{"paper":{"title":"Wythoff-Fibonacci Sequences and a Perturbed Greedy Almost-involution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Iker Malaina, Luis Mart\\'inez","submitted_at":"2026-07-01T11:40:48Z","abstract_excerpt":"We introduce the lower and upper Wythoff-Fibonacci sequences, obtained from the classical Wythoff sequences by a Fibonacci correction. Specifically, if we put $$\\epsilon(j)=\\begin{cases}(-1)^k, & \\text{if }j=F_k\\text{ for some }k\\\\ 0, & \\text{in other case}\\end{cases},$$ where $F_k$ is the $k$-th Fibonacci number, then we define the general terms of the lower and upper Wythoff-Fibonacci sequences by $$LWF(n)=\\begin{cases} 1, & \\text{if }n=1,\\\\ 3, & \\text{if }n=2,\\\\ a(n)+\\epsilon(n), & \\text{if }n\\geq 3.\\end{cases}$$ and $$UWF(n)=\\begin{cases} 2, & \\text{if }n=1,\\\\ b(n)+\\epsilon(n), & \\text{if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00814","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/2607.00814/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"}