{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SS62UTLKODTOAJN6NPGZFLCSO7","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":"6e5f12d20915e3671c5b9d3ef24d6c6a7e4705cbc5990606bc2cfba4b48c4e4e","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-06T02:49:31Z","title_canon_sha256":"b8b4ba2e54100fa1b63ff3d5c6b3f840286bf904d8199eca2b08871b4bbf8273"},"schema_version":"1.0","source":{"id":"1703.01710","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01710","created_at":"2026-05-18T00:40:13Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01710v2","created_at":"2026-05-18T00:40:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01710","created_at":"2026-05-18T00:40:13Z"},{"alias_kind":"pith_short_12","alias_value":"SS62UTLKODTO","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SS62UTLKODTOAJN6","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SS62UTLK","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:626362edf4ed1835601b197cd48b1c228aa2828197fd99e5090ca66a3096cf5f","target":"graph","created_at":"2026-05-18T00:40:13Z","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":"A standard observation in algebraic geometry and number theory is that a ramified cover of an algebraic variety $\\widetilde{X}\\rightarrow X$ over a finite field $F_q$ furnishes the rational points $x\\in X(F_q)$ with additional arithmetic structure: the Frobenius action on the fiber over $x$. For example, in the case of the Vieta cover of polynomials over $F_q$ this structure describes a polynomial's irreducible decomposition type.\n  Furthermore, the distribution of these Frobenius actions is encoded in the cohomology of $\\widetilde{X}$ via the Grothendieck-Lefschetz trace formula. This note pr","authors_text":"Nir Gadish","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-06T02:49:31Z","title":"A trace formula for the distribution of rational $G$-orbits in ramified covers, adapted to representation stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01710","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":"sha256:19d5a9fee634b81d8746e52a01c656f3505f9390e12f241feca48c23b3675534","target":"record","created_at":"2026-05-18T00:40:13Z","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":"6e5f12d20915e3671c5b9d3ef24d6c6a7e4705cbc5990606bc2cfba4b48c4e4e","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-06T02:49:31Z","title_canon_sha256":"b8b4ba2e54100fa1b63ff3d5c6b3f840286bf904d8199eca2b08871b4bbf8273"},"schema_version":"1.0","source":{"id":"1703.01710","kind":"arxiv","version":2}},"canonical_sha256":"94bdaa4d6a70e6e025be6bcd92ac5277e5735a482ec5f2095db59429cf0affc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94bdaa4d6a70e6e025be6bcd92ac5277e5735a482ec5f2095db59429cf0affc5","first_computed_at":"2026-05-18T00:40:13.266904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:13.266904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gBf2aXQu5jQ/DkZwanT8VfKuIOJec/gjIueE0FRxEppTvW35aRDsMt9p/YHKRKZ9Yuqz6+EbPjnLlRDSg3KlCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:13.267430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01710","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19d5a9fee634b81d8746e52a01c656f3505f9390e12f241feca48c23b3675534","sha256:626362edf4ed1835601b197cd48b1c228aa2828197fd99e5090ca66a3096cf5f"],"state_sha256":"7d8e7fed2fc05eb2a47d07e4e3c3d8cf08e91d9a55641f661d1eb473be022672"}