{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7ILRJMAEAUNZUEP6FZWNIYJ3JG","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":"58cb3e9df58e42484a5a560030c156258d2532c479fb4c0589a8b396c5e5e103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-31T01:26:55Z","title_canon_sha256":"f8298554c7a64d8ac5477ddd795487fb4a633f687fd2b893d01b960d9829ec7d"},"schema_version":"1.0","source":{"id":"1812.11660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11660","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11660v1","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11660","created_at":"2026-05-17T23:57:11Z"},{"alias_kind":"pith_short_12","alias_value":"7ILRJMAEAUNZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7ILRJMAEAUNZUEP6","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7ILRJMAE","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:63ddadba55dbd24da790df79fbc4238f20869a9bd1aa40e973108ed8075b0254","target":"graph","created_at":"2026-05-17T23:57:11Z","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 $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified elementary abelian $p$-extension with a single ramification break $b$. Byott and Elder defined the refined ramification breaks of $L/K$, an extension of the usual ramification data. In this paper we give an alternative definition for the refined ramification breaks, and we use Artin-Schreier theory to compute both versions of the breaks in some special cases.","authors_text":"G. Griffith Elder, Kevin Keating","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-31T01:26:55Z","title":"Refined ramification breaks in characteristic $p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11660","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:e9cb3cddaf5e0c761f0489cc4422c0b8dc326929287a9d1e3d6c1df46283940b","target":"record","created_at":"2026-05-17T23:57:11Z","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":"58cb3e9df58e42484a5a560030c156258d2532c479fb4c0589a8b396c5e5e103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-31T01:26:55Z","title_canon_sha256":"f8298554c7a64d8ac5477ddd795487fb4a633f687fd2b893d01b960d9829ec7d"},"schema_version":"1.0","source":{"id":"1812.11660","kind":"arxiv","version":1}},"canonical_sha256":"fa1714b004051b9a11fe2e6cd4613b49adcee916eb177cc55090e98de7f244ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa1714b004051b9a11fe2e6cd4613b49adcee916eb177cc55090e98de7f244ee","first_computed_at":"2026-05-17T23:57:11.431477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:11.431477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nRRrgndawPm4TN3X4pXUNcyX1+YvDVz/sdsx5WDgTBStAU48n2kFteoqKmgUEyhXRmnDGYkblXRTkTSEq3uWBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:11.431840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9cb3cddaf5e0c761f0489cc4422c0b8dc326929287a9d1e3d6c1df46283940b","sha256:63ddadba55dbd24da790df79fbc4238f20869a9bd1aa40e973108ed8075b0254"],"state_sha256":"b9886463b4ee3bc3a5888cb3009ba244e19a13608c63ba752caeded9037f6086"}