The Wake Point's Independent Address: f_W Is Free on the Whole Interval, and the Density Law That Would Fix It Is Not on Record

The separation law wakes at f_W = 0.773950, a number solved from the law's two priced conditions (the declared count u(1) = 11/411 and the T4 slope 0.236797), not predicted by the threshold sigma/s_A = 1. This paper looks for the gathering's density law rho(f) in the record's own dynamics to give f_W an independent address. Five candidate constructions are computed: uniform arrival misses by about a quarter of the axis in every normalization; geometry alone yields no rising crossing; the winding profile is barred (different coordinate, no dictionary) and misses anyway; the pull law is the wrong object; the frame-scale assembly gives R(1) = 5.953x10^-37, a gathering that never wakes. Underdetermination is then proven: under the record's constraints, R(f) can cross 1 at any point of (0, 1); the compatible family is fenced exactly. The dial table shows every route to 0.773950 passes through a number the record does not contain (linear species: R(1) = 1.292073; nearest record numbers miss by 30,945 to 257,492 ppm). The exact price: one function (the content-over-volume growth shape) and one number (R(1)). Verdict: PRICED FAILURE, underdetermination PROVEN. The vacuum catastrophe is NOT SOLVED.