Structural Impossibility of Watson–Boundary-Layer Anchor Reproduction and the Picard–Lefschetz Redefinition of the Class A Stokes Constant (Paper 15 in the Non-Holomorphic Fractal Series)

Paper 15 in the Non-Holomorphic Fractal Series. Paper 11 reported three numerical anchor values for the Class A Stokes constant S₁ᴬ(α) at α ∈ {1/4, 1/2, 3/4}, extracted via a Definition 4.1 amplitude ratio on the Stokes ray. These values, together with the sign result of Paper 12 and the α^{1/3} power law of Paper 14, formed the empirical backbone of the series. Subsequent exhaustive experiments showed that no implementation faithful to the finalized Watson–boundary-layer–Picard–Lefschetz (Watson–BL–PL) framework reproduces the anchors. Every spec-true realization of the area law, Watson factor, BL series and normalization either drives the Definition 4.1 ratio to 0 or to a large K-independent constant f(α) ≫ 1, never to the legacy triple (0.59612, 0.76328, 0.89320). This paper formalizes that impossibility as two structural theorems, one for the analytic Watson area law and one for pixel-count fractal areas with Watson scaling, and proves a forensic provenance lemma reclassifying the anchors as legacy empirical constants. In their place we introduce a reproducible Picard–Lefschetz definition of the Class A Stokes constant via the endpoint half-thimble integral, consistent with the sign from Paper 12 and the α^{1/3} exponent from Paper 14. This new definition is the foundation for the numerical Picard–Lefschetz law in Paper 16.