{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UOOGIGIY3OCK4K644IWLKFRM7M","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":"78bee13afbf91c5fe8fccb10be3ba2b5d6bb77d1522f9d3d87a9387f794abcc8","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-26T10:28:34Z","title_canon_sha256":"80e9e31d51894846b804efb1d459a862beac682a7a40cb6969c0015379329691"},"schema_version":"1.0","source":{"id":"1304.7117","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7117","created_at":"2026-05-18T02:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7117v4","created_at":"2026-05-18T02:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7117","created_at":"2026-05-18T02:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"UOOGIGIY3OCK","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UOOGIGIY3OCK4K64","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UOOGIGIY","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:086b0dc71119aeb119e77f73fa51568486b0ebea8d324fcdadca13ca73ef4e68","target":"graph","created_at":"2026-05-18T02:39:25Z","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":"It is an immediate conclusion from Bavula's papers \\cite{Bavula:GWA-def}, \\cite{Bavula:GWA-tensor-product} that if a generalized Weyl algebra $A=\\kk[z;\\lambda,\\eta,\\varphi(z)]$ is homologically smooth, then the polynomial $\\varphi(z)$ has no multiple roots. We prove in this paper that the converse is also true. Moreover, formal deformations of $A$ are studied when $\\kk$ is of characteristic zero.","authors_text":"Liyu Liu","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-26T10:28:34Z","title":"Homological smoothness and deformations of generalized Weyl algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7117","kind":"arxiv","version":4},"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":"sha256:92f2ac63b59f161b90c6b3628a4c1d0691f83b478eb6d08c2e6c2f2418df0b99","target":"record","created_at":"2026-05-18T02:39:25Z","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":"78bee13afbf91c5fe8fccb10be3ba2b5d6bb77d1522f9d3d87a9387f794abcc8","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-26T10:28:34Z","title_canon_sha256":"80e9e31d51894846b804efb1d459a862beac682a7a40cb6969c0015379329691"},"schema_version":"1.0","source":{"id":"1304.7117","kind":"arxiv","version":4}},"canonical_sha256":"a39c641918db84ae2bdce22cb5162cfb08043b1fb52aeec70df2ae9ef4d7f3f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a39c641918db84ae2bdce22cb5162cfb08043b1fb52aeec70df2ae9ef4d7f3f0","first_computed_at":"2026-05-18T02:39:25.746487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:25.746487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hXi9tdYY3ZeYSQ/zX99s5Mqhiy/y8k0WBNPbSptcLkAjFE2U4DNsorlVZFVbp9rI5KSF2m/BRE8Pq8eFs/fKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:25.746879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7117","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92f2ac63b59f161b90c6b3628a4c1d0691f83b478eb6d08c2e6c2f2418df0b99","sha256:086b0dc71119aeb119e77f73fa51568486b0ebea8d324fcdadca13ca73ef4e68"],"state_sha256":"d86cced9457623e8774bd4060fe11d1720a7023dd3b3783e64bbdbd380a2f0ff"}