{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2OPXAEI7TX3RNO6PXFKVWVUIJ3","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":"eb837c8261239ba455288a1992680a60bb7b0f8c13a18b5506a140f171e0aec6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-15T13:46:46Z","title_canon_sha256":"ed107bd1fe35b3837f844cc46275fd9c4534777620505e42836b11617675f26f"},"schema_version":"1.0","source":{"id":"1308.3394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3394","created_at":"2026-05-18T03:15:54Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3394v1","created_at":"2026-05-18T03:15:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3394","created_at":"2026-05-18T03:15:54Z"},{"alias_kind":"pith_short_12","alias_value":"2OPXAEI7TX3R","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2OPXAEI7TX3RNO6P","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2OPXAEI7","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:0792e4c2812b505908a6dfc5d9a15b242e9e4510a5e92d816abfbaee101f1635","target":"graph","created_at":"2026-05-18T03:15:54Z","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":"We prove that every non-trivial valuation on an infinite superrosy field of positive characteristic has divisible value group and algebraically closed residue field. In fact, we prove the following more general result. Let $K$ be a field such that for every finite extension $L$ of $K$ and for every natural number $n>0$ the index $[L^*:(L^*)^n]$ is finite and, if $char(K)=p>0$ and $f: L \\to L$ is given by $f(x)=x^p-x$, the index $[L^+:f[L]]$ is also finite. Then either there is a non-trivial definable valuation on $K$, or every non-trivial valuation on $K$ has divisible value group and, if $cha","authors_text":"Krzysztof Krupinski","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-15T13:46:46Z","title":"Superrosy fields and valuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3394","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:b098e882cd880eb6dab5c0e113751f59a870ddedaa150606fe0a79e84892ddc1","target":"record","created_at":"2026-05-18T03:15:54Z","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":"eb837c8261239ba455288a1992680a60bb7b0f8c13a18b5506a140f171e0aec6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-15T13:46:46Z","title_canon_sha256":"ed107bd1fe35b3837f844cc46275fd9c4534777620505e42836b11617675f26f"},"schema_version":"1.0","source":{"id":"1308.3394","kind":"arxiv","version":1}},"canonical_sha256":"d39f70111f9df716bbcfb9555b56884efcfaed7483baa448f84c683be6d9cdd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d39f70111f9df716bbcfb9555b56884efcfaed7483baa448f84c683be6d9cdd7","first_computed_at":"2026-05-18T03:15:54.752953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:54.752953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S5pg4oU51nA7Q/3ZohjQtDGO0IF76VJFgbJY58zqt9M/ZQYsEjV/M7Yhscu170qFIBjCjR4PGexS73tSjPNCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:54.753747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b098e882cd880eb6dab5c0e113751f59a870ddedaa150606fe0a79e84892ddc1","sha256:0792e4c2812b505908a6dfc5d9a15b242e9e4510a5e92d816abfbaee101f1635"],"state_sha256":"94d1b1b84dc5b07cdd6983109e91408948fea952b79862547cb345926569fbb8"}