{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PBD36MH2D57AV5CGERKLYDXMWA","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":"807e0eea5ea05ca4e82e9afeb648c840fe77308bf376027b0dcd61a047c55e12","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-03-12T01:27:12Z","title_canon_sha256":"eb42785e087c3baa14807d795c087975b19afeaeefa22e317b51567901270302"},"schema_version":"1.0","source":{"id":"2103.07027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.07027","created_at":"2026-07-05T02:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"2103.07027v1","created_at":"2026-07-05T02:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.07027","created_at":"2026-07-05T02:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"PBD36MH2D57A","created_at":"2026-07-05T02:22:27Z"},{"alias_kind":"pith_short_16","alias_value":"PBD36MH2D57AV5CG","created_at":"2026-07-05T02:22:27Z"},{"alias_kind":"pith_short_8","alias_value":"PBD36MH2","created_at":"2026-07-05T02:22:27Z"}],"graph_snapshots":[{"event_id":"sha256:036c3b5c4a33d03100afcf040b6d306269a15bb9a56dbd4682bb6d4895987702","target":"graph","created_at":"2026-07-05T02:22:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.07027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give lower bounds on the communication complexity of graph problems in the multi-party blackboard model. In this model, the edges of an $n$-vertex input graph are partitioned among $k$ parties, who communicate solely by writing messages on a shared blackboard that is visible to every party. We show that any non-trivial graph problem on $n$-vertex graphs has blackboard communication complexity $\\Omega(n)$ bits, even if the edges of the input graph are randomly assigned to the $k$ parties. We say that a graph problem is non-trivial if the output cannot be computed in a model where every party","authors_text":"Christian Konrad, Peter Robinson, Viktor Zamaraev","cross_cats":["cs.DC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-03-12T01:27:12Z","title":"Robust Lower Bounds for Graph Problems in the Blackboard Model of Communication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.07027","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":"sha256:875999b1ac8261c6b3553c6e88ab3f7b5181272f4cea34dceff9bcbc56936f33","target":"record","created_at":"2026-07-05T02:22:27Z","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":"807e0eea5ea05ca4e82e9afeb648c840fe77308bf376027b0dcd61a047c55e12","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-03-12T01:27:12Z","title_canon_sha256":"eb42785e087c3baa14807d795c087975b19afeaeefa22e317b51567901270302"},"schema_version":"1.0","source":{"id":"2103.07027","kind":"arxiv","version":1}},"canonical_sha256":"7847bf30fa1f7e0af4462454bc0eecb030c4472d70a6ee714e6f38b61e8ded4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7847bf30fa1f7e0af4462454bc0eecb030c4472d70a6ee714e6f38b61e8ded4e","first_computed_at":"2026-07-05T02:22:27.790462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:22:27.790462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cu/kCGTaDNzP3xSpfANx73ghNXLhLKPedlbfOjZ2rFqI00sCczFbhsKbBniLSns25Gzm2TJ+16Acm7gGkmmkCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:22:27.790887Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.07027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:875999b1ac8261c6b3553c6e88ab3f7b5181272f4cea34dceff9bcbc56936f33","sha256:036c3b5c4a33d03100afcf040b6d306269a15bb9a56dbd4682bb6d4895987702"],"state_sha256":"d4ae71eb1104197b86f0f39ccdf6eae9ffdea0abfc83e9509c1fb93e18dac25e"}