{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QK6PWXDTQ6HYJ36A2WNVNJZAQR","short_pith_number":"pith:QK6PWXDT","canonical_record":{"source":{"id":"1508.06018","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-08-25T03:11:14Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"5f315c7326dfd2fd4569510e686eb1926f4fc5ea405fa5d342c00c7380a3e4b3","abstract_canon_sha256":"8c1e0fa14b3b94faf816f9e447515d8dd2d37e9e7f8a11ce0c91a5c92a30b651"},"schema_version":"1.0"},"canonical_sha256":"82bcfb5c73878f84efc0d59b56a720845bf68d766ecf765a8f133d4ba7d1f176","source":{"kind":"arxiv","id":"1508.06018","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06018","created_at":"2026-05-18T00:56:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06018v4","created_at":"2026-05-18T00:56:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06018","created_at":"2026-05-18T00:56:31Z"},{"alias_kind":"pith_short_12","alias_value":"QK6PWXDTQ6HY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QK6PWXDTQ6HYJ36A","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QK6PWXDT","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QK6PWXDTQ6HYJ36A2WNVNJZAQR","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06018","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-08-25T03:11:14Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"5f315c7326dfd2fd4569510e686eb1926f4fc5ea405fa5d342c00c7380a3e4b3","abstract_canon_sha256":"8c1e0fa14b3b94faf816f9e447515d8dd2d37e9e7f8a11ce0c91a5c92a30b651"},"schema_version":"1.0"},"canonical_sha256":"82bcfb5c73878f84efc0d59b56a720845bf68d766ecf765a8f133d4ba7d1f176","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:31.624283Z","signature_b64":"UtvUlx3EtmhfrPtztnTwPlHFQtoY0GF1jyd8v/zIfpZrYtcUEyDuMLF/YPpoGbFsTxdbp3NSS5srR8f5r6SICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82bcfb5c73878f84efc0d59b56a720845bf68d766ecf765a8f133d4ba7d1f176","last_reissued_at":"2026-05-18T00:56:31.623373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:31.623373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06018","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sDct6IxvqquVqmgtxNMQ8EN/Md/gkJmqxCh9mqz0lP7p259ycNZe1cY8naQe/o7hbtDglhAJHiccN2iB768GCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:07:31.287944Z"},"content_sha256":"b11653b53f9d82ab13eacbdc53aa18cba7a88290da58962156f276ddda2396c1","schema_version":"1.0","event_id":"sha256:b11653b53f9d82ab13eacbdc53aa18cba7a88290da58962156f276ddda2396c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QK6PWXDTQ6HYJ36A2WNVNJZAQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A combination of small-gain and density propagation inequalities for stability analysis of networked systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Humberto Stein Shiromoto, Petro Feketa, Sergey Dashkovskiy","submitted_at":"2015-08-25T03:11:14Z","abstract_excerpt":"In this paper, the problem of stability analysis of a large-scale interconnection of nonlinear systems for which the small-gain condition does not hold globally is considered. A combination of the small-gain and density propagation inequalities is employed to prove almost input-to-state stability of the network."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06018","kind":"arxiv","version":4},"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":"2026-05-18T00:56:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyU1/letzr7VvfgJF2ulxw1V/5px4rQAIr3Hfo0071Y9DQG18eUQ3dM7Y7Y+8KwfsBWbOzwhz5N4ZF8x9r25Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:07:31.288277Z"},"content_sha256":"14845d553b388943bfcc562e7fb79e81602ac18f7255629d8d35aa0d58388b77","schema_version":"1.0","event_id":"sha256:14845d553b388943bfcc562e7fb79e81602ac18f7255629d8d35aa0d58388b77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR/bundle.json","state_url":"https://pith.science/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR/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":"2026-06-27T01:07:31Z","links":{"resolver":"https://pith.science/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR","bundle":"https://pith.science/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR/bundle.json","state":"https://pith.science/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QK6PWXDTQ6HYJ36A2WNVNJZAQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QK6PWXDTQ6HYJ36A2WNVNJZAQR","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":"8c1e0fa14b3b94faf816f9e447515d8dd2d37e9e7f8a11ce0c91a5c92a30b651","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-08-25T03:11:14Z","title_canon_sha256":"5f315c7326dfd2fd4569510e686eb1926f4fc5ea405fa5d342c00c7380a3e4b3"},"schema_version":"1.0","source":{"id":"1508.06018","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06018","created_at":"2026-05-18T00:56:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06018v4","created_at":"2026-05-18T00:56:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06018","created_at":"2026-05-18T00:56:31Z"},{"alias_kind":"pith_short_12","alias_value":"QK6PWXDTQ6HY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QK6PWXDTQ6HYJ36A","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QK6PWXDT","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:14845d553b388943bfcc562e7fb79e81602ac18f7255629d8d35aa0d58388b77","target":"graph","created_at":"2026-05-18T00:56:31Z","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 paper, the problem of stability analysis of a large-scale interconnection of nonlinear systems for which the small-gain condition does not hold globally is considered. A combination of the small-gain and density propagation inequalities is employed to prove almost input-to-state stability of the network.","authors_text":"Humberto Stein Shiromoto, Petro Feketa, Sergey Dashkovskiy","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-08-25T03:11:14Z","title":"A combination of small-gain and density propagation inequalities for stability analysis of networked systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06018","kind":"arxiv","version":4},"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:b11653b53f9d82ab13eacbdc53aa18cba7a88290da58962156f276ddda2396c1","target":"record","created_at":"2026-05-18T00:56:31Z","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":"8c1e0fa14b3b94faf816f9e447515d8dd2d37e9e7f8a11ce0c91a5c92a30b651","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-08-25T03:11:14Z","title_canon_sha256":"5f315c7326dfd2fd4569510e686eb1926f4fc5ea405fa5d342c00c7380a3e4b3"},"schema_version":"1.0","source":{"id":"1508.06018","kind":"arxiv","version":4}},"canonical_sha256":"82bcfb5c73878f84efc0d59b56a720845bf68d766ecf765a8f133d4ba7d1f176","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82bcfb5c73878f84efc0d59b56a720845bf68d766ecf765a8f133d4ba7d1f176","first_computed_at":"2026-05-18T00:56:31.623373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:31.623373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UtvUlx3EtmhfrPtztnTwPlHFQtoY0GF1jyd8v/zIfpZrYtcUEyDuMLF/YPpoGbFsTxdbp3NSS5srR8f5r6SICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:31.624283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06018","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b11653b53f9d82ab13eacbdc53aa18cba7a88290da58962156f276ddda2396c1","sha256:14845d553b388943bfcc562e7fb79e81602ac18f7255629d8d35aa0d58388b77"],"state_sha256":"45408d4a011a1b73ab3e901a7e248f242f53a6d7ad8324f3b481c22f55272c72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1NBkDBDzTgc6Nt1F3frgTrMt+s843mOL89SPE35LLYbgmBmyhlOdIVB2GCZAkzVnmxzy23j+NO/RvgwaajPDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:07:31.290389Z","bundle_sha256":"0a4323d2459ae03a3bcfe29401b3c45046c47c583abed7398bad0ee0a8f68988"}}