Certified Target-Sufficient Readout Design and Exact Finite-Model Reduction

This paper develops an exact computational realization of target-relative readout sufficiency within Shadow Theory’s source–readout programme. It asks which additional measurements are needed to determine a specified target from an incomplete readout, how to select them at minimum cost, and how to certify the answer without requiring full source reconstruction. For finitely described classical sources, a readout determines the target precisely when every pair of admissible sources producing the same readout also agrees on that target. The paper turns a failure of this criterion into an explicit computational witness: two sources with identical observed records but different target values. A unique-extension Boolean circuit compiler preserves the exact correspondence between these source pairs and satisfying assignments of the compiled formula. Building on this witness-producing test, a counterexample-guided synthesis procedure returns a globally minimum-cost sufficient selection from a declared sensor menu, or certifies that no jointly feasible selection exists. The framework accommodates incompatibilities, prerequisites and resource constraints, including cases where adding sensors can make a selection infeasible. An exact rational branch-and-bound implementation supplies independently checkable lower and upper cost bounds even when computation is interrupted. A nonlinear autonomous register provides an analytically solved example separating predictive sufficiency from full-source reconstruction. With unit port costs, determining every future observed bit requires b units, while reconstructing the complete source requires 2b minus 1 units. The distinction makes explicit why access sufficient for a nominated target need not recover the source that produced the record. Technical appendices develop exact signed rational factor contraction with explicit precision accounting, minimal sufficient linear parity summaries, and context-certified tensor-wire reductions with executable integer crossing factors. Supporting code and verification materials implement conventional exact algorithms and independently checkable certificates. The finite compilation, synthesis and certification results are distinguished from separate asymptotic complexity corollaries that depend on explicitly stated external preprint theorems. The supplied implementations do not implement those external algorithms or demonstrate their claimed asymptotic speedups. The results concern declared finite source models, permitted readouts and assigned resource costs. They do not assign simultaneous values to incompatible quantum observables, identify a compatible reconstruction with the actual source, or infer probabilities without a specified measure.