{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WK262GO2TRHVNA3IIS3GQOQ4DN","short_pith_number":"pith:WK262GO2","canonical_record":{"source":{"id":"1410.3969","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.SY","submitted_at":"2014-10-15T08:38:51Z","cross_cats_sorted":[],"title_canon_sha256":"0128f6c75c1c99771d9e8d64a250650a4cb9d19ed866ed80a6beaec7f0a20310","abstract_canon_sha256":"e986d596e16efa9fdf82eb52a00d2cc046635bca476fa6d8343ba161a13d70c8"},"schema_version":"1.0"},"canonical_sha256":"b2b5ed19da9c4f56836844b6683a1c1b5296522c2f6dc4f53125b1c3cd36bc3b","source":{"kind":"arxiv","id":"1410.3969","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3969","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3969v1","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3969","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"WK262GO2TRHV","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WK262GO2TRHVNA3I","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WK262GO2","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WK262GO2TRHVNA3IIS3GQOQ4DN","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3969","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.SY","submitted_at":"2014-10-15T08:38:51Z","cross_cats_sorted":[],"title_canon_sha256":"0128f6c75c1c99771d9e8d64a250650a4cb9d19ed866ed80a6beaec7f0a20310","abstract_canon_sha256":"e986d596e16efa9fdf82eb52a00d2cc046635bca476fa6d8343ba161a13d70c8"},"schema_version":"1.0"},"canonical_sha256":"b2b5ed19da9c4f56836844b6683a1c1b5296522c2f6dc4f53125b1c3cd36bc3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:02.946840Z","signature_b64":"CA9i+AGsrpoW0dmhBgdqot0diEpJvu5kcKVm1noqyWU2zsNaoeyox7244KDjm6coruBMkSPWcgQNtXmGDMrlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2b5ed19da9c4f56836844b6683a1c1b5296522c2f6dc4f53125b1c3cd36bc3b","last_reissued_at":"2026-05-18T02:40:02.946394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:02.946394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3969","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":"2026-05-18T02:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXSZULMYw7zWkEx7sbHYunUq+jKc6UnvjtDYRDRDX5PglyjRyupAyLxpMf1YV6cf81MulbwloDUpb8FuqfhwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:37:46.920762Z"},"content_sha256":"c6bbc5537bf1284bbde818b64f3bbadcaab8bc5001f6f66b5bea87724c755aa0","schema_version":"1.0","event_id":"sha256:c6bbc5537bf1284bbde818b64f3bbadcaab8bc5001f6f66b5bea87724c755aa0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WK262GO2TRHVNA3IIS3GQOQ4DN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernstein-based polynomial approach to study the stability of switched systems and formal verification using HOL Light","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Lo\\\"ic Michel","submitted_at":"2014-10-15T08:38:51Z","abstract_excerpt":"In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a polynomial expression from which an associated \"simple\" Lyapunov function can be eventually built. The HOL Light proof assistant allows verifying formally the Lyapunov functions that are identified from the proposed switching structure. Our approach is illustrated by numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3969","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":"2026-05-18T02:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/J3hqwGIVOrt34hhjFFmKUa1OfeKcYXwbOnkTU7rssnIjkpudVurvl8ynVt7zD2+Uo57IUTdeSTl6PfSoooBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:37:46.921654Z"},"content_sha256":"824ef404805db0662a3e6785393fdaa73d6d5721015153d2104b4ef228fccf58","schema_version":"1.0","event_id":"sha256:824ef404805db0662a3e6785393fdaa73d6d5721015153d2104b4ef228fccf58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WK262GO2TRHVNA3IIS3GQOQ4DN/bundle.json","state_url":"https://pith.science/pith/WK262GO2TRHVNA3IIS3GQOQ4DN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WK262GO2TRHVNA3IIS3GQOQ4DN/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":"2026-05-30T14:37:46Z","links":{"resolver":"https://pith.science/pith/WK262GO2TRHVNA3IIS3GQOQ4DN","bundle":"https://pith.science/pith/WK262GO2TRHVNA3IIS3GQOQ4DN/bundle.json","state":"https://pith.science/pith/WK262GO2TRHVNA3IIS3GQOQ4DN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WK262GO2TRHVNA3IIS3GQOQ4DN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WK262GO2TRHVNA3IIS3GQOQ4DN","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":"e986d596e16efa9fdf82eb52a00d2cc046635bca476fa6d8343ba161a13d70c8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.SY","submitted_at":"2014-10-15T08:38:51Z","title_canon_sha256":"0128f6c75c1c99771d9e8d64a250650a4cb9d19ed866ed80a6beaec7f0a20310"},"schema_version":"1.0","source":{"id":"1410.3969","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3969","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3969v1","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3969","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"WK262GO2TRHV","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WK262GO2TRHVNA3I","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WK262GO2","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:824ef404805db0662a3e6785393fdaa73d6d5721015153d2104b4ef228fccf58","target":"graph","created_at":"2026-05-18T02:40:02Z","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":"In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a polynomial expression from which an associated \"simple\" Lyapunov function can be eventually built. The HOL Light proof assistant allows verifying formally the Lyapunov functions that are identified from the proposed switching structure. Our approach is illustrated by numerical examples.","authors_text":"Lo\\\"ic Michel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.SY","submitted_at":"2014-10-15T08:38:51Z","title":"Bernstein-based polynomial approach to study the stability of switched systems and formal verification using HOL Light"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3969","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:c6bbc5537bf1284bbde818b64f3bbadcaab8bc5001f6f66b5bea87724c755aa0","target":"record","created_at":"2026-05-18T02:40:02Z","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":"e986d596e16efa9fdf82eb52a00d2cc046635bca476fa6d8343ba161a13d70c8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.SY","submitted_at":"2014-10-15T08:38:51Z","title_canon_sha256":"0128f6c75c1c99771d9e8d64a250650a4cb9d19ed866ed80a6beaec7f0a20310"},"schema_version":"1.0","source":{"id":"1410.3969","kind":"arxiv","version":1}},"canonical_sha256":"b2b5ed19da9c4f56836844b6683a1c1b5296522c2f6dc4f53125b1c3cd36bc3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2b5ed19da9c4f56836844b6683a1c1b5296522c2f6dc4f53125b1c3cd36bc3b","first_computed_at":"2026-05-18T02:40:02.946394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:02.946394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CA9i+AGsrpoW0dmhBgdqot0diEpJvu5kcKVm1noqyWU2zsNaoeyox7244KDjm6coruBMkSPWcgQNtXmGDMrlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:02.946840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3969","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6bbc5537bf1284bbde818b64f3bbadcaab8bc5001f6f66b5bea87724c755aa0","sha256:824ef404805db0662a3e6785393fdaa73d6d5721015153d2104b4ef228fccf58"],"state_sha256":"7c8c6de54161cfcf2bd366ba67515bc9e6e35faf587dee46b56e9bdadda0fd06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjoxV5JUqQbGuCRNYCzoMvPHJcIS7O1vydjzZFcUCHCPBeD56LkxbKvzAB2Wz/KQHlhD93sOaWz4WIlIQtHgBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:37:46.925707Z","bundle_sha256":"8950e64a168d592b66cc700c6fbd746f7c8b26854ac8dfefa64fb99af8e5f859"}}