{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JBHOZZGDFXSGZAGGNXNPDTVR3S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cd5d3e1ea0e702728180060f013c3ca432d91b9f414afd9acf0e5d6a05294326","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T21:45:16Z","title_canon_sha256":"5f0150ce18624959067fa171e442a5344e20228c2eebe01d810747d376f93931"},"schema_version":"1.0","source":{"id":"1204.2290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2290","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2290v1","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2290","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"JBHOZZGDFXSG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JBHOZZGDFXSGZAGG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JBHOZZGD","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:a95929c69ff9ada425a24399c00c13dcd31a688380a0dd0e67ac953c37b4719e","target":"graph","created_at":"2026-05-18T03:58:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n dimensional space X_n \\subset X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width d_n(F)_X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed ","authors_text":"Guergana Petrova, Przemyslaw Wojtaszczyk, Ronald DeVore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T21:45:16Z","title":"Greedy Algorithms for Reduced Bases in Banach Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2290","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ecc49864f53090467b41a28c42dc0cf133f543e4dfd0c981c812726eb4618f99","target":"record","created_at":"2026-05-18T03:58:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cd5d3e1ea0e702728180060f013c3ca432d91b9f414afd9acf0e5d6a05294326","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T21:45:16Z","title_canon_sha256":"5f0150ce18624959067fa171e442a5344e20228c2eebe01d810747d376f93931"},"schema_version":"1.0","source":{"id":"1204.2290","kind":"arxiv","version":1}},"canonical_sha256":"484eece4c32de46c80c66ddaf1ceb1dc99a1cb2e3dc14f6129c43850bcbc8c44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"484eece4c32de46c80c66ddaf1ceb1dc99a1cb2e3dc14f6129c43850bcbc8c44","first_computed_at":"2026-05-18T03:58:12.203066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:12.203066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sa7soZ/Q1DJfEzNu5GiIknjlLP0TrlS3DtG/+hyNcwe5pXGCOtJrZQcVZ9Jtr5Y+N7JY3UL8CO8SGPD5Zn9PBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:12.203533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecc49864f53090467b41a28c42dc0cf133f543e4dfd0c981c812726eb4618f99","sha256:a95929c69ff9ada425a24399c00c13dcd31a688380a0dd0e67ac953c37b4719e"],"state_sha256":"61805999b2c6cdc688b4e6b343ad86fca46a51ff1749ee8443e2d12a6181e807"}