{"paper":{"title":"A nonlinear version of the $\\alpha$-Kakutani equidistribution problem","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Nonlinear families of C^{1+ε} contractions equidistribute interval endpoints according to Lebesgue measure when nonlattice and thermodynamic regularity conditions hold.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ignacio Rojas","submitted_at":"2026-05-15T16:37:13Z","abstract_excerpt":"In this work, we extend results of Kakutani; Adler and Flatto; Smilansky; Pollicott and Sewell on the equidistribution of endpoints generated by interval-splitting procedures. We study a nonlinear version of the problem generated by a finite or countable family of $\\mathcal{C}^{1+ \\varepsilon}$ contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We study a nonlinear version of the problem generated by a finite or countable family of C^{1+ε} contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The family of contractions must satisfy the nonlattice condition together with thermodynamic regularity assumptions; the abstract states these are required for the equidistribution to hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves Lebesgue equidistribution of endpoints for nonlinear interval-splitting procedures under nonlattice and thermodynamic regularity assumptions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonlinear families of C^{1+ε} contractions equidistribute interval endpoints according to Lebesgue measure when nonlattice and thermodynamic regularity conditions hold.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f6268aa01cab511281918a5122299a5a9b6eb4e1ca078734b33177a78b2b1d41"},"source":{"id":"2605.16156","kind":"arxiv","version":1},"verdict":{"id":"9e868171-63bf-4923-a2aa-edf5ee4520ee","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:35:07.538048Z","strongest_claim":"We study a nonlinear version of the problem generated by a finite or countable family of C^{1+ε} contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.","one_line_summary":"Proves Lebesgue equidistribution of endpoints for nonlinear interval-splitting procedures under nonlattice and thermodynamic regularity assumptions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The family of contractions must satisfy the nonlattice condition together with thermodynamic regularity assumptions; the abstract states these are required for the equidistribution to hold.","pith_extraction_headline":"Nonlinear families of C^{1+ε} contractions equidistribute interval endpoints according to Lebesgue measure when nonlattice and thermodynamic regularity conditions hold."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16156/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.934887Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:41:02.499745Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T18:22:02.303414Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:31.039655Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.440864Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0ba0aa793144efb75ff8cef292e0c5803e5eac1d8f3c911176dc70d6d5600648"},"references":{"count":18,"sample":[{"doi":"10.1007/s11856-023-2569-6","year":2024,"title":"Pollicott, M. and Sewell, B. , TITLE =. 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