{"paper":{"title":"Higher traces as boundary averages on finite-dimensional normed spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.FA","authors_text":"Tomasz Kania","submitted_at":"2025-10-18T13:40:02Z","abstract_excerpt":"Let $X$ be an $N$-dimensional real normed space, let $1\\leqslant k\\leqslant N$, and set $V=\\Lambda^kX$ and $m=\\binom Nk$. We characterise the probability measures $\\eta$ on the unit sphere of $V$ for which \\[ \\operatorname{tr}(\\Lambda^kA)=m\\int w^\\sharp\\big((\\Lambda^kA)w\\big)d\\eta(w) \\] holds for every $A\\in\\operatorname{End}(X)$: this is equivalent to $m\\int w\\otimes w^\\sharp d\\eta(w)=\\operatorname{Id}_V$. The cone probability measure always satisfies this condition, giving a canonical higher-trace formula for every norm. Normalised Euclidean hypersurface measure also does so under a scalar-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16501","kind":"arxiv","version":2},"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/2510.16501/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"}