{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PPNBOJ37IBJKFYNL2VI7O3X42Z","short_pith_number":"pith:PPNBOJ37","canonical_record":{"source":{"id":"1403.1016","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2014-03-05T06:43:19Z","cross_cats_sorted":[],"title_canon_sha256":"49c3e0f90fd11b9e4bc36ea3f6fe36549686762fb4a0aacc34d13f4233120729","abstract_canon_sha256":"40658ffb01c1147e9daa3f86a80bc44249af2e3e7593fc73f6d203f8bdc477d7"},"schema_version":"1.0"},"canonical_sha256":"7bda17277f4052a2e1abd551f76efcd6553f48b6cede32bf88fc0e560f7a7794","source":{"kind":"arxiv","id":"1403.1016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1016","created_at":"2026-05-18T02:57:05Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1016v1","created_at":"2026-05-18T02:57:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1016","created_at":"2026-05-18T02:57:05Z"},{"alias_kind":"pith_short_12","alias_value":"PPNBOJ37IBJK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PPNBOJ37IBJKFYNL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PPNBOJ37","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PPNBOJ37IBJKFYNL2VI7O3X42Z","target":"record","payload":{"canonical_record":{"source":{"id":"1403.1016","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2014-03-05T06:43:19Z","cross_cats_sorted":[],"title_canon_sha256":"49c3e0f90fd11b9e4bc36ea3f6fe36549686762fb4a0aacc34d13f4233120729","abstract_canon_sha256":"40658ffb01c1147e9daa3f86a80bc44249af2e3e7593fc73f6d203f8bdc477d7"},"schema_version":"1.0"},"canonical_sha256":"7bda17277f4052a2e1abd551f76efcd6553f48b6cede32bf88fc0e560f7a7794","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:05.915756Z","signature_b64":"a5mp16eVS2CLPPcQJkg2tB2iYgLCa/KqAHbOCD5YlrTK4g9aIsHAravbPSI9VbwTuNSC6wSiENaU1mH04Yr1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bda17277f4052a2e1abd551f76efcd6553f48b6cede32bf88fc0e560f7a7794","last_reissued_at":"2026-05-18T02:57:05.915083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:05.915083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.1016","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVkIYn8yDvHfoPQGRma/GKIdGBSiZZg5I40lja1RaPIG6AopqZzCnSXq214+MJkYvJlHzrcWo7cGBlQNfkyoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:11:13.878936Z"},"content_sha256":"58894b2995604c7502cb6c7f15b62e1eff773038b3a2fcde3fe6c885d57930fa","schema_version":"1.0","event_id":"sha256:58894b2995604c7502cb6c7f15b62e1eff773038b3a2fcde3fe6c885d57930fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PPNBOJ37IBJKFYNL2VI7O3X42Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High-order S-Lemma with application to stability of a class of switched nonlinear systems","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fuchun Sun, Kuize Zhang, Lijun Zhang","submitted_at":"2014-03-05T06:43:19Z","abstract_excerpt":"This paper extends some results on the S-Lemma proposed by Yakubovich and uses the improved results to investigate the asymptotic stability of a class of switched nonlinear systems.\n  Firstly, the strict S-Lemma is extended from quadratic forms to homogeneous functions with respect to any dilation, where the improved S-Lemma is named the strict homogeneous S-Lemma (the SHS-Lemma for short). In detail, this paper indicates that the strict S-Lemma does not necessarily hold for homogeneous functions that are not quadratic forms, and proposes a necessary and sufficient condition under which the SH"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1016","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SM/1VIgJa9za0ixeqtSoBJ4M2zEwOsKiGcNTT2ljBUQSUgob5vBYO7Hrpz8su0KYUc+4ICqzMlgoCxSRRuNACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:11:13.879634Z"},"content_sha256":"34702e3c1b3b3d458927b38bf906801990983cdae1486d5770f0d5c979c301ae","schema_version":"1.0","event_id":"sha256:34702e3c1b3b3d458927b38bf906801990983cdae1486d5770f0d5c979c301ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z/bundle.json","state_url":"https://pith.science/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T19:11:13Z","links":{"resolver":"https://pith.science/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z","bundle":"https://pith.science/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z/bundle.json","state":"https://pith.science/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPNBOJ37IBJKFYNL2VI7O3X42Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PPNBOJ37IBJKFYNL2VI7O3X42Z","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":"40658ffb01c1147e9daa3f86a80bc44249af2e3e7593fc73f6d203f8bdc477d7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2014-03-05T06:43:19Z","title_canon_sha256":"49c3e0f90fd11b9e4bc36ea3f6fe36549686762fb4a0aacc34d13f4233120729"},"schema_version":"1.0","source":{"id":"1403.1016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1016","created_at":"2026-05-18T02:57:05Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1016v1","created_at":"2026-05-18T02:57:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1016","created_at":"2026-05-18T02:57:05Z"},{"alias_kind":"pith_short_12","alias_value":"PPNBOJ37IBJK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PPNBOJ37IBJKFYNL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PPNBOJ37","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:34702e3c1b3b3d458927b38bf906801990983cdae1486d5770f0d5c979c301ae","target":"graph","created_at":"2026-05-18T02:57:05Z","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":"This paper extends some results on the S-Lemma proposed by Yakubovich and uses the improved results to investigate the asymptotic stability of a class of switched nonlinear systems.\n  Firstly, the strict S-Lemma is extended from quadratic forms to homogeneous functions with respect to any dilation, where the improved S-Lemma is named the strict homogeneous S-Lemma (the SHS-Lemma for short). In detail, this paper indicates that the strict S-Lemma does not necessarily hold for homogeneous functions that are not quadratic forms, and proposes a necessary and sufficient condition under which the SH","authors_text":"Fuchun Sun, Kuize Zhang, Lijun Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2014-03-05T06:43:19Z","title":"High-order S-Lemma with application to stability of a class of switched nonlinear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1016","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":"sha256:58894b2995604c7502cb6c7f15b62e1eff773038b3a2fcde3fe6c885d57930fa","target":"record","created_at":"2026-05-18T02:57:05Z","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":"40658ffb01c1147e9daa3f86a80bc44249af2e3e7593fc73f6d203f8bdc477d7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OC","submitted_at":"2014-03-05T06:43:19Z","title_canon_sha256":"49c3e0f90fd11b9e4bc36ea3f6fe36549686762fb4a0aacc34d13f4233120729"},"schema_version":"1.0","source":{"id":"1403.1016","kind":"arxiv","version":1}},"canonical_sha256":"7bda17277f4052a2e1abd551f76efcd6553f48b6cede32bf88fc0e560f7a7794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bda17277f4052a2e1abd551f76efcd6553f48b6cede32bf88fc0e560f7a7794","first_computed_at":"2026-05-18T02:57:05.915083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:05.915083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5mp16eVS2CLPPcQJkg2tB2iYgLCa/KqAHbOCD5YlrTK4g9aIsHAravbPSI9VbwTuNSC6wSiENaU1mH04Yr1Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:05.915756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58894b2995604c7502cb6c7f15b62e1eff773038b3a2fcde3fe6c885d57930fa","sha256:34702e3c1b3b3d458927b38bf906801990983cdae1486d5770f0d5c979c301ae"],"state_sha256":"5c1331de25c267281db7baa116126c6512626783c7f15eb4ee532a1117c84ece"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzzC34R89dRThVUTZwvHi/Grb5Nkhhs0K+R4xwRcP6LlWCapGopsD30VNZVMa+RXdf+MGQkgJG9ppZ5k1tjYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:11:13.883286Z","bundle_sha256":"0980ede1e3372adf351eaa0b71e3213ae41af30703d0c00ec27eedde72ad008d"}}