{"paper":{"title":"Stable Phase Retrieval for Spans of Independent Random Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.FA","authors_text":"Jaume de Dios Pont, Jo\\~ao P. G. Ramos, Mitchell A. Taylor, Pedro Abdalla","submitted_at":"2026-07-07T18:10:15Z","abstract_excerpt":"We prove that, after $L^2$ normalization, stable phase retrieval holds over the $L^2$-spans of independent real-valued centered random variables if and only if all but possibly one coordinate satisfies a uniform two-sided $L^1$ bound. This provides a complete characterization of stable phase retrieval for such subspaces, building upon the pioneering work of Calderbank--Daubechies--Freeman--Freeman and confirming the conjectured characterization communicated to us by those authors.\n  We provide two different proofs of this fact, both based on a decomposition of the $\\ell^2$-coefficients of each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06693","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/2607.06693/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"}