On p-adic cascade equations of hydrodynamic type in modeling fully developed turbulence

For s = 2 with diagonal H, the paper’s stated stationary profile Vi = c_{i mod 3} p^{-5i/6} under either γ = −3β − 1/2 or γ = −(3/2)β − 1/4 agrees with the energy law Ei ∼ p^i Vi^2 and is consistent with the candidate’s derivation from Eq. (14) and relations (18) . For s = 3 with diagonal H, the paper claims a profile Vi ∝ p^{-i/3} “which corresponds to the 2/3 law” (Eq. (19) discussion), but this exponent contradicts Ei ∼ p^i Vi^2 ∼ p^{-2i/3}, which forces σ = 5/6; here the model correctly flags the exponent mismatch even though the β–γ relations remain those of (18) . For s = 2 with off-diagonal H (Eq. (20)), the paper asserts existence of 2/3-law stationary solutions for γ = −1 (all β), and for γ = −3β − 3/2 or γ = −(3/2)β − 5/4, but provides no proof; the candidate’s reduction to a single “flux polynomial” overlooks squared products (e.g., Vi±1Vi±1, Vi±2Vi±2) present in (20), so the model’s Case C derivation is not justified as written, and it does not enforce σ = 5/6 required by the 2/3 law .