{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:2TK2MVQV5G2OESHWQEHLYYJX64","short_pith_number":"pith:2TK2MVQV","schema_version":"1.0","canonical_sha256":"d4d5a65615e9b4e248f6810ebc6137f729c899fac71d6b3e7daac0fdc8b0e6b5","source":{"kind":"arxiv","id":"math/0006133","version":2},"attestation_state":"computed","paper":{"title":"Output-input stability and minimum-phase nonlinear systems","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"A. Stephen Morse, Daniel Liberzon, Eduardo D. Sontag","submitted_at":"2000-06-19T17:24:20Z","abstract_excerpt":"This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. Th"},"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":"math/0006133","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2000-06-19T17:24:20Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3680d9b21ddceaebafb7a3da53382f2a310b802e795a1b069837adf212e0a94c","abstract_canon_sha256":"4de2baae21c1f5a24dd4eed7cbb1ad842b3b0ccc89182d7aff7a7bbc8ae3e8b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:26.453539Z","signature_b64":"qzb947XvRvIFgigqIa7JZ3UJ3NSZ44whXsYA7zRAeR+1fDjXA2e2Lfkj/rKB1E3lKME1ckM9j38MPiOyWLQLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4d5a65615e9b4e248f6810ebc6137f729c899fac71d6b3e7daac0fdc8b0e6b5","last_reissued_at":"2026-05-18T00:58:26.452947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:26.452947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Output-input stability and minimum-phase nonlinear systems","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"A. Stephen Morse, Daniel Liberzon, Eduardo D. Sontag","submitted_at":"2000-06-19T17:24:20Z","abstract_excerpt":"This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0006133","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":"math/0006133","created_at":"2026-05-18T00:58:26.453049+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0006133v2","created_at":"2026-05-18T00:58:26.453049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0006133","created_at":"2026-05-18T00:58:26.453049+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TK2MVQV5G2O","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TK2MVQV5G2OESHW","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TK2MVQV","created_at":"2026-05-18T12:25:49.631198+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/2TK2MVQV5G2OESHWQEHLYYJX64","json":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64.json","graph_json":"https://pith.science/api/pith-number/2TK2MVQV5G2OESHWQEHLYYJX64/graph.json","events_json":"https://pith.science/api/pith-number/2TK2MVQV5G2OESHWQEHLYYJX64/events.json","paper":"https://pith.science/paper/2TK2MVQV"},"agent_actions":{"view_html":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64","download_json":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64.json","view_paper":"https://pith.science/paper/2TK2MVQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0006133&json=true","fetch_graph":"https://pith.science/api/pith-number/2TK2MVQV5G2OESHWQEHLYYJX64/graph.json","fetch_events":"https://pith.science/api/pith-number/2TK2MVQV5G2OESHWQEHLYYJX64/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64/action/storage_attestation","attest_author":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64/action/author_attestation","sign_citation":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64/action/citation_signature","submit_replication":"https://pith.science/pith/2TK2MVQV5G2OESHWQEHLYYJX64/action/replication_record"}},"created_at":"2026-05-18T00:58:26.453049+00:00","updated_at":"2026-05-18T00:58:26.453049+00:00"}