The Coldness Is Dynamical: How Cold a Self-Critical MOND Sector Ends Up, and Why Nothing Has To Be Tuned

A cuscuton-clock MOND sector whose clock runs faster than proper time is gradient-unstable at zero field gradient, but its own MOND nonlinearity turns the sound speed positive at a finite gradient Y*, whose marginal state has cs2 = 0 and isotropic stress (doi:10.5281/zenodo.22727111). That left one thing unestablished: whether the back-reaction actually drives the gradient to Y* and holds it there closely enough for the Lyman-alpha forest. We settle it. Exactly two rates act on the gradient variance: expansion dilutes each mode's contribution as a-2, and where the sound speed is negative a mode of physical wavenumber k pumps it at 2|cs|k. Growth switches off the instant Y passes Y*, so the two balance at |cs| = H/k, giving a residual cs2 = (H/k)2. Integrating from initial gradients spanning eight orders of magnitude around Y*, every trajectory lands on the same balance point to six digits from both sides; the residual is 1/kappa2 to six digits across four decades and at every gradient-unstable epoch of the candidate's own history; and with a spectrum evolving together the shortest wavelength carries essentially all the gradient variance. The Lyman-alpha bound cs2 ≤ 1e-9 is therefore met once the instability acts on comoving scales below about 0.8 Mpc at z = 3. The apparent requirement that the gradient track Y* to one part in a million is the same condition in different units: the attractor sits at whatever precision the available wavelength dictates, and nothing is tuned, in particular not the logarithm margin of the closure. The cost is that the residual is set by the ultraviolet reach of the instability, so the forest gate becomes a lower bound on that reach rather than a tuning of coefficients. AI-assisted research programme; not peer reviewed.