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
- 2 · 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.
Keywords Fekete lemma · subadditivity · integer connectivity · shrinking corridors · real sequences
Scope of the work
Divergent square-integral shrinking corridors force normalized convergence for arbitrary real subadditive sequences under either stated balanced predecessor condition, including the logarithmic condition beyond eventual adjacent-pair legality.
Reproduction notes
The 8-page manuscript and complete editable LaTeX sources are supplied in this 9-member package. README.md gives the build and reproduction commands. Reproducibility code: verify.py. The accompanying manuscript and reader instructions specify the mathematical scope and required dependencies.
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Cite this edition
Scott Schubr. (2026). Fekete convergence from balanced integer predecessors in shrinking corridors (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/fekete-convergence-balanced-integer-predecessors-shrinking-corridors/v/2
BibTeX
@techreport{luminary_fekete_convergence_balanced_integer_predecessors_shrinking_corridors_v2,
title = {Fekete convergence from balanced integer predecessors in shrinking corridors},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/fekete-convergence-balanced-integer-predecessors-shrinking-corridors/v/2}
}Loading discussion…