{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WAKTX7GYUISEKGEHH4M5P6YFZ7","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":"e637b4818d572d597e576106ce08ad3a7afd17b78de21aa3872c9338bcbc7bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-14T17:43:42Z","title_canon_sha256":"954a1f47c9aff9ff78df019565a875990c834651d2a3931b4b684c4dce5e5a4e"},"schema_version":"1.0","source":{"id":"1307.4298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4298","created_at":"2026-05-18T03:18:19Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4298v1","created_at":"2026-05-18T03:18:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4298","created_at":"2026-05-18T03:18:19Z"},{"alias_kind":"pith_short_12","alias_value":"WAKTX7GYUISE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WAKTX7GYUISEKGEH","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WAKTX7GY","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:b9881afe307cb77434214941e15a8d4af7c0b302e05cd0f5f6d22c9be6cc32cf","target":"graph","created_at":"2026-05-18T03:18:19Z","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":"In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric basis of relation algebras, both algebras are based on one graph such that both the relation and cylindric algebras are representable if and only if the chromatic number of the graph is infinite. We also relate the syntactic notion of algebras having a (complete) neat embedding property to the semantical notion of having various forms of (complete) relativized r","authors_text":"Mohammed Khaled, Tarek Sayed Ahmed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-14T17:43:42Z","title":"Strongly representable atom structures and neat embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4298","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:b4c484182811632b7b38da836dfa1b0ab38bac551915a76f80559984762217d5","target":"record","created_at":"2026-05-18T03:18:19Z","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":"e637b4818d572d597e576106ce08ad3a7afd17b78de21aa3872c9338bcbc7bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-14T17:43:42Z","title_canon_sha256":"954a1f47c9aff9ff78df019565a875990c834651d2a3931b4b684c4dce5e5a4e"},"schema_version":"1.0","source":{"id":"1307.4298","kind":"arxiv","version":1}},"canonical_sha256":"b0153bfcd8a2244518873f19d7fb05cfc04de07ec6f2873e985d8cdf816a2ade","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0153bfcd8a2244518873f19d7fb05cfc04de07ec6f2873e985d8cdf816a2ade","first_computed_at":"2026-05-18T03:18:19.186014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:19.186014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iXYmCN1YTHcc97yZYmXpgG0KC8cZglrsttvfo0GhL/Voji1HOqoKFt8ejgW0BwJDyO4z07gKoKBoB63fdG3tDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:19.186407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4c484182811632b7b38da836dfa1b0ab38bac551915a76f80559984762217d5","sha256:b9881afe307cb77434214941e15a8d4af7c0b302e05cd0f5f6d22c9be6cc32cf"],"state_sha256":"92210a23d77f3632aff49ab3c640497fd43ad5dd25d5c2bcc6dc0fc4489974d2"}