{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CM33C6LHFFSISLVP47HPD2GWYQ","short_pith_number":"pith:CM33C6LH","schema_version":"1.0","canonical_sha256":"1337b179672964892eafe7cef1e8d6c40f83879388f357f77c22371bc03daea9","source":{"kind":"arxiv","id":"1503.02189","version":1},"attestation_state":"computed","paper":{"title":"Splitting methods in algebraic logic: Proving results on non-atom-canonicity, non-finite axiomatizability and non-first oder definability for cylindric and relation algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2015-03-07T16:52:07Z","abstract_excerpt":"We deal with various splitting methods in algebraic logic. The word `splitting' refers to splitting some of the atoms in a given relation or cylindric algebra each into one or more subatoms obtaining a bigger algebra, where the number of subatoms obtained after splitting is adjusted for a certain combinatorial purpose. This number (of subatoms) can be an infinite cardinal. The idea originates with Leon Henkin. Splitting methods existing in a scattered form in the literature, possibly under different names, proved useful in obtaining (negative) results on non-atom canonicity, non-finite axiomat"},"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":"1503.02189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-07T16:52:07Z","cross_cats_sorted":[],"title_canon_sha256":"2df555e8527d7aad59006ed0b7b27e978f5cc412bb5c512a5d2793583b0cf548","abstract_canon_sha256":"fbfa12f30441988525f2d329b1e2c70fbbbb12ef7b7a036238d78d278a632e03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:25.661426Z","signature_b64":"/YqeXrpocY25WIIvweikv+lVNELSPIZgT7z2ri/jLxN91JeuE9fUsj/exNB7aSHgdfXTXO8Eh1AeS4F0OEtjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1337b179672964892eafe7cef1e8d6c40f83879388f357f77c22371bc03daea9","last_reissued_at":"2026-05-18T02:25:25.660977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:25.660977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Splitting methods in algebraic logic: Proving results on non-atom-canonicity, non-finite axiomatizability and non-first oder definability for cylindric and relation algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2015-03-07T16:52:07Z","abstract_excerpt":"We deal with various splitting methods in algebraic logic. The word `splitting' refers to splitting some of the atoms in a given relation or cylindric algebra each into one or more subatoms obtaining a bigger algebra, where the number of subatoms obtained after splitting is adjusted for a certain combinatorial purpose. This number (of subatoms) can be an infinite cardinal. The idea originates with Leon Henkin. Splitting methods existing in a scattered form in the literature, possibly under different names, proved useful in obtaining (negative) results on non-atom canonicity, non-finite axiomat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02189","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":"1503.02189","created_at":"2026-05-18T02:25:25.661038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02189v1","created_at":"2026-05-18T02:25:25.661038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02189","created_at":"2026-05-18T02:25:25.661038+00:00"},{"alias_kind":"pith_short_12","alias_value":"CM33C6LHFFSI","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CM33C6LHFFSISLVP","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CM33C6LH","created_at":"2026-05-18T12:29:17.054201+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/CM33C6LHFFSISLVP47HPD2GWYQ","json":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ.json","graph_json":"https://pith.science/api/pith-number/CM33C6LHFFSISLVP47HPD2GWYQ/graph.json","events_json":"https://pith.science/api/pith-number/CM33C6LHFFSISLVP47HPD2GWYQ/events.json","paper":"https://pith.science/paper/CM33C6LH"},"agent_actions":{"view_html":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ","download_json":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ.json","view_paper":"https://pith.science/paper/CM33C6LH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02189&json=true","fetch_graph":"https://pith.science/api/pith-number/CM33C6LHFFSISLVP47HPD2GWYQ/graph.json","fetch_events":"https://pith.science/api/pith-number/CM33C6LHFFSISLVP47HPD2GWYQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ/action/storage_attestation","attest_author":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ/action/author_attestation","sign_citation":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ/action/citation_signature","submit_replication":"https://pith.science/pith/CM33C6LHFFSISLVP47HPD2GWYQ/action/replication_record"}},"created_at":"2026-05-18T02:25:25.661038+00:00","updated_at":"2026-05-18T02:25:25.661038+00:00"}