CB-PFR Methodological Working Paper: A Proposed Uncertainty-Aware Selection Layer for QUBO-Generated Candidates

This methodological working paper introduces the Constraint-Bounded Penalty-Free Selection (CB-PFR) framework, an uncertainty-aware post-processing selection layer designed for candidate solutions generated by Quadratic Unconstrained Binary Optimization (QUBO) formulations. The framework evaluates candidate solutions using uncertainty-aware constraint bounds and ranks candidates according to constraint feasibility and the associated QUBO objective. The proposed selection layer is designed to operate after candidate generation and does not modify the underlying QUBO formulation through additional penalty terms. The computational evaluation consists of 1,000 controlled synthetic trials using a fixed base seed of 20261005. Four methods were evaluated under the same candidate observation pool and evaluation budget: QUBO-only selection, point-estimate selection, CB-PFR selection, and a uniform-margin baseline. The recorded true-feasibility rates were 0.857 for QUBO-only selection, 0.933 for point-estimate selection, 0.976 for CB-PFR selection, and 0.966 for the uniform-margin baseline. Paired comparisons were performed using two-sided sign tests with multiple-comparison correction. The 1,000-trial synthetic benchmark has been independently reproduced from the released source code and configuration, reproducing the reported aggregate feasibility rates and substantive trial-level results. The release also documents an evidence taxonomy distinguishing computational reproducibility and software verification from physical validation. The current work does not claim physical reactor validation or a defensible mapping between the abstract QUBO verification core and a physical reactor model. The accompanying repository provides the source code, configuration, reproducibility documentation, tests, and computational experiment procedures associated with this working paper.