Multi-Band Universality and Watson-Band Rigidity for Bird-Map Borel Transforms (Paper 33 in the Non-Holomorphic Fractal Series)
Abstract
Paper 33 in the Non-Holomorphic Fractal Series. We develop a multi-band universality framework for Borel transforms of observables on the non-holomorphic Bird map, organizing exponential types into two disjoint bands: an orbit band B_orb = [0.14, 0.19] for orbit-type observables and a Watson band B_W = [0.79, 0.87] for Watson-type kernels. We prove orbit-band placement for orbit-type observables (Theorem 3.1) and provide three-kernel numerical evidence supporting Watson-band rigidity and cross-band decoupling. On the numerical side, we show that three distinct Watson-class kernels (the real WBA kernel on the true orbit, a calibrated Lorentzian proxy, and an alien-strength kernel) all exhibit a shared, contiguous rigidity window 0.84 ≤ ε ≤ 0.90 in which their tail-averaged root-test exponents ρ_N(h, ε) lie inside B_W for all sampled large N, while remaining uniformly separated from B_orb. These results motivate conjectural cross-band decoupling and Watson-band rigidity statements.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Random Matrices and Applications
Advanced Algebra and Geometry
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 5 April 2026
- Document type
- Preprint