{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:WQBFDFGKGDIUCCLYSIQO5NUPUP","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":"85faa89fd140c47e218b909c5bd97bcf5627cfaf96afb48de3e3353de4ca30e3","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2021-03-15T18:25:41Z","title_canon_sha256":"7450303f82eb815569c022144ed93c456580cd2344a91ede2d6c905887f32abd"},"schema_version":"1.0","source":{"id":"2103.08638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.08638","created_at":"2026-07-05T08:35:32Z"},{"alias_kind":"arxiv_version","alias_value":"2103.08638v2","created_at":"2026-07-05T08:35:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.08638","created_at":"2026-07-05T08:35:32Z"},{"alias_kind":"pith_short_12","alias_value":"WQBFDFGKGDIU","created_at":"2026-07-05T08:35:32Z"},{"alias_kind":"pith_short_16","alias_value":"WQBFDFGKGDIUCCLY","created_at":"2026-07-05T08:35:32Z"},{"alias_kind":"pith_short_8","alias_value":"WQBFDFGK","created_at":"2026-07-05T08:35:32Z"}],"graph_snapshots":[{"event_id":"sha256:94302ef71da0d0cac7d7769ef711ba303178267b2415e316f01f89cf0bd33a90","target":"graph","created_at":"2026-07-05T08:35:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.08638/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous (ELLS) systems, which we show to be a strict superset of locally Lipschitz continuous (LLC) systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the over-approxi","authors_text":"Mohammad Khajenejad, Sze Zheng Yong","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2021-03-15T18:25:41Z","title":"Tight Remainder-Form Decomposition Functions with Applications to Constrained Reachability and Guaranteed State Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.08638","kind":"arxiv","version":2},"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":"sha256:04c5a58821091c17682a023352c89f4d0bf55bccfbbff9667c5c72b2f6bc88bb","target":"record","created_at":"2026-07-05T08:35:32Z","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":"85faa89fd140c47e218b909c5bd97bcf5627cfaf96afb48de3e3353de4ca30e3","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2021-03-15T18:25:41Z","title_canon_sha256":"7450303f82eb815569c022144ed93c456580cd2344a91ede2d6c905887f32abd"},"schema_version":"1.0","source":{"id":"2103.08638","kind":"arxiv","version":2}},"canonical_sha256":"b4025194ca30d14109789220eeb68fa3d11f96ba6f73714439f4a542d9bf87d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4025194ca30d14109789220eeb68fa3d11f96ba6f73714439f4a542d9bf87d8","first_computed_at":"2026-07-05T08:35:32.581515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:35:32.581515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4wOpCSg6RstRMPsO1SeVchvh/goC7TJg7Q/26u+ARR581RXBJw7jiAeaYAMTcdrSX252wQtd4nzUqaiASP/IDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:35:32.581986Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.08638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04c5a58821091c17682a023352c89f4d0bf55bccfbbff9667c5c72b2f6bc88bb","sha256:94302ef71da0d0cac7d7769ef711ba303178267b2415e316f01f89cf0bd33a90"],"state_sha256":"cf8f8ec4e8ac4ad0c84bfddc1e2d8be464fdd411c53399d580d2ce1467ab0525"}