{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BB74AFGVC2CRNSIHQCOD55LEDI","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":"e388b02332e8b7d259c0230ffb2dd8ecc0065cb5f0c25d4b6a6f8f769d230cb5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-11T16:13:18Z","title_canon_sha256":"4a2f795dd90be0c0c554c5ec2a71f433dc4f52b2b26441ff808f963df2f66f2d"},"schema_version":"1.0","source":{"id":"1006.2340","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2340","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2340v2","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2340","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"BB74AFGVC2CR","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BB74AFGVC2CRNSIH","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BB74AFGV","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:68a1b5d1fa745b1547bcae0ddc222c38383696058e8c137ba9a3e4715498f017","target":"graph","created_at":"2026-05-18T03:45:21Z","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":"Let $Z \\to X$ be a finite branched Galois cover of normal projective geometrically integral varieties of dimension $d \\geq 2$ over a perfect field $k$. For such a cover, we prove a Chebotarev-type density result describing the decomposition behaviour of geometrically integral Cartier divisors. As an application, we classify Galois covers among all finite branched covers of a given normal geometrically integral variety $X$ over $k$ by the decomposition behaviour of points of a fixed codimension $r$ with $0 < r < \\dim X$.","authors_text":"Armin Holschbach","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-11T16:13:18Z","title":"A Chebotarev-type density theorem for divisors on algebraic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2340","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":"sha256:9f966cab67eafd6303bf9ea8de3028d1c39095be41d1ef76eccd21e2806e0a9f","target":"record","created_at":"2026-05-18T03:45:21Z","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":"e388b02332e8b7d259c0230ffb2dd8ecc0065cb5f0c25d4b6a6f8f769d230cb5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-11T16:13:18Z","title_canon_sha256":"4a2f795dd90be0c0c554c5ec2a71f433dc4f52b2b26441ff808f963df2f66f2d"},"schema_version":"1.0","source":{"id":"1006.2340","kind":"arxiv","version":2}},"canonical_sha256":"087fc014d5168516c907809c3ef5641a3d5aac1be7a4b956bde70909c32e3745","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"087fc014d5168516c907809c3ef5641a3d5aac1be7a4b956bde70909c32e3745","first_computed_at":"2026-05-18T03:45:21.369333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:21.369333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9TzpRRmxOxdeR+US4GrFjVpU3iZR0uboi78Xmi4DqeOgDhekARoznyQWzD5KK+PAmZBUm9t9UWFIs5MKeWKHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:21.370106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2340","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f966cab67eafd6303bf9ea8de3028d1c39095be41d1ef76eccd21e2806e0a9f","sha256:68a1b5d1fa745b1547bcae0ddc222c38383696058e8c137ba9a3e4715498f017"],"state_sha256":"31ae671da5554788ed2a7fe6ae5a05611954c97346b395de7bf4fb65e76150db"}