{"paper":{"title":"Principal minors of effective-resistance matrices and local resistance radii","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangfu Wang","submitted_at":"2026-06-16T15:37:09Z","abstract_excerpt":"Let $G$ be a finite connected weighted graph and let $R$ be its effective-resistance matrix. For every nonempty vertex set $S$, we factor the cofactor sum and determinant of the principal resistance submatrix $R[S]$ into an enumerative term and a boundary potential-theoretic term. If $\\tau(G)$ is the weighted spanning tree enumerator and $\\kappa_G(S)$ is the weighted enumerator of $S$-rooted spanning forests, then \\[\n  \\cof R[S]=(-2)^{|S|-1}\\kappa_G(S)/\\tau(G). \\] After Kron reduction to $S$, with reduced Laplacian $K=L^S$, $Q=K^+$, and $q=\\diag(Q)$, the remaining normalized factor is \\[\n  \\de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18061","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18061/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}