One quadratic field fixes a spectral measure

Physical constants are normally inputs to a theory; here they are outputs of a chain whose first half is pure arithmetic, and this paper carries that half end to end without a fitted step. The chain begins at a single structural number, the spectral degree d_sp=16 fixed by the sector setting, and closes as follows. Spectral closure forces the discriminant 17; the discriminant–field bijection then selects Q(17) uniquely, so no field is picked from a menu; and the arithmetic of that field supplies the invariant pair (w_2,|K_2|)=(24,8) from its unit-root and K-theoretic sides. Two locked constraints on the Beta shape parameters—sum 2+10=12=w_2/2 and difference 9-1=8=|K_2|—have the unique positive solution (2,10). The spectral measure is therefore forced to be (x)=110\,x(1-x)^9. The same arithmetic yields the integer invariant 136=_K|K_2|, the prime norms 1879 and 613, and the four-sided identity w_2/|K_2|=48/N_J=1/_K(-1)=N_c=3, which fixes the exponent pair (1,9) instead of assuming it. The chain carries discriminating power rather than merely fitting: for Q(5) the analogous invariants give |K_2|=4 where the closure would require 32, so the mechanism is specific to this field. The pinned spectral family built on the forced measure ends at 0.8480856676, the value the confinement theorems of the framework consume, while the five-dimensional sector setting remains a registered postulate and no measured number enters any step.