{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DKKPAHBUBBF2TZHNHHHUMUHLJG","short_pith_number":"pith:DKKPAHBU","schema_version":"1.0","canonical_sha256":"1a94f01c34084ba9e4ed39cf4650eb49b8bf0187e829cd4a740b9c37112879b0","source":{"kind":"arxiv","id":"1907.02398","version":2},"attestation_state":"computed","paper":{"title":"Metastable convergence and logical compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Eduardo Duenez, Jose Iovino, Xavier Caicedo","submitted_at":"2019-07-04T13:34:43Z","abstract_excerpt":"The concept of metastable convergence was identified by Tao;it allows converting theorems about convergence into stronger theorems about uniform convergence. The Uniform Metastability Principle (UMP) states that if $T$ is a theorem about convergence, then the fact that $T$ is valid implies automatically that its (stronger) uniform version is valid, provided that $T$ can be stated in certain logical frameworks. In this paper we identify precisely the logical frameworks $L$ for which UMP holds. More precisely, we prove that the UMP holds for $L$ if and only if $L$ is a compact logic. We also pro"},"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":"1907.02398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-04T13:34:43Z","cross_cats_sorted":[],"title_canon_sha256":"f8c27a664f787ac2e183ef033751ae2d0c519a62d4f8290f95ff500c4226ec4c","abstract_canon_sha256":"13e909d4cea4736bb0618223b6cc0e4e43241241ea5b633d5c496d51d8fa2e19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:07.020825Z","signature_b64":"eiQjaOGxUZHKI4mXWkwBpxpb4SgjbD/w9vuig5aDRby1kHgp9bUoPJbU5zUTSJgwReXG3hTsnTmxrKRF0a78Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a94f01c34084ba9e4ed39cf4650eb49b8bf0187e829cd4a740b9c37112879b0","last_reissued_at":"2026-05-17T23:41:07.020183Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:07.020183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metastable convergence and logical compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Eduardo Duenez, Jose Iovino, Xavier Caicedo","submitted_at":"2019-07-04T13:34:43Z","abstract_excerpt":"The concept of metastable convergence was identified by Tao;it allows converting theorems about convergence into stronger theorems about uniform convergence. The Uniform Metastability Principle (UMP) states that if $T$ is a theorem about convergence, then the fact that $T$ is valid implies automatically that its (stronger) uniform version is valid, provided that $T$ can be stated in certain logical frameworks. In this paper we identify precisely the logical frameworks $L$ for which UMP holds. More precisely, we prove that the UMP holds for $L$ if and only if $L$ is a compact logic. We also pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02398","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":""},"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":"1907.02398","created_at":"2026-05-17T23:41:07.020284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02398v2","created_at":"2026-05-17T23:41:07.020284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02398","created_at":"2026-05-17T23:41:07.020284+00:00"},{"alias_kind":"pith_short_12","alias_value":"DKKPAHBUBBF2","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DKKPAHBUBBF2TZHN","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DKKPAHBU","created_at":"2026-05-18T12:33:15.570797+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/DKKPAHBUBBF2TZHNHHHUMUHLJG","json":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG.json","graph_json":"https://pith.science/api/pith-number/DKKPAHBUBBF2TZHNHHHUMUHLJG/graph.json","events_json":"https://pith.science/api/pith-number/DKKPAHBUBBF2TZHNHHHUMUHLJG/events.json","paper":"https://pith.science/paper/DKKPAHBU"},"agent_actions":{"view_html":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG","download_json":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG.json","view_paper":"https://pith.science/paper/DKKPAHBU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02398&json=true","fetch_graph":"https://pith.science/api/pith-number/DKKPAHBUBBF2TZHNHHHUMUHLJG/graph.json","fetch_events":"https://pith.science/api/pith-number/DKKPAHBUBBF2TZHNHHHUMUHLJG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG/action/storage_attestation","attest_author":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG/action/author_attestation","sign_citation":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG/action/citation_signature","submit_replication":"https://pith.science/pith/DKKPAHBUBBF2TZHNHHHUMUHLJG/action/replication_record"}},"created_at":"2026-05-17T23:41:07.020284+00:00","updated_at":"2026-05-17T23:41:07.020284+00:00"}