{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CFZO24GDS7T2YKHIKDARHA6HW7","short_pith_number":"pith:CFZO24GD","canonical_record":{"source":{"id":"1708.07953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-26T09:12:30Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"eabf9b16a9fde6e12a72cbad0825e7dfd97318d03118fcb04a7af20b8d2ac13b","abstract_canon_sha256":"dcff4a7b6d052a08fca17173c30bfd52c9eb7713f658cd552d5a6abda7dde7cd"},"schema_version":"1.0"},"canonical_sha256":"1172ed70c397e7ac28e850c11383c7b7d6bca10dc09b3aee03045421c89d9bba","source":{"kind":"arxiv","id":"1708.07953","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07953","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07953v1","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07953","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"CFZO24GDS7T2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CFZO24GDS7T2YKHI","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CFZO24GD","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CFZO24GDS7T2YKHIKDARHA6HW7","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-26T09:12:30Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"eabf9b16a9fde6e12a72cbad0825e7dfd97318d03118fcb04a7af20b8d2ac13b","abstract_canon_sha256":"dcff4a7b6d052a08fca17173c30bfd52c9eb7713f658cd552d5a6abda7dde7cd"},"schema_version":"1.0"},"canonical_sha256":"1172ed70c397e7ac28e850c11383c7b7d6bca10dc09b3aee03045421c89d9bba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:37.532508Z","signature_b64":"tSrFu9rH5Vn/rKECNOs6yq/QdVvkTD00ejIS2wGSemJAb7fPYAN+uzQQ86AVkUwitRXV1lz0ERAwmPf3zAAPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1172ed70c397e7ac28e850c11383c7b7d6bca10dc09b3aee03045421c89d9bba","last_reissued_at":"2026-05-18T00:36:37.531861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:37.531861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07953","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":"2026-05-18T00:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iuP9K8L3kFZOQloEhf5Q92O7mdVkdNu6+SHbgnPEKNNIXTWQUFqQyb46PBogeh062VCx2o9G9858pgxlk+sOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:54:45.490613Z"},"content_sha256":"3baadc6acc51d4e0aeac946887827db79e0203ac21245910e985dbd4ec7c404b","schema_version":"1.0","event_id":"sha256:3baadc6acc51d4e0aeac946887827db79e0203ac21245910e985dbd4ec7c404b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CFZO24GDS7T2YKHIKDARHA6HW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.OC","authors_text":"Andrii Mironchenko, Fabian Wirth","submitted_at":"2017-08-26T09:12:30Z","abstract_excerpt":"We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that ISS is equivalent to existence of a non-coercive ISS Lyapunov function and provide two simpler constructions of coercive and non-coercive ISS Lyapunov functions for input-to-state stable linear systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07953","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":"2026-05-18T00:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9MGAdlhW9TkYjUjgncyP7nOUJuOWZdvpX0uuJJe3+Z3+/9AZNZA5roYxSocWE6SvhTj3fuVA9Gp9Ti4qVYNGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:54:45.491210Z"},"content_sha256":"cd4f91398c79df009dee702fd0647b68a0260ead697c16ed281ee377425b668d","schema_version":"1.0","event_id":"sha256:cd4f91398c79df009dee702fd0647b68a0260ead697c16ed281ee377425b668d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFZO24GDS7T2YKHIKDARHA6HW7/bundle.json","state_url":"https://pith.science/pith/CFZO24GDS7T2YKHIKDARHA6HW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFZO24GDS7T2YKHIKDARHA6HW7/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":"2026-06-07T23:54:45Z","links":{"resolver":"https://pith.science/pith/CFZO24GDS7T2YKHIKDARHA6HW7","bundle":"https://pith.science/pith/CFZO24GDS7T2YKHIKDARHA6HW7/bundle.json","state":"https://pith.science/pith/CFZO24GDS7T2YKHIKDARHA6HW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFZO24GDS7T2YKHIKDARHA6HW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CFZO24GDS7T2YKHIKDARHA6HW7","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":"dcff4a7b6d052a08fca17173c30bfd52c9eb7713f658cd552d5a6abda7dde7cd","cross_cats_sorted":["math.AP","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-26T09:12:30Z","title_canon_sha256":"eabf9b16a9fde6e12a72cbad0825e7dfd97318d03118fcb04a7af20b8d2ac13b"},"schema_version":"1.0","source":{"id":"1708.07953","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07953","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07953v1","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07953","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"CFZO24GDS7T2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CFZO24GDS7T2YKHI","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CFZO24GD","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:cd4f91398c79df009dee702fd0647b68a0260ead697c16ed281ee377425b668d","target":"graph","created_at":"2026-05-18T00:36:37Z","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":"We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that ISS is equivalent to existence of a non-coercive ISS Lyapunov function and provide two simpler constructions of coercive and non-coercive ISS Lyapunov functions for input-to-state stable linear systems.","authors_text":"Andrii Mironchenko, Fabian Wirth","cross_cats":["math.AP","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-26T09:12:30Z","title":"Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07953","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":"sha256:3baadc6acc51d4e0aeac946887827db79e0203ac21245910e985dbd4ec7c404b","target":"record","created_at":"2026-05-18T00:36:37Z","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":"dcff4a7b6d052a08fca17173c30bfd52c9eb7713f658cd552d5a6abda7dde7cd","cross_cats_sorted":["math.AP","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-26T09:12:30Z","title_canon_sha256":"eabf9b16a9fde6e12a72cbad0825e7dfd97318d03118fcb04a7af20b8d2ac13b"},"schema_version":"1.0","source":{"id":"1708.07953","kind":"arxiv","version":1}},"canonical_sha256":"1172ed70c397e7ac28e850c11383c7b7d6bca10dc09b3aee03045421c89d9bba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1172ed70c397e7ac28e850c11383c7b7d6bca10dc09b3aee03045421c89d9bba","first_computed_at":"2026-05-18T00:36:37.531861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:37.531861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSrFu9rH5Vn/rKECNOs6yq/QdVvkTD00ejIS2wGSemJAb7fPYAN+uzQQ86AVkUwitRXV1lz0ERAwmPf3zAAPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:37.532508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07953","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3baadc6acc51d4e0aeac946887827db79e0203ac21245910e985dbd4ec7c404b","sha256:cd4f91398c79df009dee702fd0647b68a0260ead697c16ed281ee377425b668d"],"state_sha256":"6a05a8ed0ef91e90213fe46d22060b8beaac2d915646cfa3d7f343396639aae0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNfoNJasRta7DgWPk7i9mzYLlGQrTTaWMTu2DozK9NRovA0JzuJm6BB1ChVgPZcYb28BAltONjDtp+YgGKlTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:54:45.495090Z","bundle_sha256":"72e4cb393dd56058740698721a00f83897d4454706ba09bc639bed3d3695296e"}}