{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NKEK5IPWZLWG6TNPOACA6NMH6D","short_pith_number":"pith:NKEK5IPW","canonical_record":{"source":{"id":"1408.4471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-19T20:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"7493076d9d5ab7a1ba64d96f98fde61df01641121255633969ab41c95a4963ea","abstract_canon_sha256":"e05b662f41a62982bbd75a2e9a3a765d78b2f3936a0790a68f4f2ec07ba6c790"},"schema_version":"1.0"},"canonical_sha256":"6a88aea1f6caec6f4daf70040f3587f0c351e99b07cb4229265f74159d742f28","source":{"kind":"arxiv","id":"1408.4471","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4471","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4471v2","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4471","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"NKEK5IPWZLWG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NKEK5IPWZLWG6TNP","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NKEK5IPW","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NKEK5IPWZLWG6TNPOACA6NMH6D","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-19T20:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"7493076d9d5ab7a1ba64d96f98fde61df01641121255633969ab41c95a4963ea","abstract_canon_sha256":"e05b662f41a62982bbd75a2e9a3a765d78b2f3936a0790a68f4f2ec07ba6c790"},"schema_version":"1.0"},"canonical_sha256":"6a88aea1f6caec6f4daf70040f3587f0c351e99b07cb4229265f74159d742f28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:55.973335Z","signature_b64":"Ai3O93UizhdiL/UdtfVP94XG1eWcd8QXdizTgPauIpLhdefS6twVqUOC7HfT6TKZbNwxxLxhULY34lJgAKpRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a88aea1f6caec6f4daf70040f3587f0c351e99b07cb4229265f74159d742f28","last_reissued_at":"2026-05-18T02:25:55.972934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:55.972934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4471","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qri3Ukv/VwodhG6FPhxexlBXfPbM4XqfOXhdL6Bs162IL6pMTPWPRNeDH9N5wCoDBeUjbGasWMp1cUjLumrWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:48:31.800671Z"},"content_sha256":"9551ba6336bedf33aff4f7090db97859ea0882125f924d51875789d0c4445a4b","schema_version":"1.0","event_id":"sha256:9551ba6336bedf33aff4f7090db97859ea0882125f924d51875789d0c4445a4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NKEK5IPWZLWG6TNPOACA6NMH6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Robustness of Uncertain Consensus Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Zelazo, Mathias B\\\"urger","submitted_at":"2014-08-19T20:22:53Z","abstract_excerpt":"This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in the graph, or any single negative edge weight has magnitude less than the inverse of the effective resistance between the two incident nodes, then the resulting network is unstable. These results are then applied to analyze the robustness properties of the consensus network with additive but bounded perturbations of the edge weights. It is shown that the smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4471","kind":"arxiv","version":2},"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":"2026-05-18T02:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/CyNuWOidJwJWsTnihEOpozizFX5+2HqjpZ9P64gaULXlVS+TQC0pxNUxtrus8fG40FWy5rY+yr9JSdDEYsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:48:31.801298Z"},"content_sha256":"13bde07fbcf8f250cdc92538b8cd75f0bea030907b740b216261b80d523c18ff","schema_version":"1.0","event_id":"sha256:13bde07fbcf8f250cdc92538b8cd75f0bea030907b740b216261b80d523c18ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKEK5IPWZLWG6TNPOACA6NMH6D/bundle.json","state_url":"https://pith.science/pith/NKEK5IPWZLWG6TNPOACA6NMH6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKEK5IPWZLWG6TNPOACA6NMH6D/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":"2026-06-04T06:48:31Z","links":{"resolver":"https://pith.science/pith/NKEK5IPWZLWG6TNPOACA6NMH6D","bundle":"https://pith.science/pith/NKEK5IPWZLWG6TNPOACA6NMH6D/bundle.json","state":"https://pith.science/pith/NKEK5IPWZLWG6TNPOACA6NMH6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKEK5IPWZLWG6TNPOACA6NMH6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NKEK5IPWZLWG6TNPOACA6NMH6D","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":"e05b662f41a62982bbd75a2e9a3a765d78b2f3936a0790a68f4f2ec07ba6c790","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-19T20:22:53Z","title_canon_sha256":"7493076d9d5ab7a1ba64d96f98fde61df01641121255633969ab41c95a4963ea"},"schema_version":"1.0","source":{"id":"1408.4471","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4471","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4471v2","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4471","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"NKEK5IPWZLWG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NKEK5IPWZLWG6TNP","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NKEK5IPW","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:13bde07fbcf8f250cdc92538b8cd75f0bea030907b740b216261b80d523c18ff","target":"graph","created_at":"2026-05-18T02:25:55Z","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 work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in the graph, or any single negative edge weight has magnitude less than the inverse of the effective resistance between the two incident nodes, then the resulting network is unstable. These results are then applied to analyze the robustness properties of the consensus network with additive but bounded perturbations of the edge weights. It is shown that the smal","authors_text":"Daniel Zelazo, Mathias B\\\"urger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-19T20:22:53Z","title":"On the Robustness of Uncertain Consensus Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4471","kind":"arxiv","version":2},"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":"sha256:9551ba6336bedf33aff4f7090db97859ea0882125f924d51875789d0c4445a4b","target":"record","created_at":"2026-05-18T02:25:55Z","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":"e05b662f41a62982bbd75a2e9a3a765d78b2f3936a0790a68f4f2ec07ba6c790","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-19T20:22:53Z","title_canon_sha256":"7493076d9d5ab7a1ba64d96f98fde61df01641121255633969ab41c95a4963ea"},"schema_version":"1.0","source":{"id":"1408.4471","kind":"arxiv","version":2}},"canonical_sha256":"6a88aea1f6caec6f4daf70040f3587f0c351e99b07cb4229265f74159d742f28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a88aea1f6caec6f4daf70040f3587f0c351e99b07cb4229265f74159d742f28","first_computed_at":"2026-05-18T02:25:55.972934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:55.972934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ai3O93UizhdiL/UdtfVP94XG1eWcd8QXdizTgPauIpLhdefS6twVqUOC7HfT6TKZbNwxxLxhULY34lJgAKpRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:55.973335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4471","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9551ba6336bedf33aff4f7090db97859ea0882125f924d51875789d0c4445a4b","sha256:13bde07fbcf8f250cdc92538b8cd75f0bea030907b740b216261b80d523c18ff"],"state_sha256":"155c0164440ec35e153288919c3a9de9b5b8aa1cc6a912e8bf74c03baca79e60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzFYE6mS5Pg2oGuGm6BuxDP9+6uGza0+jWacmLvSGwOOjYNWvOfXRbGaYzbtPfgiPdApbhc4/SrVC0KZJEtuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:48:31.804260Z","bundle_sha256":"dfff9b5329341ab6991c905ea401ff6f354a8ef60e57ae1c862a2950c4bee40f"}}