{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:74W2IQBWE75BGB46L56M3XBJNO","short_pith_number":"pith:74W2IQBW","schema_version":"1.0","canonical_sha256":"ff2da4403627fa13079e5f7ccddc296bab4cf5c43c9314c9c3241d05ef104310","source":{"kind":"arxiv","id":"1305.5151","version":1},"attestation_state":"computed","paper":{"title":"On neat atom structures for cylindric like algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2013-04-23T12:17:12Z","abstract_excerpt":"(1) Let 1\\leq k\\leq \\omega. Call an atom structure \\alpha weakly k neat representable, the term algebra is in \\RCA_n\\cap \\Nr_n\\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra \\A, such that \\At\\A=\\alpha, \\A\\in \\Nr_n\\CA_{\\omega} and for every algebra $\\B$ based on this atom structure there exists k\\in \\omega$, k\\geq 1, such that \\B\\in \\Nr_n\\CA_{n+k}.\n  (2) Let k\\leq \\omega. Call an atom structure \\alpha k complete, if there exists \\A such that \\At\\A=\\alpha and \\A\\in S_c\\Nr_n\\CA_{n+k}.\n  (3) Let k\\leq \\omega. Call an atom structure"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.5151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-23T12:17:12Z","cross_cats_sorted":[],"title_canon_sha256":"e68c7c38e9db1ba6876a7a9c75065b050cff4bd50a54585af9ebcd37ee8eb582","abstract_canon_sha256":"64212159ca99b5f6edafc62af2be5d3f58b4b7d9399948775c97f9550113a63b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:13.520498Z","signature_b64":"0RMB2mtgzCmHzi2K+/1jPynqyqVGwkPS+32qzN+E0DMpjOUaswLTNikVLRDVuuGBOhw7euHo4ok6BUY5yreiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff2da4403627fa13079e5f7ccddc296bab4cf5c43c9314c9c3241d05ef104310","last_reissued_at":"2026-05-18T03:25:13.519780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:13.519780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On neat atom structures for cylindric like algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2013-04-23T12:17:12Z","abstract_excerpt":"(1) Let 1\\leq k\\leq \\omega. Call an atom structure \\alpha weakly k neat representable, the term algebra is in \\RCA_n\\cap \\Nr_n\\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra \\A, such that \\At\\A=\\alpha, \\A\\in \\Nr_n\\CA_{\\omega} and for every algebra $\\B$ based on this atom structure there exists k\\in \\omega$, k\\geq 1, such that \\B\\in \\Nr_n\\CA_{n+k}.\n  (2) Let k\\leq \\omega. Call an atom structure \\alpha k complete, if there exists \\A such that \\At\\A=\\alpha and \\A\\in S_c\\Nr_n\\CA_{n+k}.\n  (3) Let k\\leq \\omega. Call an atom structure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5151","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.5151","created_at":"2026-05-18T03:25:13.519894+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5151v1","created_at":"2026-05-18T03:25:13.519894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5151","created_at":"2026-05-18T03:25:13.519894+00:00"},{"alias_kind":"pith_short_12","alias_value":"74W2IQBWE75B","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"74W2IQBWE75BGB46","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"74W2IQBW","created_at":"2026-05-18T12:27:36.564083+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO","json":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO.json","graph_json":"https://pith.science/api/pith-number/74W2IQBWE75BGB46L56M3XBJNO/graph.json","events_json":"https://pith.science/api/pith-number/74W2IQBWE75BGB46L56M3XBJNO/events.json","paper":"https://pith.science/paper/74W2IQBW"},"agent_actions":{"view_html":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO","download_json":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO.json","view_paper":"https://pith.science/paper/74W2IQBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5151&json=true","fetch_graph":"https://pith.science/api/pith-number/74W2IQBWE75BGB46L56M3XBJNO/graph.json","fetch_events":"https://pith.science/api/pith-number/74W2IQBWE75BGB46L56M3XBJNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO/action/storage_attestation","attest_author":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO/action/author_attestation","sign_citation":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO/action/citation_signature","submit_replication":"https://pith.science/pith/74W2IQBWE75BGB46L56M3XBJNO/action/replication_record"}},"created_at":"2026-05-18T03:25:13.519894+00:00","updated_at":"2026-05-18T03:25:13.519894+00:00"}