The Mean-Field Survival Model for Stripe Formation in Zebrafish Exhibits Turing Instability

The paper’s linearization, definition of F, region P, and Theorems 1–2 (instability for (b,d) in P with large h,N; stability outside P; bounds ⌈N/(4h)⌉ ≤ k ≤ ⌈N/(2h)⌉; and the h=1,2 stability) are internally consistent and supported by detailed arguments and appendices. The candidate solution broadly follows the paper’s logic and matches its main constructions (DFT block-diagonalization; negative, k-independent trace; det governed by F; k-window). However, its proof of stability for h=1,2 is incorrect: it asserts det(A_k) ≥ a q > 0 from c_k ≤ 0 and p_k ≤ 0, but for a 2×2 matrix det = a q − c p, and with c≤0, p≤0 one has c p ≥ 0 so det ≤ a q, not ≥ a q. This sign error invalidates the claimed global stability proof for h=1,2. There is also a minor algebra slip in the explicit expression for q. The remaining parts of the model’s argument align with the paper.