{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HXOJ7SBIS2TBB5NIUWPL6RTESE","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":"d2d8f509f010e30f6ec78a37bf15b38e7e59b53ae769d2317daaffc093f2a06f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-11T07:39:55Z","title_canon_sha256":"8fddbd8ebb90cb168f431ddf3ce365a836b3329022137eabe08bf58452efa012"},"schema_version":"1.0","source":{"id":"1304.3625","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3625","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3625v1","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3625","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"HXOJ7SBIS2TB","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HXOJ7SBIS2TBB5NI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HXOJ7SBI","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:2ee83695cee393a6ab014086495b5f8e4a3c22fc7ebf5cb4d0162aa03aa2e969","target":"graph","created_at":"2026-05-18T03:28:07Z","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 give a sufficient condition that implies that SNr_nCA_{n+k}, n\\geq 3, k\\geq 3 (both finite)is not closed under completions. We compare this condition to existing results in literature.","authors_text":"Tarek Sayed Ahmed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-11T07:39:55Z","title":"On completions of algebras in SNr_nCA_{n+k}, n\\geq 3, k\\geq 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3625","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":"sha256:824dd25bd5180cb4f8889ee08edbdb6bf49606a9e56c1605182f73af4465a112","target":"record","created_at":"2026-05-18T03:28:07Z","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":"d2d8f509f010e30f6ec78a37bf15b38e7e59b53ae769d2317daaffc093f2a06f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-11T07:39:55Z","title_canon_sha256":"8fddbd8ebb90cb168f431ddf3ce365a836b3329022137eabe08bf58452efa012"},"schema_version":"1.0","source":{"id":"1304.3625","kind":"arxiv","version":1}},"canonical_sha256":"3ddc9fc82896a610f5a8a59ebf466491317a4b580022a594b0695058251e5534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddc9fc82896a610f5a8a59ebf466491317a4b580022a594b0695058251e5534","first_computed_at":"2026-05-18T03:28:07.029448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:07.029448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hjsBK9Gp9ooGckridvIOveG5WqDy8XgCyY9bIRkemcFEGsTolk3D+F4a+VU+jzcN56pSKdY8fEk/q2BBNVmmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:07.030154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3625","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:824dd25bd5180cb4f8889ee08edbdb6bf49606a9e56c1605182f73af4465a112","sha256:2ee83695cee393a6ab014086495b5f8e4a3c22fc7ebf5cb4d0162aa03aa2e969"],"state_sha256":"04e8f79853b9b208fa63033f00a253a40e585f7d928922ebd43e9b14a2767ac3"}