Toy Watson ε-Family Ladders for Bird-Map Borel Coefficients: Phase 0–1.5 Diagnostics, Local Rigidity, and Lorentzian Calibration (Paper 31 in the Non-Holomorphic Fractal Series)

Paper 31 in the Non-Holomorphic Fractal Series. We construct and calibrate a first toy ε-family Watson-side ladder for the non-holomorphic Bird map, tuned to the Class C Watson band B_W ≈ [0.79, 0.87] identified in Paper 30 while leaving the Paper 28 orbit generator untouched. At ε = 1.0 with normalization exponent p = 2.2, the toy ladder achieves ρ_40 ≈ 0.80 and ρ_80 ≈ 0.88, cleanly inside or adjacent to B_W and well separated from the orbit band B_orb ≈ [0.14, 0.19]. A local rigidity proposition records the ε-sweep behavior over ε ∈ [0.90, 1.10] and identifies the B_W-membership window ε ∈ (0.93, 1.08) at N ≤ 80. Phase 1.5 Lorentzian calibration confirms that the Watson-side band placement is kernel-robust within the p = 2.2 normalization class.