{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IC3RLLDBL5MND5AXTMCVFIOBBI","short_pith_number":"pith:IC3RLLDB","schema_version":"1.0","canonical_sha256":"40b715ac615f58d1f4179b0552a1c10a037755f3a2f4bc69b19257665847852a","source":{"kind":"arxiv","id":"1105.1922","version":3},"attestation_state":"computed","paper":{"title":"Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"math.NA","authors_text":"Fabian R. Wirth, Roman Geiselhart","submitted_at":"2011-05-10T11:56:01Z","abstract_excerpt":"In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and"},"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":"1105.1922","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-10T11:56:01Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"5349163a6a07e7638784294bba098462cd24e6e72edd3a1811fd64ee0445477e","abstract_canon_sha256":"d8d7dcaaa3b3422f81932e13b0b959efa8608508826dcbb56eefd22e2914c57b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:48.199655Z","signature_b64":"wyaYchteH+2cOQIXrddUHGeGkjtyQl9Hj5bVk/GM5qDhw5acYjOPi+xLQx9zL9p35XZ5748BhY3YyiElkKyiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40b715ac615f58d1f4179b0552a1c10a037755f3a2f4bc69b19257665847852a","last_reissued_at":"2026-05-18T03:48:48.198993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:48.198993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"math.NA","authors_text":"Fabian R. Wirth, Roman Geiselhart","submitted_at":"2011-05-10T11:56:01Z","abstract_excerpt":"In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1922","kind":"arxiv","version":3},"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":"1105.1922","created_at":"2026-05-18T03:48:48.199111+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1922v3","created_at":"2026-05-18T03:48:48.199111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1922","created_at":"2026-05-18T03:48:48.199111+00:00"},{"alias_kind":"pith_short_12","alias_value":"IC3RLLDBL5MN","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"IC3RLLDBL5MND5AX","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"IC3RLLDB","created_at":"2026-05-18T12:26:30.835961+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/IC3RLLDBL5MND5AXTMCVFIOBBI","json":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI.json","graph_json":"https://pith.science/api/pith-number/IC3RLLDBL5MND5AXTMCVFIOBBI/graph.json","events_json":"https://pith.science/api/pith-number/IC3RLLDBL5MND5AXTMCVFIOBBI/events.json","paper":"https://pith.science/paper/IC3RLLDB"},"agent_actions":{"view_html":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI","download_json":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI.json","view_paper":"https://pith.science/paper/IC3RLLDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1922&json=true","fetch_graph":"https://pith.science/api/pith-number/IC3RLLDBL5MND5AXTMCVFIOBBI/graph.json","fetch_events":"https://pith.science/api/pith-number/IC3RLLDBL5MND5AXTMCVFIOBBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI/action/storage_attestation","attest_author":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI/action/author_attestation","sign_citation":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI/action/citation_signature","submit_replication":"https://pith.science/pith/IC3RLLDBL5MND5AXTMCVFIOBBI/action/replication_record"}},"created_at":"2026-05-18T03:48:48.199111+00:00","updated_at":"2026-05-18T03:48:48.199111+00:00"}