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To bridge this gap, we introduce the concept of balance rate, a metric for quantifying the degree of balance in uncertain signed graphs, and prove that computing it exactly is NP-hard, motivating the need for effic"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce the concept of balance rate, a metric for quantifying the degree of balance in uncertain signed graphs, and prove that computing it exactly is NP-hard... We propose a novel Rao-Blackwellized spanning-tree estimator that achieves near-linear time complexity per sample by leveraging graph decomposition and structural properties. We also construct asymptotically justified confidence intervals using the Delta method.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The uncertainty model for signed edges permits a graph decomposition into spanning trees whose balance contributions can be Rao-Blackwellized to yield an unbiased estimator whose variance is controlled by the structural properties invoked in the proof.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Balance rate quantifies stability in uncertain signed graphs; exact computation is NP-hard but a Rao-Blackwellized spanning-tree estimator achieves near-linear time per sample with Delta-method intervals.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Balance rate quantifies stability in uncertain signed graphs and can be estimated efficiently even though exact computation is NP-hard.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"06df8d51b3577d3c7b5b375dbd27ab1ac37250eea5007a0939ef494ab00a50d5"},"source":{"id":"2605.17492","kind":"arxiv","version":1},"verdict":{"id":"4432f82c-cb59-4daa-81fb-b9df16e52f17","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:27:00.078223Z","strongest_claim":"We introduce the concept of balance rate, a metric for quantifying the degree of balance in uncertain signed graphs, and prove that computing it exactly is NP-hard... We propose a novel Rao-Blackwellized spanning-tree estimator that achieves near-linear time complexity per sample by leveraging graph decomposition and structural properties. We also construct asymptotically justified confidence intervals using the Delta method.","one_line_summary":"Balance rate quantifies stability in uncertain signed graphs; exact computation is NP-hard but a Rao-Blackwellized spanning-tree estimator achieves near-linear time per sample with Delta-method intervals.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The uncertainty model for signed edges permits a graph decomposition into spanning trees whose balance contributions can be Rao-Blackwellized to yield an unbiased estimator whose variance is controlled by the structural properties invoked in the proof.","pith_extraction_headline":"Balance rate quantifies stability in uncertain signed graphs and can be estimated efficiently even though exact computation is NP-hard."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17492/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.530692Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:41:18.739181Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.678374Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.641832Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d671cd2af1496db25e77b10e915a0b1acc72c5fc634f0f23156aa68f9603ea1d"},"references":{"count":67,"sample":[{"doi":"","year":2017,"title":"Robert P Abelson and Milton J Rosenberg. 2017. Symbolic psycho-logic: A model of attitudinal cognition. InAttitude change. Routledge, 86–115","work_id":"a737436d-8400-4f95-8210-c882603a9ee4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Lada A Adamic and Natalie Glance. 2005. The political blogosphere and the 2004 US election: divided they blog. InProceedings of the 3rd international workshop on Link discovery. 36–43","work_id":"734c0377-41c1-40cb-9fe4-d7f61a5ba925","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1975,"title":"KK Aggarwal, KB Misra, and JS Gupta. 1975. Reliability evaluation a comparative study of different techniques.Microelectronics Reliability14, 1 (1975), 49–56","work_id":"a5f91678-737f-49cb-9580-8d1466d0434b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Samin Aref, Andrew J Mason, and Mark C Wilson. 2020. 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