{"paper":{"title":"Normal approximation of the numbers of isolated edges and isolated 2-stars in uniform simple graphs with given vertex degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"New Stein couplings deliver the first finite-sample normal approximation bounds for isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees.","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Ryo Imai","submitted_at":"2026-05-09T05:41:38Z","abstract_excerpt":"We consider the configuration model and the uniform simple graph with given degree sequence $\\boldsymbol{d}=\\left(d_i\\right)_{i=1}^n$. We derive quantitative bounds for the errors in (i) joint normal-Poisson approximation to the numbers of isolated edges, isolated 2-stars, self-loops and double edges in the configuration model, and (ii) normal approximation to the numbers of isolated edges and isolated 2-stars conditioned on that the configuration model is simple. The latter provides the first finite sample normal approximation results for the uniform simple graph with given vertex degrees. To"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The latter provides the first finite sample normal approximation results for the uniform simple graph with given vertex degrees.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The degree sequence satisfies the (unspecified in abstract) regularity conditions under which the configuration model is simple with high probability and the new Stein couplings yield the stated quantitative error bounds.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper establishes the first finite-sample normal approximation bounds for the numbers of isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees, via new joint normal-Poisson Stein's method and indicator coupling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"New Stein couplings deliver the first finite-sample normal approximation bounds for isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6311fbda862bfee354978491b61bf39ea55df7ecc15f7d0f87aeff6a9ec8ea63"},"source":{"id":"2605.08706","kind":"arxiv","version":3},"verdict":{"id":"032c2904-6ffb-4dba-b56c-6e055d93d67b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T21:52:27.512388Z","strongest_claim":"The latter provides the first finite sample normal approximation results for the uniform simple graph with given vertex degrees.","one_line_summary":"The paper establishes the first finite-sample normal approximation bounds for the numbers of isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees, via new joint normal-Poisson Stein's method and indicator coupling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The degree sequence satisfies the (unspecified in abstract) regularity conditions under which the configuration model is simple with high probability and the new Stein couplings yield the stated quantitative error bounds.","pith_extraction_headline":"New Stein couplings deliver the first finite-sample normal approximation bounds for isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.08706/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T09:02:01.967488Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:35:55.417258Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T14:31:17.722441Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:51:40.197992Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"78ed81d90789ba35cd6eaed65c403ea4e14eda885a9915bd4e62a69e5a6db090"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"17fa93056ae46948f08e9193024221db58f3501a78e8cad930ac1af67b96b105"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}