{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZCXDESSRBOJIS4J2HCMHJH2OHS","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":"d16d2bb13a56db96ee6fd553210012b957fbeccbde865a8214af0d63444e5929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-18T17:57:16Z","title_canon_sha256":"28352e165cfd6e0b6dae68f1202b10e55167e37cebcfd18428a19e3ecbc6f3f4"},"schema_version":"1.0","source":{"id":"1601.04625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04625","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04625v2","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04625","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZCXDESSRBOJI","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZCXDESSRBOJIS4J2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZCXDESSR","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:3d0f47bd4da7b71544d2834dbd935df5fc3de1b6cef2905bfc506965d84735ab","target":"graph","created_at":"2026-05-18T00:50:22Z","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":"A noncommutative analogue of the Zariski cancellation problem asks whether $A[x]\\cong B[x]$ implies $A\\cong B$ when $A$ and $B$ are noncommutative algebras. We resolve this affirmatively in the case when $A$ is a noncommutative finitely generated domain over the complex field of Gelfand-Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin-Schelter regular algebras of higher Gelfand-Kirillov dimension.","authors_text":"James J. Zhang, Jason Bell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-18T17:57:16Z","title":"Zariski Cancellation Problem for Noncommutative Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04625","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":"sha256:8894df80f63936ab4add8ba588d439788ad379b04a72366ef6658138d388d0fd","target":"record","created_at":"2026-05-18T00:50:22Z","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":"d16d2bb13a56db96ee6fd553210012b957fbeccbde865a8214af0d63444e5929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-18T17:57:16Z","title_canon_sha256":"28352e165cfd6e0b6dae68f1202b10e55167e37cebcfd18428a19e3ecbc6f3f4"},"schema_version":"1.0","source":{"id":"1601.04625","kind":"arxiv","version":2}},"canonical_sha256":"c8ae324a510b9289713a3898749f4e3c86cdb9cd72305491f05c20a67a8ca21e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8ae324a510b9289713a3898749f4e3c86cdb9cd72305491f05c20a67a8ca21e","first_computed_at":"2026-05-18T00:50:22.713049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:22.713049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m9AVmpi7nHdsBLL4BwaDdAQRpjGXZQ9lmL2yOJdkKVkmInJC0M14oFREJtLVhJeGeHI+J+vI7aX7y6pMCqP2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:22.713892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8894df80f63936ab4add8ba588d439788ad379b04a72366ef6658138d388d0fd","sha256:3d0f47bd4da7b71544d2834dbd935df5fc3de1b6cef2905bfc506965d84735ab"],"state_sha256":"ede5df9f63740f6afc8630cbc7d0f421c21de44a6f5527ee8734224758d21fd1"}