{"paper":{"title":"Stealthy point processes and lattice induction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Michael Bj\\\"orklund","submitted_at":"2026-07-28T11:45:42Z","abstract_excerpt":"We prove a realization theorem for stealthy point processes based on lattice induction, together with a converse in dimension one. Every probability-preserving $\\mathbb R^d$-action induced from a full-rank lattice admits a generating Delone cross-section whose Bartlett spectrum vanishes on a neighborhood of the origin. The construction can be chosen so that first-order linear statistics detect a nonzero part of the inducing spectral type. Bernoulli bases yield a nonzero absolutely continuous component, while weakly mixing bases of singular maximal spectral type yield a nonzero singular-continu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25616","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/2607.25616/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"}