Research Article · Preprint Mathematics
Fekete convergence from balanced integer predecessors in shrinking corridors
- Primary subject
- Mathematics
- Subject subfields
- Classical and Real Analysis
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
Let w be positive, measurable and nonincreasing, with divergent square integral. Consider real sequences satisfying exact subadditivity only for integer pairs n≤ m≤ n+n w(log n). We replace eventual legality of adjacent pairs by a weaker condition: every sufficiently large output has a legal decomposition whose two summands differ by O(N^α) for some α<1, or by O(N/(log N)^(3/2+ε)) for some ε>0. Under either condition, a_n/n converges in ℝ ∪ {−∞}, without sign, monotonicity or growth assumptions. The proof regularizes the sequence by growing local maxima, proves exact integer corridor inequalities for that majorant, and separately transfers its limit back by propagation of low values along dyadic orbits. An explicit staircase width has arbitrarily long windows of illegal adjacent pairs, satisfies the logarithmic condition, and fails every fixed power condition. Both this convergence example and an oscillating isolated-output example can have divergent integrals of every finite positive power of w. Thus analytic width budgets and integer connectivity play different roles. No sharp connectivity characterization or optimal logarithmic exponent is claimed.
Keywords Fekete lemma · subadditivity · integer connectivity · shrinking corridors · real sequences
Scope of the work
Convergence for arbitrary real sequences under exact corridor subadditivity, divergent square integral and quantitative balanced predecessor hypotheses. No optimal logarithmic exponent or full connectivity characterization.
Reproduction notes
Editable LaTeX source and exact standard-library finite controls are included. With Python 3.10 or later, run python verify.py and python -O verify.py; the output verification.json records integer window, allocation and staircase checks. These finite controls do not replace the analytic convergence proof. Compile main.tex with Tectonic or run pdfLaTeX twice.
The manuscript
Read the paper
The complete manuscript, as published in this edition.
If the reader is unavailable on your device, open or download the PDF directly.
Author disclosures
AI tools assisted in developing and checking the arguments and preparing the manuscript. This assistance does not constitute external peer review.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Fekete convergence from balanced integer predecessors in shrinking corridors (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/fekete-convergence-balanced-integer-predecessors-shrinking-corridors/v/1
BibTeX
@techreport{luminary_fekete_convergence_balanced_integer_predecessors_shrinking_corridors_v1,
title = {Fekete convergence from balanced integer predecessors in shrinking corridors},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/fekete-convergence-balanced-integer-predecessors-shrinking-corridors/v/1}
}Loading discussion…