{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:HQGZN54V5RYKDZUVOHNWMADCBD","short_pith_number":"pith:HQGZN54V","schema_version":"1.0","canonical_sha256":"3c0d96f795ec70a1e69571db66006208ef09883ae4955c2c5c1e0267a3128011","source":{"kind":"arxiv","id":"0707.3151","version":10},"attestation_state":"computed","paper":{"title":"Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Arno van den Essen, David Wright, Joost Berson","submitted_at":"2007-07-23T17:42:17Z","abstract_excerpt":"In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger results are obtained. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if A is a Q-algebra. Another crucial ingredient, of interest in itself, is that stable tameness is a local property: If an automorphism is locally tame, then it is stably tame."},"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":"0707.3151","kind":"arxiv","version":10},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2007-07-23T17:42:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a9acb56de0ef2f4c2890fd551e61c5cf4fce1972187eb5871982ff8b289385e4","abstract_canon_sha256":"b6618f5c20210d4fa3c88eb424f136475fead1dfe2817b53a59b5818db3e145b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:37.561029Z","signature_b64":"DkWixuIHmtMReIVieuOVJcKJR0SCNwhGw5Qr/CA0TKt+ibtrjXTTQ7NJ+wP+X0RX0YRiVwfs+pBzvwvpt1IEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c0d96f795ec70a1e69571db66006208ef09883ae4955c2c5c1e0267a3128011","last_reissued_at":"2026-05-18T03:57:37.560504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:37.560504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Arno van den Essen, David Wright, Joost Berson","submitted_at":"2007-07-23T17:42:17Z","abstract_excerpt":"In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger results are obtained. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if A is a Q-algebra. Another crucial ingredient, of interest in itself, is that stable tameness is a local property: If an automorphism is locally tame, then it is stably tame."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3151","kind":"arxiv","version":10},"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":"0707.3151","created_at":"2026-05-18T03:57:37.560582+00:00"},{"alias_kind":"arxiv_version","alias_value":"0707.3151v10","created_at":"2026-05-18T03:57:37.560582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3151","created_at":"2026-05-18T03:57:37.560582+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQGZN54V5RYK","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQGZN54V5RYKDZUV","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQGZN54V","created_at":"2026-05-18T12:25:55.427421+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/HQGZN54V5RYKDZUVOHNWMADCBD","json":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD.json","graph_json":"https://pith.science/api/pith-number/HQGZN54V5RYKDZUVOHNWMADCBD/graph.json","events_json":"https://pith.science/api/pith-number/HQGZN54V5RYKDZUVOHNWMADCBD/events.json","paper":"https://pith.science/paper/HQGZN54V"},"agent_actions":{"view_html":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD","download_json":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD.json","view_paper":"https://pith.science/paper/HQGZN54V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0707.3151&json=true","fetch_graph":"https://pith.science/api/pith-number/HQGZN54V5RYKDZUVOHNWMADCBD/graph.json","fetch_events":"https://pith.science/api/pith-number/HQGZN54V5RYKDZUVOHNWMADCBD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD/action/storage_attestation","attest_author":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD/action/author_attestation","sign_citation":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD/action/citation_signature","submit_replication":"https://pith.science/pith/HQGZN54V5RYKDZUVOHNWMADCBD/action/replication_record"}},"created_at":"2026-05-18T03:57:37.560582+00:00","updated_at":"2026-05-18T03:57:37.560582+00:00"}