Generalized Decoupling for Bird-Map Borel Coefficients: Multi-Band Exponential-Type Universality and Phase 1 Diagnostics (Paper 30 in the Non-Holomorphic Fractal Series)
Abstract
Paper 30 in the Non-Holomorphic Fractal Series. We investigate whether the orbit-multiplier Decoupling Lemma of Paper 26, the sharp Hartman–Wintner LIL constants of Paper 28, and the exponential-type analytic-disk bound of Paper 29 extend to other Borel ladders in the Bird-map coefficient atlas. Phase 1 diagnostics assemble three ladder sequences under a common data model and compare the empirical growth rate log|a_n| versus n. The ε-family orbit-multiplier ladder sits in a tight orbit band B_orb ⊂ [0.14, 0.19] with LIL-scale residuals, fully consistent with Papers 26–29. The Class C Watson-side proxies (WBA and alien-strength) cluster in a Watson band B_W ≈ [0.79, 0.87] with residuals of order 1, establishing that exponential type is not universal across observables. We state and sketch the proof of an Orbit-Multiplier Generalized Decoupling Theorem, derive a conditional statement for Watson-side observables, formalize the Multi-Band Universality Conjecture, and outline a construction plan for a true ε-family WBA ladder.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Holomorphic and Operator Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 April 2026
- Document type
- Preprint