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From this construction (with R=K[z]) we obtain non tame automorphisms s of K[x,y,z] (where K is a field of characteristic 0) such that the sub-group generated by s and the affine automorphisms contains all tame automorphisms."},"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":"1206.5876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-06-26T02:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"c22643048c17dcc0371809f40fc4a43cec381e961c7218c096d122a96f6c65bc","abstract_canon_sha256":"915021fd8bcbd65689d4864cb91162cdad1c50afc66087dc0787954fe00a905e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:37.859340Z","signature_b64":"+7KFxFIpNnpqcnKKTZA8YtFIhEKKBmRbKpnYLjqjK1mgzn/G2b58E7r/38Om7H9uuhY/g3mVazqtwPow2LEIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dddadd6f36b8fd3e90f4e5e6fc608e9c2acad0aa47c7400457d11690e2621700","last_reissued_at":"2026-05-18T03:52:37.858544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:37.858544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coordinates of R[x,y]: Constructions and classifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eric Edo","submitted_at":"2012-06-26T02:49:00Z","abstract_excerpt":"Let R be a PID. 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From this construction (with R=K[z]) we obtain non tame automorphisms s of K[x,y,z] (where K is a field of characteristic 0) such that the sub-group generated by s and the affine automorphisms contains all tame automorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5876","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":"1206.5876","created_at":"2026-05-18T03:52:37.858662+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.5876v1","created_at":"2026-05-18T03:52:37.858662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5876","created_at":"2026-05-18T03:52:37.858662+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XNN23ZWXD6T","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XNN23ZWXD6T5EHU","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XNN23ZW","created_at":"2026-05-18T12:26:53.410803+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/3XNN23ZWXD6T5EHU4XTPYYEOTQ","json":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ.json","graph_json":"https://pith.science/api/pith-number/3XNN23ZWXD6T5EHU4XTPYYEOTQ/graph.json","events_json":"https://pith.science/api/pith-number/3XNN23ZWXD6T5EHU4XTPYYEOTQ/events.json","paper":"https://pith.science/paper/3XNN23ZW"},"agent_actions":{"view_html":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ","download_json":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ.json","view_paper":"https://pith.science/paper/3XNN23ZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.5876&json=true","fetch_graph":"https://pith.science/api/pith-number/3XNN23ZWXD6T5EHU4XTPYYEOTQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3XNN23ZWXD6T5EHU4XTPYYEOTQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ/action/storage_attestation","attest_author":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ/action/author_attestation","sign_citation":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ/action/citation_signature","submit_replication":"https://pith.science/pith/3XNN23ZWXD6T5EHU4XTPYYEOTQ/action/replication_record"}},"created_at":"2026-05-18T03:52:37.858662+00:00","updated_at":"2026-05-18T03:52:37.858662+00:00"}