Fibre stability for dominated self-affine sets

The paper proves the constancy of V ↦ dim_A π_{V⊥}(K) on XF and establishes the exact dimension-conservation identity via weak tangents, plus the slice equality under a separation hypothesis (Theorem B), using a new product-structure construction for coarse microsets (Theorem 4.9), together with a slicing theorem for weak tangents (Proposition A) and a nontrivial constancy argument (Proposition 4.7). These ingredients are explicitly combined in the proof of Theorem 4.1 and its corollaries to yield Theorem B; the statements match the claimed results in the candidate solution. However, the candidate’s proof relies on incorrect steps: (i) it asserts a finiteness/rigid orbit description of XF which the paper does not assume and which is generally false, (ii) it claims a functoriality A_u(E) ∈ Tan(K) for all words u that is not valid under the no-rotation definition of weak tangents, and (iii) it replaces the core product-structure lower bound (Theorem 4.9) with an unsubstantiated “direct covering” argument. The paper’s arguments address these delicate points rigorously, while the model’s proof elides them. Therefore the paper is correct and the model’s proof is flawed. Key references: Theorem B and its precise statement and scope ; constancy on XF (Proposition 4.7) ; construction of product coarse microsets (Theorem 4.9) and the proof of Theorem 4.1 ; weak-tangent slicing (Proposition A) ; consequences and equality under separation (Corollary 5.6 / 5.4 scope) .