The Intrinsic Reductions and the Intrinsic Depths in Non-Archimedean Dynamics

The paper’s slope formula for the hyperbolic resultant (Theorem 2) is stated and proved correctly via the difference formula and a 0/1 directional derivative computation. The candidate model reaches the same final slope formula but its derivation contains substantive errors: (i) an incorrect coefficient in front of ρ(ξ,ξ_g) (3/2 instead of (d+1)/2), which prevents the necessary cancellation of Gauss-direction terms; (ii) a misuse of the Gromov product identity with a moving target φ(ξ) that omits a derivative term; and (iii) an unsupported “unit speed” assumption in the ‘two-rays’ lemma. Part (B) of the model (equidistribution of intrinsic depths) is essentially correct as a pushforward of the standard pullback equidistribution, but Part (A) — the core slope computation — is flawed. Hence overall: paper correct, model wrong.