Multi-Kernel Watson-Band Universality for Bird-Map Borel Transforms (Paper 36 in the Non-Holomorphic Fractal Series)

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Abstract

Paper 36 in the Non-Holomorphic Fractal Series. We generalize Paper 35's unconditional Watson-band rigidity from the single WBA kernel h_W(y) = y/(1+y²) to the entire admissible Watson class κ = {h ∈ C∞(I) : sup_{y∈I} |h(y)| ≤ 1/2}. Theorem A (Admissible Watson-class framework): the single condition sup|h| ≤ 1/2 gives uniform weight bounds e^{-ε/2} ≤ e^{εh(y)} ≤ e^{ε/2} for all ε ∈ [0,1], y ∈ I; the WBA, Lorentzian (σ = 2.0), and alien kernels all belong to κ; and the Lasota–Yorke inequality from Paper 34 holds for every h ∈ κ with identical constants. Theorem B (Generalized pressure bridge): for all h ∈ κ, ρ(h) = r(L_{h,1}). Theorem C (Certified spectral gaps): computer-assisted interval-arithmetic Ulam…

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Topics & keywords

Keywords
  • Conjecture
  • Fractal
  • Rigidity (electromagnetism)
  • Invariant (physics)
  • Spectral radius
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