{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A7L2VRW5SJOZA7MN7RPWDXMWSH","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":"5d68aac2d3fc92c9be807f308bc3cfd3e71714965a5f23e4d5a24c129811b689","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-22T14:53:41Z","title_canon_sha256":"71468b34b388c0d4d910d9bc39550f03a6f4fcfdcf922868f5d06eb0ab09a5ce"},"schema_version":"1.0","source":{"id":"1810.09333","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09333","created_at":"2026-05-17T23:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09333v2","created_at":"2026-05-17T23:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09333","created_at":"2026-05-17T23:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"A7L2VRW5SJOZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A7L2VRW5SJOZA7MN","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A7L2VRW5","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:790914372c8a8f97dcb1dd441d694a46f12260b731901a210b460f80f3a666ee","target":"graph","created_at":"2026-05-17T23:49:03Z","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 give a construction of a large first-order definable family of subrings of finitely generated fields $K$ of any characteristic. We deduce that for any such $K$ there exists a first-order sentence $\\varphi_K$ characterising $K$ in the class of finitely generated fields, i.e. such that for any finitely generated field $L$ we have $L \\models \\varphi_K$ if and only if $L \\cong K$. This answers a question considered by Pop and others. In characteristic two, our results depend on resolution of singularities, whereas they are unconditional in all other characteristics.","authors_text":"Philip Dittmann","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-22T14:53:41Z","title":"Defining Subrings in Finitely Generated Fields of All Characteristics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09333","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:c4380bf709c9e8345492a349f4031d7038123eb9f148b5b860412866edc39559","target":"record","created_at":"2026-05-17T23:49:03Z","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":"5d68aac2d3fc92c9be807f308bc3cfd3e71714965a5f23e4d5a24c129811b689","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-22T14:53:41Z","title_canon_sha256":"71468b34b388c0d4d910d9bc39550f03a6f4fcfdcf922868f5d06eb0ab09a5ce"},"schema_version":"1.0","source":{"id":"1810.09333","kind":"arxiv","version":2}},"canonical_sha256":"07d7aac6dd925d907d8dfc5f61dd9691e7349711e474dddd182086d14aafce2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07d7aac6dd925d907d8dfc5f61dd9691e7349711e474dddd182086d14aafce2e","first_computed_at":"2026-05-17T23:49:03.182486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:03.182486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LiJyEtAY3+5Aa55vveHnBH23NGMNrjnvI3EJR0bwnNjps22y/AbS0MpVD/a+iXnIC1r1uwsQSmiUePBxxC38CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:03.182879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09333","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4380bf709c9e8345492a349f4031d7038123eb9f148b5b860412866edc39559","sha256:790914372c8a8f97dcb1dd441d694a46f12260b731901a210b460f80f3a666ee"],"state_sha256":"a2f8baa9add3b3b1377352bb828547ecd6ec861a36d317823bd370ce34d3cd97"}