{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:B7ZK7PQIEVRZJBXU7VXXFFL23L","short_pith_number":"pith:B7ZK7PQI","schema_version":"1.0","canonical_sha256":"0ff2afbe0825639486f4fd6f72957adae5e4c96e5aba60a4436ebcf19f9ad397","source":{"kind":"arxiv","id":"2512.21278","version":2},"attestation_state":"computed","paper":{"title":"Taking model-complete cores","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bertalan Bodor, Manuel Bodirsky, Paolo Marimon","submitted_at":"2025-12-24T16:49:10Z","abstract_excerpt":"A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; a core companion of a theory $T$ is a model-complete core theory $S$ such that every model of $T$ maps homomorphically to a model of $S$ and vice-versa. Whilst core companions may not exist in general, if they exist, they are unique. Moreover, $\\omega$-categorical theories always have a core companion, which is also $\\omega$-categorical. We show that many model-theoretic properties, such as stability, $\\mathrm{NIP}$, simplicity, and $\\mathrm{NSOP}_k"},"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":"2512.21278","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-12-24T16:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"2ce97db9fb49d32319413249063dc43f82ff5e802447607d5c4b17326cdef280","abstract_canon_sha256":"80703580dacbdf132997305a1bc5a6c49725d5030f38b55dba47a24d58acc605"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T01:24:27.309837Z","signature_b64":"TOfyak+50gSbMS3v7xNCdiL4o7IICRxMuM8MMh6t0Kxk2SV089IU3wvPa/QCTB4ooNcGWSMsGOyjgj7LMr6EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff2afbe0825639486f4fd6f72957adae5e4c96e5aba60a4436ebcf19f9ad397","last_reissued_at":"2026-07-29T01:24:27.308870Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T01:24:27.308870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Taking model-complete cores","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bertalan Bodor, Manuel Bodirsky, Paolo Marimon","submitted_at":"2025-12-24T16:49:10Z","abstract_excerpt":"A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; a core companion of a theory $T$ is a model-complete core theory $S$ such that every model of $T$ maps homomorphically to a model of $S$ and vice-versa. Whilst core companions may not exist in general, if they exist, they are unique. Moreover, $\\omega$-categorical theories always have a core companion, which is also $\\omega$-categorical. We show that many model-theoretic properties, such as stability, $\\mathrm{NIP}$, simplicity, and $\\mathrm{NSOP}_k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.21278","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.21278/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2512.21278","created_at":"2026-07-29T01:24:27.309329+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.21278v2","created_at":"2026-07-29T01:24:27.309329+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.21278","created_at":"2026-07-29T01:24:27.309329+00:00"},{"alias_kind":"pith_short_12","alias_value":"B7ZK7PQIEVRZ","created_at":"2026-07-29T01:24:27.309329+00:00"},{"alias_kind":"pith_short_16","alias_value":"B7ZK7PQIEVRZJBXU","created_at":"2026-07-29T01:24:27.309329+00:00"},{"alias_kind":"pith_short_8","alias_value":"B7ZK7PQI","created_at":"2026-07-29T01:24:27.309329+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2606.18533","citing_title":"On the notion of a patterning property in model theory","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28740","citing_title":"Some applications of the real strict order property hierarchy","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L","json":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L.json","graph_json":"https://pith.science/api/pith-number/B7ZK7PQIEVRZJBXU7VXXFFL23L/graph.json","events_json":"https://pith.science/api/pith-number/B7ZK7PQIEVRZJBXU7VXXFFL23L/events.json","paper":"https://pith.science/paper/B7ZK7PQI"},"agent_actions":{"view_html":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L","download_json":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L.json","view_paper":"https://pith.science/paper/B7ZK7PQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.21278&json=true","fetch_graph":"https://pith.science/api/pith-number/B7ZK7PQIEVRZJBXU7VXXFFL23L/graph.json","fetch_events":"https://pith.science/api/pith-number/B7ZK7PQIEVRZJBXU7VXXFFL23L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L/action/storage_attestation","attest_author":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L/action/author_attestation","sign_citation":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L/action/citation_signature","submit_replication":"https://pith.science/pith/B7ZK7PQIEVRZJBXU7VXXFFL23L/action/replication_record"}},"created_at":"2026-07-29T01:24:27.309329+00:00","updated_at":"2026-07-29T01:24:27.309329+00:00"}