{"paper":{"title":"Weight Certificates for Convex Multi-Objective MPC: Geometric Characterization, $\\ell^1$ Construction, and $\\ell^2$ Foreclosure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.AG"],"primary_cat":"math.OC","authors_text":"Benedikt Walter, Chaitanya Shinde, Hadi Hajieghrary, Miguel Hurtadoand Jerry Lopez","submitted_at":"2026-08-12T18:53:39Z","abstract_excerpt":"Automated-driving rulebooks rank rule violations lexicographically, and model predictive control enforces that ranking either exactly, through $L{+}1$ sequential programs per tick, or approximately, through a weighted sum tuned by the separation heuristic $w_1\\gg w_2\\gg\\cdots\\gg w_L$. We show the heuristic answers the wrong question. For a convex priority-ordered program, a weighted sum reproduces the lexicographic optimum precisely when its weight, augmented by a unit performance coefficient, supports the upper image of the achievement map at the lexicographic point; the admissible weights fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12520","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/2608.12520/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"}