{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GZX4KTHT4FXOKP2KD2GVF65VSG","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":"acae265ccc0c4ee70aad2f6374c26bbe73475c80419ce54f4ca847d135cc4453","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-17T18:00:22Z","title_canon_sha256":"8a702f3305f7144b17c49d8050de0c9a99394a4bc24252843bb6b99ab27c64d4"},"schema_version":"1.0","source":{"id":"2507.13452","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13452","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13452v2","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13452","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"GZX4KTHT4FXO","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZX4KTHT4FXOKP2K","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZX4KTHT","created_at":"2026-05-20T00:05:30Z"}],"graph_snapshots":[{"event_id":"sha256:b06c1823ae731de09c5edf748f820ed898981ea039b499f6aa594b43d09c37d1","target":"graph","created_at":"2026-05-20T00:05:30Z","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/2507.13452/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a proper homogeneous space for a connected algebraic group $G$ over an algebraically closed field. For locally closed smooth affine subvarieties $W,Z\\subset X$, we show that \\[ (-1)^{\\dim X-\\dim W+\\dim Z}\\chi(gW\\cap Z)\\geq 0 \\] for generic $g\\in G$. This extends the characteristic-zero theorem of Sch\\\"urmann--Simpson--Wang. Over finite fields, our methods give a trace-function identity on a dense open subset of $G$ and a Lang--Weil estimate for the non-generic locus.","authors_text":"Ankit Rai, K. V. Shuddhodan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-17T18:00:22Z","title":"Generic vanishing on homogeneous spaces in arbitrary characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13452","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":"sha256:6dda6d69bca3e294068bda16a54b8c977d5bcb6a9cd256ef9c92a58d4ec0d6be","target":"record","created_at":"2026-05-20T00:05:30Z","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":"acae265ccc0c4ee70aad2f6374c26bbe73475c80419ce54f4ca847d135cc4453","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-17T18:00:22Z","title_canon_sha256":"8a702f3305f7144b17c49d8050de0c9a99394a4bc24252843bb6b99ab27c64d4"},"schema_version":"1.0","source":{"id":"2507.13452","kind":"arxiv","version":2}},"canonical_sha256":"366fc54cf3e16ee53f4a1e8d52fbb591a075a5cc1498cd39648f10bbce84463c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"366fc54cf3e16ee53f4a1e8d52fbb591a075a5cc1498cd39648f10bbce84463c","first_computed_at":"2026-05-20T00:05:30.596206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:30.596206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eau6k5KDJ0Fzb7uzNnhrQ5NliiCazJ1pOmvXINn4SDZzl77mn4SjopmRufd8PaXoL6Emm/nSFkMACSzDSznbCw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:30.596945Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13452","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dda6d69bca3e294068bda16a54b8c977d5bcb6a9cd256ef9c92a58d4ec0d6be","sha256:b06c1823ae731de09c5edf748f820ed898981ea039b499f6aa594b43d09c37d1"],"state_sha256":"68607abdb9c17e93afa2ee81b2498a22680503d333eb61ee25a8ca6ad2ebc210"}