{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:A5QYQNXDZWLRBGN7C7OMLXBY5R","short_pith_number":"pith:A5QYQNXD","canonical_record":{"source":{"id":"1107.3979","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-20T13:52:19Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"cef74ab85f848ffa338c3d518ce9dffe3d9ce5382f4252a8ea5f2137fe84b1ea","abstract_canon_sha256":"9b5358c293cb6fda6674ff231c84671e88de21888a1cb5fb5324eca77d16ec1b"},"schema_version":"1.0"},"canonical_sha256":"07618836e3cd971099bf17dcc5dc38ec4058df47398ad9abef294ea809c5d078","source":{"kind":"arxiv","id":"1107.3979","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3979","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3979v3","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3979","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"A5QYQNXDZWLR","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A5QYQNXDZWLRBGN7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A5QYQNXD","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:A5QYQNXDZWLRBGN7C7OMLXBY5R","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3979","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-20T13:52:19Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"cef74ab85f848ffa338c3d518ce9dffe3d9ce5382f4252a8ea5f2137fe84b1ea","abstract_canon_sha256":"9b5358c293cb6fda6674ff231c84671e88de21888a1cb5fb5324eca77d16ec1b"},"schema_version":"1.0"},"canonical_sha256":"07618836e3cd971099bf17dcc5dc38ec4058df47398ad9abef294ea809c5d078","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:12.340749Z","signature_b64":"rUYhwJCnfHYPUju1DGT7XxsXZg+nwYYw1l+HchU/S+VeVwqVuVXgggH0LO5cwn5xSSxPzcaeyYC31OuMCj2ADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07618836e3cd971099bf17dcc5dc38ec4058df47398ad9abef294ea809c5d078","last_reissued_at":"2026-05-18T04:08:12.340150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:12.340150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3979","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zcrrz21HxpHa703pSGCaL4MpdivPIQXKtcx3KoedS+vnKzGL0f7NgOb0zpTI/qKwEjwAljS/EQ8ql2XycYL1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:37:51.276652Z"},"content_sha256":"14f76fa5807bed3a530782f161a67a34b6d562ecbc169281e184cca6b644e150","schema_version":"1.0","event_id":"sha256:14f76fa5807bed3a530782f161a67a34b6d562ecbc169281e184cca6b644e150"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:A5QYQNXDZWLRBGN7C7OMLXBY5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuous-time quantized consensus: convergence of Krasowskii solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Paolo Frasca","submitted_at":"2011-07-20T13:52:19Z","abstract_excerpt":"This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE system are intended in the sense of Krasovskii. A limit connectivity graph is defined, which encodes persistent interactions between nodes: if such graph has a globally reachable node, Krasovskii solutions reach consensus (up to the quantizer precision) after a finite time. Under the additional assumption of a time-invariant topology, the convergence time is upper bounded by a quantity whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3979","kind":"arxiv","version":3},"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":"2026-05-18T04:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYJL1wUuD/aOgmuBjRSMtITG+u4rWfIaztT9pR47J4YAbTXC1yoKqp4HTS1alN5bE/osvd0XRQ93VdEtC44NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:37:51.276986Z"},"content_sha256":"49140128386e6974bf87db45c3c9a5801fdee93749fce40957f73ae8f0123abe","schema_version":"1.0","event_id":"sha256:49140128386e6974bf87db45c3c9a5801fdee93749fce40957f73ae8f0123abe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R/bundle.json","state_url":"https://pith.science/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R/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":"2026-06-09T12:37:51Z","links":{"resolver":"https://pith.science/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R","bundle":"https://pith.science/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R/bundle.json","state":"https://pith.science/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5QYQNXDZWLRBGN7C7OMLXBY5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A5QYQNXDZWLRBGN7C7OMLXBY5R","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":"9b5358c293cb6fda6674ff231c84671e88de21888a1cb5fb5324eca77d16ec1b","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-20T13:52:19Z","title_canon_sha256":"cef74ab85f848ffa338c3d518ce9dffe3d9ce5382f4252a8ea5f2137fe84b1ea"},"schema_version":"1.0","source":{"id":"1107.3979","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3979","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3979v3","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3979","created_at":"2026-05-18T04:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"A5QYQNXDZWLR","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A5QYQNXDZWLRBGN7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A5QYQNXD","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:49140128386e6974bf87db45c3c9a5801fdee93749fce40957f73ae8f0123abe","target":"graph","created_at":"2026-05-18T04:08:12Z","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":"This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE system are intended in the sense of Krasovskii. A limit connectivity graph is defined, which encodes persistent interactions between nodes: if such graph has a globally reachable node, Krasovskii solutions reach consensus (up to the quantizer precision) after a finite time. Under the additional assumption of a time-invariant topology, the convergence time is upper bounded by a quantity whic","authors_text":"Paolo Frasca","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-20T13:52:19Z","title":"Continuous-time quantized consensus: convergence of Krasowskii solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3979","kind":"arxiv","version":3},"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":"sha256:14f76fa5807bed3a530782f161a67a34b6d562ecbc169281e184cca6b644e150","target":"record","created_at":"2026-05-18T04:08:12Z","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":"9b5358c293cb6fda6674ff231c84671e88de21888a1cb5fb5324eca77d16ec1b","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-20T13:52:19Z","title_canon_sha256":"cef74ab85f848ffa338c3d518ce9dffe3d9ce5382f4252a8ea5f2137fe84b1ea"},"schema_version":"1.0","source":{"id":"1107.3979","kind":"arxiv","version":3}},"canonical_sha256":"07618836e3cd971099bf17dcc5dc38ec4058df47398ad9abef294ea809c5d078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07618836e3cd971099bf17dcc5dc38ec4058df47398ad9abef294ea809c5d078","first_computed_at":"2026-05-18T04:08:12.340150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:12.340150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rUYhwJCnfHYPUju1DGT7XxsXZg+nwYYw1l+HchU/S+VeVwqVuVXgggH0LO5cwn5xSSxPzcaeyYC31OuMCj2ADA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:12.340749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3979","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14f76fa5807bed3a530782f161a67a34b6d562ecbc169281e184cca6b644e150","sha256:49140128386e6974bf87db45c3c9a5801fdee93749fce40957f73ae8f0123abe"],"state_sha256":"a2a10ad0bad3074ce7870f362f965db669f11ce94a2ad938d456530eba899a99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KenfAG2xNCjxi2xwjJS2V6KNPoYOIYwGMSDaGMMY16OkWpSVOI9+pZVXmhjg0GcpGxCzQeUFX7Dv584n7GdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:37:51.278721Z","bundle_sha256":"5ad66072d6359fa446d5fb2b384b811b0f9746a6f7c913599be9b2b6bf1f05ea"}}