{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I5A3GDCQNFWHDPBG7EXAMBTF3X","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":"9539f1859fe5a88f502df245849e87683388dc5a41e0c5c1f5b511e401e8903d","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2020-11-28T10:56:37Z","title_canon_sha256":"1c654f5645ad30508cc751ce792393d0e4af66c7ba920bcca60814ec0dfa1500"},"schema_version":"1.0","source":{"id":"2011.14105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.14105","created_at":"2026-07-05T02:52:00Z"},{"alias_kind":"arxiv_version","alias_value":"2011.14105v2","created_at":"2026-07-05T02:52:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.14105","created_at":"2026-07-05T02:52:00Z"},{"alias_kind":"pith_short_12","alias_value":"I5A3GDCQNFWH","created_at":"2026-07-05T02:52:00Z"},{"alias_kind":"pith_short_16","alias_value":"I5A3GDCQNFWHDPBG","created_at":"2026-07-05T02:52:00Z"},{"alias_kind":"pith_short_8","alias_value":"I5A3GDCQ","created_at":"2026-07-05T02:52:00Z"}],"graph_snapshots":[{"event_id":"sha256:b59853b39c9a3a32083fc776dde46e74b7254134e09ccd401d9150260cca8b5e","target":"graph","created_at":"2026-07-05T02:52:00Z","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/2011.14105/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In contrast with the scalar-weighted networks, where bipartite consensus can be achieved if and only if the underlying signed network is structurally balanced, the structural balance property is no longer a graph-theoretic equivalence to the bipartite consensus in the case of signed matrix-weighted networks. To re-establish the relationship between the network structure and the bipartite consensus solution, the non-trivial balancing set is introduced which is a set of edges whose sign negation can transform a structurally imbalanced network into a structurally balanced one and the weight matri","authors_text":"Chongzhi Wang, Dewei Li, Haibin Shao, Lulu Pan, Yugeng Xi","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2020-11-28T10:56:37Z","title":"Characterizing Bipartite Consensus on Signed Matrix-Weighted Networks via Balancing Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.14105","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:aeebf6f03d520f0d832180a89f3ca0bdc54c7a6cb0a1e2aa7b3c7423bf75dfdf","target":"record","created_at":"2026-07-05T02:52:00Z","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":"9539f1859fe5a88f502df245849e87683388dc5a41e0c5c1f5b511e401e8903d","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2020-11-28T10:56:37Z","title_canon_sha256":"1c654f5645ad30508cc751ce792393d0e4af66c7ba920bcca60814ec0dfa1500"},"schema_version":"1.0","source":{"id":"2011.14105","kind":"arxiv","version":2}},"canonical_sha256":"4741b30c50696c71bc26f92e060665dde4b556a0c39f4da9f52caed62f0127ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4741b30c50696c71bc26f92e060665dde4b556a0c39f4da9f52caed62f0127ef","first_computed_at":"2026-07-05T02:52:00.435932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:52:00.435932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UvGXLOzxaKYeaUML/iRHUJ6Mzm8sdfU6aQJIx0fi3rkn/k8ukcN4JM6hwWWxHrLMIxh6gAeNpOs/015cLCJoDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:52:00.436390Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.14105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeebf6f03d520f0d832180a89f3ca0bdc54c7a6cb0a1e2aa7b3c7423bf75dfdf","sha256:b59853b39c9a3a32083fc776dde46e74b7254134e09ccd401d9150260cca8b5e"],"state_sha256":"ea69316203d820c5a3533313985d1974f2f00758e7f56cc3a8385013270f053b"}