{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SEJCDRXAJ4JEX64HG7T3YT6FRY","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":"d68da19d5952f6b67601e2560cc57c8ff8c246e881775b7227c5d09840dc1cc9","cross_cats_sorted":["cs.NI","math.OC"],"license":"","primary_cat":"cs.MA","submitted_at":"2007-08-23T17:53:54Z","title_canon_sha256":"f69893ddcf48736ff48b0e10a89d6070ddb9e149ceec2ff9fe04e96e5bfb9568"},"schema_version":"1.0","source":{"id":"0708.3220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.3220","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0708.3220v1","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.3220","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"SEJCDRXAJ4JE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SEJCDRXAJ4JEX64H","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SEJCDRXA","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:16c10fdcf52b195bf651d5f8cf872d2dd2c609fe987e6f430e2f494a078c6cbb","target":"graph","created_at":"2026-05-18T03:13:11Z","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 prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely many steps. A more general family of strategies, constructed by block Kronecker products, is investigated and compared to Cayley strategies.","authors_text":"Jean-Charles Delvenne, Ruggero Carli, Sandro Zampieri","cross_cats":["cs.NI","math.OC"],"headline":"","license":"","primary_cat":"cs.MA","submitted_at":"2007-08-23T17:53:54Z","title":"Optimal strategies in the average consensus problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.3220","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:ebe6b8a5a68072cffb518643e767705ff5ac9a179f54c7cf27519d1ef839e2e2","target":"record","created_at":"2026-05-18T03:13:11Z","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":"d68da19d5952f6b67601e2560cc57c8ff8c246e881775b7227c5d09840dc1cc9","cross_cats_sorted":["cs.NI","math.OC"],"license":"","primary_cat":"cs.MA","submitted_at":"2007-08-23T17:53:54Z","title_canon_sha256":"f69893ddcf48736ff48b0e10a89d6070ddb9e149ceec2ff9fe04e96e5bfb9568"},"schema_version":"1.0","source":{"id":"0708.3220","kind":"arxiv","version":1}},"canonical_sha256":"911221c6e04f124bfb8737e7bc4fc58e18b020f6683d4c5b653c2557ca395f50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911221c6e04f124bfb8737e7bc4fc58e18b020f6683d4c5b653c2557ca395f50","first_computed_at":"2026-05-18T03:13:11.302252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:11.302252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3cGwo+xmb1Csc7gXdmlb/Wy+Kfjbev4j7YT1+mXWjI7HLZsxthIDgU9Z3+eOZqe8ATNzLB9a67qWGH9JIxPJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:11.303026Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.3220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebe6b8a5a68072cffb518643e767705ff5ac9a179f54c7cf27519d1ef839e2e2","sha256:16c10fdcf52b195bf651d5f8cf872d2dd2c609fe987e6f430e2f494a078c6cbb"],"state_sha256":"aa3d9a44f59d6a9a11666f6430b7a28bb8f0e0fdbbfa2cb14f2c5071a39f8ba9"}