{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:27UIAHGUWEFNMUQLWPBCPW26AU","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":"207c3e04ee8f2ece6a30b03db6269ff21337b38c2dc3e722df7847290be16845","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-20T02:20:56Z","title_canon_sha256":"2a5b8005d613e4780944d474a49979d65a09ab61f1858a0cfebc0c828a8055f7"},"schema_version":"1.0","source":{"id":"1208.3909","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3909","created_at":"2026-05-18T00:33:28Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3909v3","created_at":"2026-05-18T00:33:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3909","created_at":"2026-05-18T00:33:28Z"},{"alias_kind":"pith_short_12","alias_value":"27UIAHGUWEFN","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"27UIAHGUWEFNMUQL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"27UIAHGU","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:96505181d31c10d7a2dbf5cff3ec941e27dda93fb572d8e458026419c222a5d7","target":"graph","created_at":"2026-05-18T00:33:28Z","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":"Michel Raynaud gave a criterion for a three-point G-cover f : Y \\rightarrow X = P^1, defined over a p-adic field K, to have good reduction. In particular, if the order of a p-Sylow subgroup of G is p, and the number of conjugacy classes of elements of order p is greater than the absolute ramification index e of K, then f has potentially good reduction. We give a different proof of this criterion, which extends to the case where G has an arbitrarily large cyclic p-Sylow subgroup, answering a question of Raynaud. We then use the criterion to give a family of examples of three-point covers with g","authors_text":"Andrew Obus","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-20T02:20:56Z","title":"Good reduction of three-point Galois covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3909","kind":"arxiv","version":3},"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:d0b2699960afa6c7c1d173d17aba68f9c2a015c23fa98bc3ed99eae66343e3ec","target":"record","created_at":"2026-05-18T00:33:28Z","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":"207c3e04ee8f2ece6a30b03db6269ff21337b38c2dc3e722df7847290be16845","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-20T02:20:56Z","title_canon_sha256":"2a5b8005d613e4780944d474a49979d65a09ab61f1858a0cfebc0c828a8055f7"},"schema_version":"1.0","source":{"id":"1208.3909","kind":"arxiv","version":3}},"canonical_sha256":"d7e8801cd4b10ad6520bb3c227db5e0505150156731ded7e4c6ea8d39c81d72f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7e8801cd4b10ad6520bb3c227db5e0505150156731ded7e4c6ea8d39c81d72f","first_computed_at":"2026-05-18T00:33:28.101163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:28.101163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OtlAbilKVkp2ARXbCwF02RF/6GvxY+IAYSvjo/t9w1QjwuN+lDUbFGlAPLlArT3u8FxqoEaW7Zu0lc7SiDR2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:28.101769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3909","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b2699960afa6c7c1d173d17aba68f9c2a015c23fa98bc3ed99eae66343e3ec","sha256:96505181d31c10d7a2dbf5cff3ec941e27dda93fb572d8e458026419c222a5d7"],"state_sha256":"9a6ee928048a7a77727583014313c8cb169cb7784d7d10c8ac3d552db1608743"}