IDMate: Window-resolved self-consistent-field proposal screening with finite-temperature response bounds

We introduce IDMate, a Kohn–Sham framework for screening approximate self-consistent-field (SCF) states with a finite-temperature response bound and deterministic reference-map recovery. A charge-neutral factorization separates electronic conditioning from mixer amplification, while fixed-point-preserving rank-one interventions test their roles in the linearized dynamics. For a fixed Hamiltonian, exact electron number, and temperature, strong convexity of the Mermin free-energy functional yields an a posteriori density-matrix bound in a selected spectral window. Across $\mathrm{3,586}$ stress trials, $\mathrm{1,942}$ proposals were accepted and none exceeded the window criterion. Under trial independence, the one-sided $95\mathrm{\%}$ zero-event upper bound is $8.4\times {10}^{-4}$; treating the 70 correlated ladders as independent units gives $4.2\times {10}^{-2}$ per ladder. In three reference configurations, the integrated screening rule replaced ten reference-map evaluations, reproduced the reference-scoring trajectories, and satisfied every terminal comparison criterion. Window and full-space deviations differ by six to eleven orders of magnitude; full-space distance classifies the window decisions with a descriptive pooled AUC of $0.694$ (row-bootstrap $95\mathrm{\%}$ interval $[0.544,0.831]$). A predefined cross-lineage work model does not meet its acceptance criterion, and serial proposal construction makes the production implementation $7.87$ times as costly under the predefined charged-cost accounting as its all-reference counterfactual. IDMate establishes a rigorous exact-trace window bound, a tested accept-or-recover rule, and explicit full-space and implementation targets for net acceleration.