{"paper":{"title":"Extreme points and faces in the moment problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.PR","authors_text":"Didier Henrion, Martin Kru\\v{z}\\'ik, Stephan Weis","submitted_at":"2026-06-19T12:54:41Z","abstract_excerpt":"The polyconvex envelope, used in the calculus of variations and elasticity theory, was expressed by Dacorogna pointwise as a linear program on finitely atomic measures on the space of $m\\times n$ matrices. Weizs\\\"acker and Winkler proved that the corresponding linear program on Borel measures restricts to the extreme points without increasing the infimum. Combining the two, one obtains a speed-up of grid-based algorithms and a new proof that the polyconvex envelope can be computed by the moment sum-of-squares hierarchy. Motivated by these applications, we seize the essence of extreme points in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21391","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/2606.21391/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"}