{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WQ6APDNEYJJUBUZ2SDUU5LZ6AF","short_pith_number":"pith:WQ6APDNE","schema_version":"1.0","canonical_sha256":"b43c078da4c25340d33a90e94eaf3e0160a5901c4e24a3662e4edfceef2776eb","source":{"kind":"arxiv","id":"1011.3349","version":4},"attestation_state":"computed","paper":{"title":"On the lifting of the Nagata automorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.AC","authors_text":"Alexei Belov-Kanel, Jie-Tai Yu","submitted_at":"2010-11-15T11:45:39Z","abstract_excerpt":"It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra $F[x,y,z]$ over a field $F$ cannot be lifted to a $z$-automorphism ($z$-coordinate, respectively) of the free associative algebra $K<x,y,z>$. The proof is based on the following two new results which have their own interests: degree estimate of ${Q*_FF<x_1,...,x_n>}$ and tameness of the automorphism group ${\\text{Aut}_Q(Q*_FF<x,y>)}$."},"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":"1011.3349","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-11-15T11:45:39Z","cross_cats_sorted":["math.AG","math.RA"],"title_canon_sha256":"f0c0ce283132b933665739baeb0138c682e1fa7b3f6240aab0e17defca8bb2f1","abstract_canon_sha256":"55b7ec6e05956feda6be1a89aabdfd368c3570e18e6bbf629cb316bbcc0fe2d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:06.157994Z","signature_b64":"PSyS2575rrn2FzmraqwKTl4slLfWN9aUmSHGdn4lc+C7EQbCGJGy4DdfQDbkumKoR6Dx4TqNy+FPjKCUmdmeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b43c078da4c25340d33a90e94eaf3e0160a5901c4e24a3662e4edfceef2776eb","last_reissued_at":"2026-05-18T00:29:06.157458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:06.157458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the lifting of the Nagata automorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.AC","authors_text":"Alexei Belov-Kanel, Jie-Tai Yu","submitted_at":"2010-11-15T11:45:39Z","abstract_excerpt":"It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra $F[x,y,z]$ over a field $F$ cannot be lifted to a $z$-automorphism ($z$-coordinate, respectively) of the free associative algebra $K<x,y,z>$. The proof is based on the following two new results which have their own interests: degree estimate of ${Q*_FF<x_1,...,x_n>}$ and tameness of the automorphism group ${\\text{Aut}_Q(Q*_FF<x,y>)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3349","kind":"arxiv","version":4},"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":"1011.3349","created_at":"2026-05-18T00:29:06.157539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3349v4","created_at":"2026-05-18T00:29:06.157539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3349","created_at":"2026-05-18T00:29:06.157539+00:00"},{"alias_kind":"pith_short_12","alias_value":"WQ6APDNEYJJU","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"WQ6APDNEYJJUBUZ2","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"WQ6APDNE","created_at":"2026-05-18T12:26:17.028572+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/WQ6APDNEYJJUBUZ2SDUU5LZ6AF","json":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF.json","graph_json":"https://pith.science/api/pith-number/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/graph.json","events_json":"https://pith.science/api/pith-number/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/events.json","paper":"https://pith.science/paper/WQ6APDNE"},"agent_actions":{"view_html":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF","download_json":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF.json","view_paper":"https://pith.science/paper/WQ6APDNE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3349&json=true","fetch_graph":"https://pith.science/api/pith-number/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/graph.json","fetch_events":"https://pith.science/api/pith-number/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/action/storage_attestation","attest_author":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/action/author_attestation","sign_citation":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/action/citation_signature","submit_replication":"https://pith.science/pith/WQ6APDNEYJJUBUZ2SDUU5LZ6AF/action/replication_record"}},"created_at":"2026-05-18T00:29:06.157539+00:00","updated_at":"2026-05-18T00:29:06.157539+00:00"}