{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Q5HVIF2TLWUMRQ6ZIQMEBOPD6N","short_pith_number":"pith:Q5HVIF2T","schema_version":"1.0","canonical_sha256":"874f5417535da8c8c3d9441840b9e3f3749d61b1526415cf58cb4b4082b7a36b","source":{"kind":"arxiv","id":"1407.8156","version":2},"attestation_state":"computed","paper":{"title":"Uniformly defining $p$-henselian valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Franziska Jahnke, Jochen Koenigsmann","submitted_at":"2014-07-30T18:50:30Z","abstract_excerpt":"Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply this to show that there is a definable valuation inducing the ($t$-)henselian topology on any ($t$-)he"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.8156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-30T18:50:30Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5ef45f695b345209fe39d845b2ae1ceadde9de90224f26ceffd35834fbb5e8fc","abstract_canon_sha256":"b8c8485471cc821963dc94602b5666cb6c592edc533d4fbd9274b1d54958748c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:53.567395Z","signature_b64":"Og31Y8tPV/o9edkqLXJKZ0Ll070CoZ4gvfMGbALAA2CQZMQW6mgTBib522Ya02hYFqV/VEBCVvCGadcDVWC4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"874f5417535da8c8c3d9441840b9e3f3749d61b1526415cf58cb4b4082b7a36b","last_reissued_at":"2026-05-18T02:32:53.566755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:53.566755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformly defining $p$-henselian valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Franziska Jahnke, Jochen Koenigsmann","submitted_at":"2014-07-30T18:50:30Z","abstract_excerpt":"Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply this to show that there is a definable valuation inducing the ($t$-)henselian topology on any ($t$-)he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8156","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.8156","created_at":"2026-05-18T02:32:53.566838+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.8156v2","created_at":"2026-05-18T02:32:53.566838+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8156","created_at":"2026-05-18T02:32:53.566838+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5HVIF2TLWUM","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5HVIF2TLWUMRQ6Z","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5HVIF2T","created_at":"2026-05-18T12:28:43.426989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N","json":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N.json","graph_json":"https://pith.science/api/pith-number/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/graph.json","events_json":"https://pith.science/api/pith-number/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/events.json","paper":"https://pith.science/paper/Q5HVIF2T"},"agent_actions":{"view_html":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N","download_json":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N.json","view_paper":"https://pith.science/paper/Q5HVIF2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.8156&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/action/storage_attestation","attest_author":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/action/author_attestation","sign_citation":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/action/citation_signature","submit_replication":"https://pith.science/pith/Q5HVIF2TLWUMRQ6ZIQMEBOPD6N/action/replication_record"}},"created_at":"2026-05-18T02:32:53.566838+00:00","updated_at":"2026-05-18T02:32:53.566838+00:00"}