RC-MIFT: Sharp Robustness Bounds and Screening-Conditioned Response in Materials

This work develops a task-aligned Schur-complement framework for quantifying the robustness of material response under simultaneous errors in internal curvature, bare stiffness, and coupling. We identify the screening leverage κ as a conditioning coordinate governing response softening and structured error amplification, derive sharp nonasymptotic robustness bounds, and establish conditional precision-scaling laws. The framework also includes a black-box theorem for projected response extraction and no-go results for finite-source and state-transfer inference. Numerical audits and reanalysis of published data-including 42 stable response records, 72 matched cDFPT/DFPT cases, a near-critical meta-nitroaniline benchmark, a TaS2 stability crossing, and a Peierls-model sequence-provide complementary tests. The results establish screening leverage as a useful measure of response conditioning, rather than a universal single-variable error law.