{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UMBYKINFJNGCMKESMP6MLILIKQ","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":"907e55667bd4ffa7fb23d8d44ad6f9182e0575b72e90de291089a3ab36b5cbda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-22T10:15:04Z","title_canon_sha256":"4bdacec841ce82439709cd6f1c0f9babcf215288e3c07a2700978ae5516e95a5"},"schema_version":"1.0","source":{"id":"1601.05939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05939","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05939v1","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05939","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"UMBYKINFJNGC","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UMBYKINFJNGCMKES","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UMBYKINF","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:dd83f9320c7df7baa53bc02cd62a54b3df3a6012cf5a7f95064f6ecad4436e3a","target":"graph","created_at":"2026-05-18T00:43:43Z","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 paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field, restricting to the case of extensions without intermediate fields. We establish a correspondence between the isomorphism classes of these extensions and some Kummer extensions of a suitable field F containing K. We then describe such classes in terms of the representations of Gal(F/K). Finally, for k = 2 and for each possible Galois group G, we count the number of isomorphism classes of the extensions whose normal closure has a Galois group isomorphic to G. As a byproduct,","authors_text":"I. Del Corso, M. Monge, R. Dvornicich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-22T10:15:04Z","title":"On wild extensions of a p-adic field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05939","kind":"arxiv","version":1},"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:fc2bbe85e407626c6feffd2f04290416a229b519827ee8966ce2f11807f8a2cd","target":"record","created_at":"2026-05-18T00:43:43Z","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":"907e55667bd4ffa7fb23d8d44ad6f9182e0575b72e90de291089a3ab36b5cbda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-22T10:15:04Z","title_canon_sha256":"4bdacec841ce82439709cd6f1c0f9babcf215288e3c07a2700978ae5516e95a5"},"schema_version":"1.0","source":{"id":"1601.05939","kind":"arxiv","version":1}},"canonical_sha256":"a3038521a54b4c26289263fcc5a168543a0e0daf74fc14ac290661a00e25cb51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3038521a54b4c26289263fcc5a168543a0e0daf74fc14ac290661a00e25cb51","first_computed_at":"2026-05-18T00:43:43.698177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:43.698177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GtkOpSYpdQTz2vvp7oao/oooDZKWu+D0+YqqKyImJklHhRRZOfa/1L02Z0/rEnA8qXMeFcnhujbz107u3wulAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:43.698943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc2bbe85e407626c6feffd2f04290416a229b519827ee8966ce2f11807f8a2cd","sha256:dd83f9320c7df7baa53bc02cd62a54b3df3a6012cf5a7f95064f6ecad4436e3a"],"state_sha256":"c1ba719da355b0eebd7b3b375978bb8e39d123711bb3effcd2acc608d594fa3f"}