Quantitative Exponential Mixing Rates for Twisted Bird-Map Transfer Operators (Paper 38 in the Non-Holomorphic Fractal Series)

Paper 38 in the Non-Holomorphic Fractal Series. Building on the certified positive BV spectral gap established in Paper 37 for all 27 cells of the widened grid ε_wide (three kernels, nine ε values), we extract the first explicit exponential mixing rates for the twisted Bird-map transfer operators. The Ruelle–Perron–Frobenius spectral decomposition on BV(I) converts the certified spectral gap into a quantitative L¹ decay bound ‖Lⁿ_{h,ε}f − π(f)‖_{L¹} ≤ Cθⁿ‖f‖_{BV}, where the constants C and θ < 1 are explicit in terms of γ_{cert}(h, ε) and μ₁(h, ε) from Paper 37 Table 2. The worst-case γ_{min} = 0.6509 (alien kernel, ε = 0.80) yields a uniform mixing rate θ_{max} = 0.8720 valid for all three kernels on the full enlarged rigidity interval I_{rig}. A full 27-cell table of explicit θ(h, ε) and C(h, ε) values is provided in Appendix A.