{"paper":{"title":"Exact Nonnegative Matrix Factorization via Cone-Ray Witnesses: Obtuseness Ranking, Saturation Curves, and an Augmented Alt-LP Breakthrough","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.NA"],"primary_cat":"math.NA","authors_text":"Mithil Ramteke","submitted_at":"2026-06-21T11:51:35Z","abstract_excerpt":"We study exact nonnegative matrix factorization (NMF) of small exact-rank-r matrices via a cone-ray pipeline combining the truncated SVD, the polyhedral cone of nonnegative preimages, the Double Description Method (DDM, via Fukuda's cddlib), and an alternating linear program (alt-LP) for slack minimisation. Under a uniform-support restriction the factorisation constraint Q P^T = I_r reduces to entrywise nonnegativity of an r x r witness matrix M_T = R_T^{-1} (R_K^T)^{-1} for an r-subset pair (T, K) of cone rays; this closed-form witness recovers an exact NMF in microseconds when feasible.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22451","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/2606.22451/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"}