{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2X6NA3VCKKMA64QN6G3YVXYSVV","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":"c4070c1a2e268369b9c84329f43fae1199a9cc155e361de61114154add10978f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T16:29:12Z","title_canon_sha256":"f7a21a16043eb277f6fdf43d583728d1e3086a991e4157eca0bbd03ce89fb4b0"},"schema_version":"1.0","source":{"id":"1604.06024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06024","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06024v2","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06024","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"2X6NA3VCKKMA","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2X6NA3VCKKMA64QN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2X6NA3VC","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:48e69c2e391e010899e890991cbd366b7f1feeb024e2d759dca7f036c54164d0","target":"graph","created_at":"2026-05-18T00:42:23Z","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":"In this article I define and study the overconvergent rigid fundamental group of a variety over an equicharacteristic local field. This is a non-abelian $(\\varphi,\\nabla)$-module over the bounded Robba ring $\\mathcal{E}_K^\\dagger$, whose underlying unipotent group (after base changing to the Amice ring $\\mathcal{E}_K$) is exactly the classical rigid fundamental group. I then use this to prove an equicharacteristic, $p$-adic analogue of Oda's theorem that a semistable curve over a $p$-adic field has good reduction iff the Galois action on its $\\ell$-adic unipotent fundamental group is unramifie","authors_text":"Christopher Lazda","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T16:29:12Z","title":"Fundamental groups and good reduction criteria for curves over positive characteristic local fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06024","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:d0b7fc1fbf5af82219cc34c4d08c6d205c64e08b26a1d59003b33341e6117ea3","target":"record","created_at":"2026-05-18T00:42:23Z","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":"c4070c1a2e268369b9c84329f43fae1199a9cc155e361de61114154add10978f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T16:29:12Z","title_canon_sha256":"f7a21a16043eb277f6fdf43d583728d1e3086a991e4157eca0bbd03ce89fb4b0"},"schema_version":"1.0","source":{"id":"1604.06024","kind":"arxiv","version":2}},"canonical_sha256":"d5fcd06ea252980f720df1b78adf12ad588eb1c00f4e0e63c71554b222123523","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5fcd06ea252980f720df1b78adf12ad588eb1c00f4e0e63c71554b222123523","first_computed_at":"2026-05-18T00:42:23.956774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:23.956774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pRCNR1/z7o8bYlsjIHj83pEwCQmnBc+ZHEex0L0Yt9w0aQxFs+YYbIulwaFxWig9vRJaNb9/gRp8aZyv7Nf9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:23.957459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b7fc1fbf5af82219cc34c4d08c6d205c64e08b26a1d59003b33341e6117ea3","sha256:48e69c2e391e010899e890991cbd366b7f1feeb024e2d759dca7f036c54164d0"],"state_sha256":"51b929fe427106d83d9d475aa772827c6a7a3eaf65f6449e1b93e679d07bde6e"}