Multi-Band Universality and Watson-Band Rigidity for Bird-Map Borel Transforms (Paper 33 in the Non-Holomorphic Fractal Series)

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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,…

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Topics & keywords

Keywords
  • Observable
  • Rigidity (electromagnetism)
  • Intermittency
  • Fractal
  • Universality (dynamical systems)
  • Disjoint sets
  • Bounded function
  • Decoupling (probability)
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