{"paper":{"title":"Excess Obstructions and Star-Isolated Certificates for the Hypergraph Nash--Williams--Tutte Conjecture","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yaoran Yang, Yutong Zhang","submitted_at":"2026-05-21T03:47:25Z","abstract_excerpt":"Guo, Li, Shangguan, Tamo, and Wootters formulated in SIAM Journal on Computing a hypergraph Nash--Williams--Tutte conjecture: every $k$-weakly-partition-connected hypergraph on $t$ vertices should admit a $k$-distinguishable tree assignment. We show that the conjecture, in its literal published form, is false for a sharp and structural reason. A tree assignment replaces every hyperedge $e$ by a tree with $|e|-1$ labelled edges, so its edge number is the excess $\\rho(H)=\\sum_e(|e|-1)$. A $k$-tree decomposition, however, has exactly $k(t-1)$ edges. Thus $\\rho(H)=k(t-1)$ is a necessary condition,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21961","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/2605.21961/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"}