Robustness of the Twisted BV Spectral Gap Under a Widened Bird–Watson Parameter Window (Paper 37 in the Non-Holomorphic Fractal Series)

Paper 37 in the Non-Holomorphic Fractal Series. Building on the twisted Lasota–Yorke infrastructure of Paper 34, the unconditional Watson-band rigidity results of Paper 35, and the multi-kernel universality theorem of Paper 36, we show that the existing BV spectral gap for the Bird map transfer operators with WBA, Lorentzian, and alien kernels persists uniformly on a widened parameter window in the coupling parameter ε. Our main contribution is a robustness theorem: using the certified Ulam scheme from Papers 34–36 as a stress-test tool, we verify that the twisted BV gap extends from the original window ε ∈ [0.84, 0.90] to a larger interval containing {0.70, …, 1.10}. Combining this with a tightened Kullback–Leibler constant C_{KL} in the rigidity bridge, we obtain an enlarged rigidity interval I_{rig} for the Watson band.