SELF-SIMILAR DIRICHLET FORMS ON POLYGON CARPETS

The paper proves existence of a local regular self-similar Dirichlet form on polygon carpets (perfect, or bordered under (H) and (C)) via the Kusuoka–Zhou scheme under condition (B), then constructs a self-similar form with ri = ρi^θ and establishes the Hölder–resistance bound. By contrast, the model asserts a one-step renormalization equation Λ(θ)=1, a monotonicity argument in θ, and a compatibility-of-traces construction that the paper explicitly avoids on these non-p.c.f. carpets. The model provides no proof of (B) or of the required monotonicity/compatibility; several claims are unsubstantiated. Hence the paper’s result is correct and rigorous, while the model’s solution is incomplete and relies on unproven steps.