{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:667FC2NN4YUXGWPFBSTNKSLISD","short_pith_number":"pith:667FC2NN","canonical_record":{"source":{"id":"1709.10171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T21:15:48Z","cross_cats_sorted":[],"title_canon_sha256":"cc3555baa249371466bae2d1801af42926c10777a13f7840f356ac3c8a2faa18","abstract_canon_sha256":"f5626ca479506d8773c6dd6f4b01349731bf97e1d4dabc26a5faebe1b55d250c"},"schema_version":"1.0"},"canonical_sha256":"f7be5169ade6297359e50ca6d5496890d648efe48c578e52dee59a46116e311a","source":{"kind":"arxiv","id":"1709.10171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10171","created_at":"2026-05-18T00:34:04Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10171v1","created_at":"2026-05-18T00:34:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10171","created_at":"2026-05-18T00:34:04Z"},{"alias_kind":"pith_short_12","alias_value":"667FC2NN4YUX","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"667FC2NN4YUXGWPF","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"667FC2NN","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:667FC2NN4YUXGWPFBSTNKSLISD","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T21:15:48Z","cross_cats_sorted":[],"title_canon_sha256":"cc3555baa249371466bae2d1801af42926c10777a13f7840f356ac3c8a2faa18","abstract_canon_sha256":"f5626ca479506d8773c6dd6f4b01349731bf97e1d4dabc26a5faebe1b55d250c"},"schema_version":"1.0"},"canonical_sha256":"f7be5169ade6297359e50ca6d5496890d648efe48c578e52dee59a46116e311a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:04.113371Z","signature_b64":"TC6thNNMAgbEnis8JkgMc3vkyeaf9p3RDwnbdwMVRih4MNVqIGAojZksLbxa4R9rMOaTTYUgQmvgludJo2nGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7be5169ade6297359e50ca6d5496890d648efe48c578e52dee59a46116e311a","last_reissued_at":"2026-05-18T00:34:04.112599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:04.112599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10171","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":"2026-05-18T00:34:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOGk84bEGYDAcoKuV0rOtO4sTnaGufdix7Mz8DlRPjHFpaVLxYr0/KG0lSX/89dZyRPQHZVwBoGhXIH9S2bKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:08:12.195470Z"},"content_sha256":"1ea1149de31ad1c347fea74af733d3e9b9954c6ef42820ec34837d6e1a46bee1","schema_version":"1.0","event_id":"sha256:1ea1149de31ad1c347fea74af733d3e9b9954c6ef42820ec34837d6e1a46bee1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:667FC2NN4YUXGWPFBSTNKSLISD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diagonal stability of a class of discrete-time positive switched systems with delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Aleksandrov, Oliver Mason","submitted_at":"2017-09-28T21:15:48Z","abstract_excerpt":"A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L--K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete-time models of digital filters and neural networks. Finally, a numerical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10171","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":"2026-05-18T00:34:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tt1sigbcmMBhUqjUORoEftKNNdeqR4bFMNqT7Gvxp3EkI+/JX7hjzaBF7mnzTQeoauVtmU76vs7n0ZZqLeJjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:08:12.195823Z"},"content_sha256":"cf067e8ade120b2aa56e9781f87ea1f1fa795bb334b0a48231939c1b8e410b61","schema_version":"1.0","event_id":"sha256:cf067e8ade120b2aa56e9781f87ea1f1fa795bb334b0a48231939c1b8e410b61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/667FC2NN4YUXGWPFBSTNKSLISD/bundle.json","state_url":"https://pith.science/pith/667FC2NN4YUXGWPFBSTNKSLISD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/667FC2NN4YUXGWPFBSTNKSLISD/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":"2026-06-27T08:08:12Z","links":{"resolver":"https://pith.science/pith/667FC2NN4YUXGWPFBSTNKSLISD","bundle":"https://pith.science/pith/667FC2NN4YUXGWPFBSTNKSLISD/bundle.json","state":"https://pith.science/pith/667FC2NN4YUXGWPFBSTNKSLISD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/667FC2NN4YUXGWPFBSTNKSLISD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:667FC2NN4YUXGWPFBSTNKSLISD","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":"f5626ca479506d8773c6dd6f4b01349731bf97e1d4dabc26a5faebe1b55d250c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T21:15:48Z","title_canon_sha256":"cc3555baa249371466bae2d1801af42926c10777a13f7840f356ac3c8a2faa18"},"schema_version":"1.0","source":{"id":"1709.10171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10171","created_at":"2026-05-18T00:34:04Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10171v1","created_at":"2026-05-18T00:34:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10171","created_at":"2026-05-18T00:34:04Z"},{"alias_kind":"pith_short_12","alias_value":"667FC2NN4YUX","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"667FC2NN4YUXGWPF","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"667FC2NN","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:cf067e8ade120b2aa56e9781f87ea1f1fa795bb334b0a48231939c1b8e410b61","target":"graph","created_at":"2026-05-18T00:34:04Z","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":"A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L--K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete-time models of digital filters and neural networks. Finally, a numerical","authors_text":"Alexander Aleksandrov, Oliver Mason","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T21:15:48Z","title":"Diagonal stability of a class of discrete-time positive switched systems with delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10171","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":"sha256:1ea1149de31ad1c347fea74af733d3e9b9954c6ef42820ec34837d6e1a46bee1","target":"record","created_at":"2026-05-18T00:34:04Z","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":"f5626ca479506d8773c6dd6f4b01349731bf97e1d4dabc26a5faebe1b55d250c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T21:15:48Z","title_canon_sha256":"cc3555baa249371466bae2d1801af42926c10777a13f7840f356ac3c8a2faa18"},"schema_version":"1.0","source":{"id":"1709.10171","kind":"arxiv","version":1}},"canonical_sha256":"f7be5169ade6297359e50ca6d5496890d648efe48c578e52dee59a46116e311a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7be5169ade6297359e50ca6d5496890d648efe48c578e52dee59a46116e311a","first_computed_at":"2026-05-18T00:34:04.112599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:04.112599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TC6thNNMAgbEnis8JkgMc3vkyeaf9p3RDwnbdwMVRih4MNVqIGAojZksLbxa4R9rMOaTTYUgQmvgludJo2nGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:04.113371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ea1149de31ad1c347fea74af733d3e9b9954c6ef42820ec34837d6e1a46bee1","sha256:cf067e8ade120b2aa56e9781f87ea1f1fa795bb334b0a48231939c1b8e410b61"],"state_sha256":"57c955708af2fde14cae9abe73c32724f6351e9482eb3dc15997fc427cdd6e94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"df/88/K80VL5X/RwGbf7CjFtUFZTMQr5gYrsBD52yAr/jNjeKrigTgMiRybQxGNSijXSO4dSEnraAduV7crCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:08:12.197676Z","bundle_sha256":"3f849d812cca3126daae9db4c1c3dad4369ab0a1714d574c052017df54128d12"}}