{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NG26SPNR5VKU4ZZHTBK55LXPRI","short_pith_number":"pith:NG26SPNR","schema_version":"1.0","canonical_sha256":"69b5e93db1ed554e67279855deaeef8a0ff2be3038bf43babf2bbfdb49cc0171","source":{"kind":"arxiv","id":"1803.09116","version":1},"attestation_state":"computed","paper":{"title":"Uniform interpolation and coherence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"George Metcalfe, Tomasz Kowalski","submitted_at":"2018-03-24T14:11:08Z","abstract_excerpt":"A variety V is said to be coherent if any finitely generated subalgebra of a finitely presented member of V is finitely presented. It is shown here that V is coherent if and only if it satisfies a restricted form of uniform deductive interpolation: that is, any compact congruence on a finitely generated free algebra of V restricted to a free algebra over a subset of the generators is again compact. A general criterion is obtained for establishing failures of coherence, and hence also of uniform deductive interpolation. This criterion is then used in conjunction with properties of canonical ext"},"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":"1803.09116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-24T14:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"a8062df4b333f631c4d0a82fa71298801cd179bfdb185c4dd9517668b4f37f08","abstract_canon_sha256":"2db980c8ec4717d57728e1df311d3bc894260111a944e50bf231bdc3a9fe6446"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:12.580174Z","signature_b64":"vS7A1Tg77ZqVlDrmFl3yFGmR9ueuGFuS5fpzd1P76tteYA/Z354AskgMQlYDaCZcdNgw5eys2ZhVJkpXGX+HBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69b5e93db1ed554e67279855deaeef8a0ff2be3038bf43babf2bbfdb49cc0171","last_reissued_at":"2026-05-18T00:20:12.579673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:12.579673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform interpolation and coherence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"George Metcalfe, Tomasz Kowalski","submitted_at":"2018-03-24T14:11:08Z","abstract_excerpt":"A variety V is said to be coherent if any finitely generated subalgebra of a finitely presented member of V is finitely presented. It is shown here that V is coherent if and only if it satisfies a restricted form of uniform deductive interpolation: that is, any compact congruence on a finitely generated free algebra of V restricted to a free algebra over a subset of the generators is again compact. A general criterion is obtained for establishing failures of coherence, and hence also of uniform deductive interpolation. This criterion is then used in conjunction with properties of canonical ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09116","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":"1803.09116","created_at":"2026-05-18T00:20:12.579749+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09116v1","created_at":"2026-05-18T00:20:12.579749+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09116","created_at":"2026-05-18T00:20:12.579749+00:00"},{"alias_kind":"pith_short_12","alias_value":"NG26SPNR5VKU","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NG26SPNR5VKU4ZZH","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NG26SPNR","created_at":"2026-05-18T12:32:40.477152+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/NG26SPNR5VKU4ZZHTBK55LXPRI","json":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI.json","graph_json":"https://pith.science/api/pith-number/NG26SPNR5VKU4ZZHTBK55LXPRI/graph.json","events_json":"https://pith.science/api/pith-number/NG26SPNR5VKU4ZZHTBK55LXPRI/events.json","paper":"https://pith.science/paper/NG26SPNR"},"agent_actions":{"view_html":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI","download_json":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI.json","view_paper":"https://pith.science/paper/NG26SPNR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09116&json=true","fetch_graph":"https://pith.science/api/pith-number/NG26SPNR5VKU4ZZHTBK55LXPRI/graph.json","fetch_events":"https://pith.science/api/pith-number/NG26SPNR5VKU4ZZHTBK55LXPRI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI/action/storage_attestation","attest_author":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI/action/author_attestation","sign_citation":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI/action/citation_signature","submit_replication":"https://pith.science/pith/NG26SPNR5VKU4ZZHTBK55LXPRI/action/replication_record"}},"created_at":"2026-05-18T00:20:12.579749+00:00","updated_at":"2026-05-18T00:20:12.579749+00:00"}