{"paper":{"title":"On the spectra of Cantor measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Leandro Zuberman","submitted_at":"2026-05-18T14:28:14Z","abstract_excerpt":"We consider Cantor measures on the line, with contraction factor $N^{-1}=p^{-\\alpha}$ (where $p$ a positive prime, $\\alpha$ a positive integer) and $m$ positive integer digits lying in distinct residue classes modulo $N$. We obtain a complete characterization of maximal orthogonal sets of exponentials in $L^2(\\mu)$, for a class of such measures $\\mu$. It is proved that the $n+1$-th digit in the base-$N$ expansion of frequencies in a maximal orthogonal set, with the first $n$ digits prescribed, has $m$ possible values. In consequence, there are a correspondence between labelings of the $m$-homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18471","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/2605.18471/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"}