{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YBJVFIL7P2DI6YJGS4WPAM76QE","short_pith_number":"pith:YBJVFIL7","canonical_record":{"source":{"id":"2606.03797","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T15:46:13Z","cross_cats_sorted":[],"title_canon_sha256":"1ca51b522ab8ab90979d6cfcf9b2980ce7dc7b1eff5b1551e7cadc7bb3b84459","abstract_canon_sha256":"c2f9dd6d8f9d93bb8e6b17e77162372f6dc66d0a2db9eb38eb9e0868b8cc9040"},"schema_version":"1.0"},"canonical_sha256":"c05352a17f7e868f6126972cf033fe81290ac875b1375f3f1852f5aeb510b51a","source":{"kind":"arxiv","id":"2606.03797","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03797","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03797v1","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03797","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"pith_short_12","alias_value":"YBJVFIL7P2DI","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"pith_short_16","alias_value":"YBJVFIL7P2DI6YJG","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"pith_short_8","alias_value":"YBJVFIL7","created_at":"2026-06-03T02:06:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YBJVFIL7P2DI6YJGS4WPAM76QE","target":"record","payload":{"canonical_record":{"source":{"id":"2606.03797","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T15:46:13Z","cross_cats_sorted":[],"title_canon_sha256":"1ca51b522ab8ab90979d6cfcf9b2980ce7dc7b1eff5b1551e7cadc7bb3b84459","abstract_canon_sha256":"c2f9dd6d8f9d93bb8e6b17e77162372f6dc66d0a2db9eb38eb9e0868b8cc9040"},"schema_version":"1.0"},"canonical_sha256":"c05352a17f7e868f6126972cf033fe81290ac875b1375f3f1852f5aeb510b51a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:06:02.711426Z","signature_b64":"O8CIo2ZEEtx/Z62t0RRLetEpgJJ1RWEpPkLjIxStgUNo1WjUcddn8THueu5bUajW5DtaTS5HXcOMbM6nJB+qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c05352a17f7e868f6126972cf033fe81290ac875b1375f3f1852f5aeb510b51a","last_reissued_at":"2026-06-03T02:06:02.711014Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:06:02.711014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.03797","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":"2026-06-03T02:06:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9xBPWHux4CBiE33T2Nr6seag0cD6Qq5r/hBlT42GMC44nhZBhGjjtIc42pN7uoTs7RZwX4ApOoS+atQOqarjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:45:05.989999Z"},"content_sha256":"59b02c493a177288f7cb7785f2563693baa78590ef629267f4bc492df8d295a9","schema_version":"1.0","event_id":"sha256:59b02c493a177288f7cb7785f2563693baa78590ef629267f4bc492df8d295a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YBJVFIL7P2DI6YJGS4WPAM76QE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of an algorithm for constructing Lyapunov functions for switched systems using meshfree collocation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jay Ward, Nicos Georgiou, Peter Giesl","submitted_at":"2026-06-02T15:46:13Z","abstract_excerpt":"Switched systems are a class of dynamical systems where trajectories switch between different systems based on a switching rule. This rule can depend on time and/or the position of the trajectory in the state space. The existence of a Lyapunov function implies the existence of a uniformly asymptotically stable equilibrium point at the origin, which we prove in this paper. A method to construct Lyapunov functions for switched systems using meshfree collocation and quadratic programming was described in a related article. We prove that, under suitable assumptions, the algorithm described in this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03797","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03797/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T02:06:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HgAQCBvfhJMXKWFOLWv6r5Ntd+lW0Jz3lYEvNR1EcXrFG6DqP76epvgMsvO0riF4KQ8sSEUHdo9iB0yHKaZCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:45:05.990377Z"},"content_sha256":"29dfea21b82d8cb9f91929aefa5741f3b994850f3d0f4cb00869ccb5233e7752","schema_version":"1.0","event_id":"sha256:29dfea21b82d8cb9f91929aefa5741f3b994850f3d0f4cb00869ccb5233e7752"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBJVFIL7P2DI6YJGS4WPAM76QE/bundle.json","state_url":"https://pith.science/pith/YBJVFIL7P2DI6YJGS4WPAM76QE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBJVFIL7P2DI6YJGS4WPAM76QE/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":"2026-06-22T11:45:05Z","links":{"resolver":"https://pith.science/pith/YBJVFIL7P2DI6YJGS4WPAM76QE","bundle":"https://pith.science/pith/YBJVFIL7P2DI6YJGS4WPAM76QE/bundle.json","state":"https://pith.science/pith/YBJVFIL7P2DI6YJGS4WPAM76QE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBJVFIL7P2DI6YJGS4WPAM76QE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YBJVFIL7P2DI6YJGS4WPAM76QE","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":"c2f9dd6d8f9d93bb8e6b17e77162372f6dc66d0a2db9eb38eb9e0868b8cc9040","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T15:46:13Z","title_canon_sha256":"1ca51b522ab8ab90979d6cfcf9b2980ce7dc7b1eff5b1551e7cadc7bb3b84459"},"schema_version":"1.0","source":{"id":"2606.03797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03797","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03797v1","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03797","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"pith_short_12","alias_value":"YBJVFIL7P2DI","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"pith_short_16","alias_value":"YBJVFIL7P2DI6YJG","created_at":"2026-06-03T02:06:02Z"},{"alias_kind":"pith_short_8","alias_value":"YBJVFIL7","created_at":"2026-06-03T02:06:02Z"}],"graph_snapshots":[{"event_id":"sha256:29dfea21b82d8cb9f91929aefa5741f3b994850f3d0f4cb00869ccb5233e7752","target":"graph","created_at":"2026-06-03T02:06:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.03797/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Switched systems are a class of dynamical systems where trajectories switch between different systems based on a switching rule. This rule can depend on time and/or the position of the trajectory in the state space. The existence of a Lyapunov function implies the existence of a uniformly asymptotically stable equilibrium point at the origin, which we prove in this paper. A method to construct Lyapunov functions for switched systems using meshfree collocation and quadratic programming was described in a related article. We prove that, under suitable assumptions, the algorithm described in this","authors_text":"Jay Ward, Nicos Georgiou, Peter Giesl","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T15:46:13Z","title":"Convergence of an algorithm for constructing Lyapunov functions for switched systems using meshfree collocation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03797","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":"sha256:59b02c493a177288f7cb7785f2563693baa78590ef629267f4bc492df8d295a9","target":"record","created_at":"2026-06-03T02:06:02Z","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":"c2f9dd6d8f9d93bb8e6b17e77162372f6dc66d0a2db9eb38eb9e0868b8cc9040","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T15:46:13Z","title_canon_sha256":"1ca51b522ab8ab90979d6cfcf9b2980ce7dc7b1eff5b1551e7cadc7bb3b84459"},"schema_version":"1.0","source":{"id":"2606.03797","kind":"arxiv","version":1}},"canonical_sha256":"c05352a17f7e868f6126972cf033fe81290ac875b1375f3f1852f5aeb510b51a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c05352a17f7e868f6126972cf033fe81290ac875b1375f3f1852f5aeb510b51a","first_computed_at":"2026-06-03T02:06:02.711014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T02:06:02.711014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O8CIo2ZEEtx/Z62t0RRLetEpgJJ1RWEpPkLjIxStgUNo1WjUcddn8THueu5bUajW5DtaTS5HXcOMbM6nJB+qDA==","signature_status":"signed_v1","signed_at":"2026-06-03T02:06:02.711426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59b02c493a177288f7cb7785f2563693baa78590ef629267f4bc492df8d295a9","sha256:29dfea21b82d8cb9f91929aefa5741f3b994850f3d0f4cb00869ccb5233e7752"],"state_sha256":"c010f73d101fcbe9614525e0c4fc7ac5c19b3d5fade3d11532b4bcaa36e06786"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMhlKWZIxC1I/pZdtqheknpT/6fcp+k5WDASXWbbN8ae6mPyPD26rqcaGPn94aqdWxrMoWRr+hR3gUBUBnUrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:45:05.992329Z","bundle_sha256":"fbc78e8487837ef2cccb325872c710d2c63de5c781de59ada009d66e735fd478"}}