Watson-Band Placement for Real WBA Ladders on the Bird Map: Rigidity Windows and Watson-Class Proxies (Paper 32 in the Non-Holomorphic Fractal Series)

Paper 32 in the Non-Holomorphic Fractal Series. We construct the real WBA kernel and ladder for the non-holomorphic Bird map and measure its tail-averaged root-test exponents along the autonomous orbit. Phase 2 gate runs at ε = 1.0 and N ∈ {40, 80} reproduce the Class C Watson band B_W = [0.79, 0.87] identified in Paper 30 and calibrated in Paper 31. An ε-sweep at N ≤ 400 exhibits an N-dependent rigidity window drifting left and narrowing in ε, with the true WBA ladder remaining in or adjacent to B_W for 0.84 ≲ ε ≲ 0.93. At N = 400 the real WBA kernel, a Lorentzian proxy, and an alien-strength Watson-class proxy agree numerically across this window, providing a numerical robustness check that the real WBA kernel remains inside the Watson band B_W.