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This error does not, however, affect the geometric characterization given in Theorem 3.4 but only the attempt in Theorem 4.3 to express it as a first-order set of axioms. That attempt is incorrect; the main problem being that in general {\\tau}V(f_1,..., f_s) 6= V(f_1..., f_s, {\\tau}f_1,..., {\\tau}f_s). But a different, indeed simpler, set of first-order axioms, which we will now describe, does express the geometric charact"},"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":"1210.3258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-11T14:37:47Z","cross_cats_sorted":[],"title_canon_sha256":"374a07accabc549b204989e1994ad5c9dcc9ba29a5ce15b0a346e7684bab3099","abstract_canon_sha256":"f6fac29eb1d5f3caeecd9a21bef461aab8cb879cbb8c7be3ea688bbecf0b051e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:27.877800Z","signature_b64":"I8Em8Y5213G3LjcuO+T+87HIaZwEgEeSpESM2BZu5nZo2ys9JdY+1pPsMbM97vor5JhlYWnLmgM7dt+4NCY9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6625278170e0dacaf84276f73f95bc2282b2ccea79ff2d26818709174be2642e","last_reissued_at":"2026-05-18T03:43:27.877240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:27.877240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Corrigendum to the paper: Geometric Axioms for Differentially Closed Fields with Several Commuting Derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Omar Leon Sanchez","submitted_at":"2012-10-11T14:37:47Z","abstract_excerpt":"In the proof of Lemma 2.6 (2) the iteration of the map {\\tau} was not performed\nproperly and in fact the lemma is wrong; a counterexample is given by f = \\bar{x}_1and k = 2. This error does not, however, affect the geometric characterization given in Theorem 3.4 but only the attempt in Theorem 4.3 to express it as a first-order set of axioms. That attempt is incorrect; the main problem being that in general {\\tau}V(f_1,..., f_s) 6= V(f_1..., f_s, {\\tau}f_1,..., {\\tau}f_s). But a different, indeed simpler, set of first-order axioms, which we will now describe, does express the geometric charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3258","kind":"arxiv","version":1},"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":"1210.3258","created_at":"2026-05-18T03:43:27.877325+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.3258v1","created_at":"2026-05-18T03:43:27.877325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3258","created_at":"2026-05-18T03:43:27.877325+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYSSPALQ4DNM","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYSSPALQ4DNMV6CC","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYSSPALQ","created_at":"2026-05-18T12:27:14.488303+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/MYSSPALQ4DNMV6CCO33T7FN4EK","json":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK.json","graph_json":"https://pith.science/api/pith-number/MYSSPALQ4DNMV6CCO33T7FN4EK/graph.json","events_json":"https://pith.science/api/pith-number/MYSSPALQ4DNMV6CCO33T7FN4EK/events.json","paper":"https://pith.science/paper/MYSSPALQ"},"agent_actions":{"view_html":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK","download_json":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK.json","view_paper":"https://pith.science/paper/MYSSPALQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.3258&json=true","fetch_graph":"https://pith.science/api/pith-number/MYSSPALQ4DNMV6CCO33T7FN4EK/graph.json","fetch_events":"https://pith.science/api/pith-number/MYSSPALQ4DNMV6CCO33T7FN4EK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK/action/storage_attestation","attest_author":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK/action/author_attestation","sign_citation":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK/action/citation_signature","submit_replication":"https://pith.science/pith/MYSSPALQ4DNMV6CCO33T7FN4EK/action/replication_record"}},"created_at":"2026-05-18T03:43:27.877325+00:00","updated_at":"2026-05-18T03:43:27.877325+00:00"}