{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ID3U7X2QLXUMKFHGXPZUX4JN3U","short_pith_number":"pith:ID3U7X2Q","schema_version":"1.0","canonical_sha256":"40f74fdf505de8c514e6bbf34bf12ddd23cf2761aac9c61f6ae8b9d0d1c29d01","source":{"kind":"arxiv","id":"1402.6750","version":2},"attestation_state":"computed","paper":{"title":"Tight Bounds for Averaging Multi-Frequency Differential Inclusions, Applied to Control Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ido Bright","submitted_at":"2014-02-27T00:20:43Z","abstract_excerpt":"We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of order O\\left(\\epsilon\\right) on the approximation error. These results are then applied to control systems consisting of a sum of time-periodic functions."},"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":"1402.6750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-02-27T00:20:43Z","cross_cats_sorted":[],"title_canon_sha256":"9bfe847b9e2ff17ac53a301e4701c3ae42c217ccc060107246ae1e64cbb029d6","abstract_canon_sha256":"06ec0f6c714ec8ee13c9635c960d446ddb21368bb7f5d0318793b6714c6a4556"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:51.425591Z","signature_b64":"zRirp8O5fxvs0d408+siPPIDCBM++nl4ozOyLwpvApAM/fmvDzRjr+HgNejL63WFPyPOP4CHXtCuQKHfN+itAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f74fdf505de8c514e6bbf34bf12ddd23cf2761aac9c61f6ae8b9d0d1c29d01","last_reissued_at":"2026-05-18T02:56:51.425163Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:51.425163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight Bounds for Averaging Multi-Frequency Differential Inclusions, Applied to Control Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ido Bright","submitted_at":"2014-02-27T00:20:43Z","abstract_excerpt":"We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of order O\\left(\\epsilon\\right) on the approximation error. These results are then applied to control systems consisting of a sum of time-periodic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6750","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":"1402.6750","created_at":"2026-05-18T02:56:51.425223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.6750v2","created_at":"2026-05-18T02:56:51.425223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6750","created_at":"2026-05-18T02:56:51.425223+00:00"},{"alias_kind":"pith_short_12","alias_value":"ID3U7X2QLXUM","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"ID3U7X2QLXUMKFHG","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"ID3U7X2Q","created_at":"2026-05-18T12:28:33.132498+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/ID3U7X2QLXUMKFHGXPZUX4JN3U","json":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U.json","graph_json":"https://pith.science/api/pith-number/ID3U7X2QLXUMKFHGXPZUX4JN3U/graph.json","events_json":"https://pith.science/api/pith-number/ID3U7X2QLXUMKFHGXPZUX4JN3U/events.json","paper":"https://pith.science/paper/ID3U7X2Q"},"agent_actions":{"view_html":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U","download_json":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U.json","view_paper":"https://pith.science/paper/ID3U7X2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.6750&json=true","fetch_graph":"https://pith.science/api/pith-number/ID3U7X2QLXUMKFHGXPZUX4JN3U/graph.json","fetch_events":"https://pith.science/api/pith-number/ID3U7X2QLXUMKFHGXPZUX4JN3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U/action/storage_attestation","attest_author":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U/action/author_attestation","sign_citation":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U/action/citation_signature","submit_replication":"https://pith.science/pith/ID3U7X2QLXUMKFHGXPZUX4JN3U/action/replication_record"}},"created_at":"2026-05-18T02:56:51.425223+00:00","updated_at":"2026-05-18T02:56:51.425223+00:00"}