing of the Eisenstein series. This extends earlier work of Feng--Yun--Zhang, who proved the higher Siegel--Weil formula for the non-singular (corank zero) terms.","authors_text":"Benjamin Howard, Mikayel Mkrtchyan, Tony Feng","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-17T18:31:13Z","title":"Higher Siegel--Weil formula for unitary groups II: corank one terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13473","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":"sha256:6ecf14e90a516fc599b80ca8046969c23a06e9955c62d3f0a8d8ef3890e6192f","target":"record","created_at":"2026-07-05T11:39:17Z","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":"75568eb8b986899f4b422e6c469636cafefe0cb19ec89f281ceb0c039eadf553","cross_cats_sorted":["math.AG","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-17T18:31:13Z","title_canon_sha256":"7a79ead9f56cb58f89f913b3b6967130477b4819420ebfc700ccb12e4257dfe3"},"schema_version":"1.0","source":{"id":"2507.13473","kind":"arxiv","version":1}},"canonical_sha256":"e73d50dbd44157b9983a2617e7b74483a9c5c7b81d466508bd0ec8051779c3a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e73d50dbd44157b9983a2617e7b74483a9c5c7b81d466508bd0ec8051779c3a0","first_computed_at":"2026-07-05T11:39:17.937960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:17.937960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IepjVL6OXdmSwdFN6rMDzUIB4rOZuO6nVoZHoaYTkg8kP9TbaeY3QvkgxwPIJ/q6BADWExwqXqVO8454YeatCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:17.938370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ecf14e90a516fc599b80ca8046969c23a06e9955c62d3f0a8d8ef3890e6192f","sha256:2e4c7e6055d69b771ad791bb0494b3dd30d9899308811b9c75d344761b6ceb9a"],"state_sha256":"91dd79dab86b307eaa68faa93ec6b2159bece347e2a87ed09318b99ada3f248d"}