Assignment Bounds for Citrate-Synthase-Normalized Respiration in POLG D257A Arrays

**Background:** Unknown cross-assay specimen assignments can change the direction of a normalized comparison. Released POLG D257A mitochondrial respiration and citrate-synthase activity arrays permit a finite calculation, but do not establish paired specimen identity. **Objective:** Determine which mutant/control directions of mean observed-peak FCCP respiration divided by citrate-synthase activity survive every within-genotype one-to-one assignment, conditional on shared preparation sets and common assay scales. **Methods:** Six positive released slots per genotype were analyzed in brown adipose tissue (BAT), brain, colon and heart. All 720 assignments per group were compared with sorting extrema. Attainable mutant/control bounds and explicit witnesses were calculated; exploratory scale and estimand checks were replayed separately. Permutations were scenarios, not biological replicates. **Results:** Conditional dimensionless bounds were 0.640794–0.915489 for BAT, 1.070541–1.361803 for brain, 0.833813–1.121657 for colon and 0.818893–1.066251 for heart. Assignment alone could not reverse the BAT or brain direction; attainable extrema demonstrated both directions in colon and heart. Common rescaling left bounds unchanged. Exact relative quotient-scale thresholds reached equality at 1.092313 in BAT and 0.934108 in brain; genotype-specific scaling can therefore remove assignment robustness. **Conclusions:** Specimen linkage is numerically consequential for colon and heart, whereas BAT and brain directions are insensitive to assignment alone under the declared conditions. Shared preparation sets and common scales remain unverified. These deterministic bounds are neither sampling intervals nor observed paired phenotypes and establish no molecular mechanism or clinical benefit.