The $2048$ Chrysopoeia: An Explicit Construction Program for the $d=2048$ SIC-POVM Moduli

Companion to the SIC–Stark–12th formalization, this paper lays out an explicit program for the diagonal moduli Nₖ=|ψₖ|² of the $d=2048$ SIC-POVM. It reports what direct computation has settled and what remains open. Five results are in place. The $a=0$ stratum reduces to a flat autocorrelation condition on the real moduli, a condition verified on $d=12$ to a residual near 10⁻⁵⁸. Unconstrained numerical recovery is blocked by a genuine local minimum (residual 3.9× 10⁻³). The moduli field is the real index-2 subfield, of degree 2²⁷, of the ray class field of conductor (d)\,∞₁∞₂, calibrated on the $d=12$ fiducial where the moduli have degree 4 or 8 and generate a field of degree 16; its unramified ascent is verified to degree 128. Stark-unit L-values supply the moduli without building the full field, a method validated end to end on $d=12$. An integer norm sieve separates degenerate S-unit aliases by discriminant -md. Still open: the reduced character set for the 1024 moduli and unconditional existence.