{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q77IUVDHOCSEVEDXMA2M75QOLK","short_pith_number":"pith:Q77IUVDH","canonical_record":{"source":{"id":"1112.4011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-17T02:35:24Z","cross_cats_sorted":["cs.MA","cs.SY"],"title_canon_sha256":"1f9cd90769bdf855a5dec6b1ae5afc4e65aafbf2d15dbd44386d67e13718749c","abstract_canon_sha256":"1d9841869bfc59bb18afb65b802ff1c298fa2b713ae39349707a5cb0006f3294"},"schema_version":"1.0"},"canonical_sha256":"87fe8a546770a44a90776034cff60e5abc0509d758f2229d61f46238f78c2e45","source":{"kind":"arxiv","id":"1112.4011","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4011","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4011v1","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4011","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"pith_short_12","alias_value":"Q77IUVDHOCSE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q77IUVDHOCSEVEDX","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q77IUVDH","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q77IUVDHOCSEVEDXMA2M75QOLK","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-17T02:35:24Z","cross_cats_sorted":["cs.MA","cs.SY"],"title_canon_sha256":"1f9cd90769bdf855a5dec6b1ae5afc4e65aafbf2d15dbd44386d67e13718749c","abstract_canon_sha256":"1d9841869bfc59bb18afb65b802ff1c298fa2b713ae39349707a5cb0006f3294"},"schema_version":"1.0"},"canonical_sha256":"87fe8a546770a44a90776034cff60e5abc0509d758f2229d61f46238f78c2e45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:33.009722Z","signature_b64":"vJd89Oq0Q2+Su7feXtP00EFAOZRCTixEYtK1rdnmwPTQRW1fobOLVv5T/xfiLbiZm1H32Pa8KJVTj2gB0VsbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87fe8a546770a44a90776034cff60e5abc0509d758f2229d61f46238f78c2e45","last_reissued_at":"2026-05-18T03:27:33.009277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:33.009277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4011","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":"2026-05-18T03:27:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hUXFi07HZFzgbQJWf5YrIEgyJmYxlkrNVHl6Q7mizpOCWBn1Loojhj7HlF3/rc/FwajuA8YAydJlk4D6Y9eMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:14:23.750882Z"},"content_sha256":"9abded7920b1c8d9b5d6dbff3d6b2e7fe073b71c1a984acccc115a526fa4a087","schema_version":"1.0","event_id":"sha256:9abded7920b1c8d9b5d6dbff3d6b2e7fe073b71c1a984acccc115a526fa4a087"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q77IUVDHOCSEVEDXMA2M75QOLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","cs.SY"],"primary_cat":"math.OC","authors_text":"Bassam Bamieh, Mihailo R. Jovanovi\\'c, Partha Mitra, Stacy Patterson","submitted_at":"2011-12-17T02:35:24Z","abstract_excerpt":"We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4011","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":"2026-05-18T03:27:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFyQ5E5T34X4y0V5IgtT42puWkXc2eujChGRPXEaSTrWyC5LEZ2X9FyWDHCVpjGlqZLYdsFzO8mVk915LIJSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:14:23.751465Z"},"content_sha256":"723afb4c391f89ea2527193a7a6771ec1dcead2693bcf80606a78ec379c2537c","schema_version":"1.0","event_id":"sha256:723afb4c391f89ea2527193a7a6771ec1dcead2693bcf80606a78ec379c2537c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q77IUVDHOCSEVEDXMA2M75QOLK/bundle.json","state_url":"https://pith.science/pith/Q77IUVDHOCSEVEDXMA2M75QOLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q77IUVDHOCSEVEDXMA2M75QOLK/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":"2026-06-07T06:14:23Z","links":{"resolver":"https://pith.science/pith/Q77IUVDHOCSEVEDXMA2M75QOLK","bundle":"https://pith.science/pith/Q77IUVDHOCSEVEDXMA2M75QOLK/bundle.json","state":"https://pith.science/pith/Q77IUVDHOCSEVEDXMA2M75QOLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q77IUVDHOCSEVEDXMA2M75QOLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q77IUVDHOCSEVEDXMA2M75QOLK","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":"1d9841869bfc59bb18afb65b802ff1c298fa2b713ae39349707a5cb0006f3294","cross_cats_sorted":["cs.MA","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-17T02:35:24Z","title_canon_sha256":"1f9cd90769bdf855a5dec6b1ae5afc4e65aafbf2d15dbd44386d67e13718749c"},"schema_version":"1.0","source":{"id":"1112.4011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4011","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4011v1","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4011","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"pith_short_12","alias_value":"Q77IUVDHOCSE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q77IUVDHOCSEVEDX","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q77IUVDH","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:723afb4c391f89ea2527193a7a6771ec1dcead2693bcf80606a78ec379c2537c","target":"graph","created_at":"2026-05-18T03:27:33Z","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 consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons ","authors_text":"Bassam Bamieh, Mihailo R. Jovanovi\\'c, Partha Mitra, Stacy Patterson","cross_cats":["cs.MA","cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-17T02:35:24Z","title":"Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4011","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":"sha256:9abded7920b1c8d9b5d6dbff3d6b2e7fe073b71c1a984acccc115a526fa4a087","target":"record","created_at":"2026-05-18T03:27:33Z","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":"1d9841869bfc59bb18afb65b802ff1c298fa2b713ae39349707a5cb0006f3294","cross_cats_sorted":["cs.MA","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-17T02:35:24Z","title_canon_sha256":"1f9cd90769bdf855a5dec6b1ae5afc4e65aafbf2d15dbd44386d67e13718749c"},"schema_version":"1.0","source":{"id":"1112.4011","kind":"arxiv","version":1}},"canonical_sha256":"87fe8a546770a44a90776034cff60e5abc0509d758f2229d61f46238f78c2e45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87fe8a546770a44a90776034cff60e5abc0509d758f2229d61f46238f78c2e45","first_computed_at":"2026-05-18T03:27:33.009277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:33.009277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vJd89Oq0Q2+Su7feXtP00EFAOZRCTixEYtK1rdnmwPTQRW1fobOLVv5T/xfiLbiZm1H32Pa8KJVTj2gB0VsbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:33.009722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9abded7920b1c8d9b5d6dbff3d6b2e7fe073b71c1a984acccc115a526fa4a087","sha256:723afb4c391f89ea2527193a7a6771ec1dcead2693bcf80606a78ec379c2537c"],"state_sha256":"aa04e85a08438d9e069e60732753118bef8ed5240cd1832124bf692f5d69f034"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8wU3qa3nf007QEQgYblRE10sCRER+/wCbDB6Tp4MN0yaZjZavo9My5dqNGpzj4dw5oWRD6OKxnQhmPOkWlt0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:14:23.754611Z","bundle_sha256":"f6430061365d2677ab709b81d2a8f2d89ee6633b923dc6a117d37e52566bad2e"}}