{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZWTZ2I3G2N243QEP65XEVETDSJ","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":"c3d051ad4ffb4282004dec71e17fb0ef45671b984a6a623a56a13abda0e70e73","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-16T22:45:53Z","title_canon_sha256":"acdfa16e264455575c4a4963247b332d77d3e4e3d25b419f16eda42e9cedc2b4"},"schema_version":"1.0","source":{"id":"1404.4399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4399","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4399v1","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4399","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZWTZ2I3G2N24","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZWTZ2I3G2N243QEP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZWTZ2I3G","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f9bc23f197d31b65245ad0db5a6026b5769e0792c144a329c06a163023830b8b","target":"graph","created_at":"2026-05-18T01:22:24Z","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":"We show that locally acyclic cluster algebras have (at worst) canonical singularities. In fact, we prove that locally acyclic cluster algebras of positive characteristic are strongly F-regular. In addition, we show that upper cluster algebras are always Frobenius split by a canonically defined splitting, and that they have a free canonical module of rank one. We also give examples to show that not all upper cluster algebras are F-regular if the local acyclicity is dropped.","authors_text":"Ang\\'elica Benito, Greg Muller, Jenna Rajchgot, Karen E. Smith","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-16T22:45:53Z","title":"Singularities of locally acyclic cluster algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4399","kind":"arxiv","version":1},"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:c9af485da081afdb602e051da1db570ff2e03c59d8f7cf06122e40232af49131","target":"record","created_at":"2026-05-18T01:22:24Z","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":"c3d051ad4ffb4282004dec71e17fb0ef45671b984a6a623a56a13abda0e70e73","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-16T22:45:53Z","title_canon_sha256":"acdfa16e264455575c4a4963247b332d77d3e4e3d25b419f16eda42e9cedc2b4"},"schema_version":"1.0","source":{"id":"1404.4399","kind":"arxiv","version":1}},"canonical_sha256":"cda79d2366d375cdc08ff76e4a9263925e5c031a53ab42db27cbda574eb50bff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cda79d2366d375cdc08ff76e4a9263925e5c031a53ab42db27cbda574eb50bff","first_computed_at":"2026-05-18T01:22:24.098202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:24.098202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iHZYRCyA46ZpYUTOROkcJ9j+noQ1an9wFGTYAfky7wGKVRODgP5IMcq9uvLfUWUqRPGFOSlnlkk8muiF9NKKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:24.098922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9af485da081afdb602e051da1db570ff2e03c59d8f7cf06122e40232af49131","sha256:f9bc23f197d31b65245ad0db5a6026b5769e0792c144a329c06a163023830b8b"],"state_sha256":"cbc4ae4a545881a52b0ab001fef8e10912e188e051de475c29d8b7a13ee23231"}