{"paper":{"title":"On $q$-real and $q$-complex numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CO","math.DS","math.NT"],"primary_cat":"math.CV","authors_text":"Pavel Etingof","submitted_at":"2025-08-11T19:56:33Z","abstract_excerpt":"In arXiv:1812.00170, S. Morier-Genoud and V. Ovsienko introduced the notion of the $q$-rational number $[x]_q$, $x\\in \\Bbb Q$, a rational function specializing to $x$ at $q=1$, obtained by $q$-deforming the continued fraction expansion of $x$. In arXiv:1908.04365 they introduced $q$-real numbers $[x]_q$, $x\\in \\Bbb R$ - a Laurent series in $q$ converging to the rational function $[x]_q$ when $x\\in \\Bbb Q$. In arXiv:2102.00891 it is proved that if $x\\in \\Bbb Q_{>1}$ then the series $[x]_q$ converges for $|q|<3-2\\sqrt{2}\\approx 0.17$ and conjectured that for all $x\\in \\Bbb R_{>1}$ this series co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08440","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/2508.08440/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"}