Adjacent Period Ratios as Partition Coordinates: A Conservative Reanalysis of Exoplanet Spacing and a Null-Model Failure

This revised technical note reanalyzes an early exploratory study of adjacent exoplanet period ratios. The original version interpreted a feature near (R_P \approx 1.78) as possible evidence for a special exponential or geometric threshold. The present revision rejects that interpretation. The adjacent period ratio (R_P=P_{i+1}/P_i) is retained as a useful coordinate for organizing multi-planet architectures, but the value near (1.78) is treated only as a descriptive coordinate location, not as a constant, invariant, or dynamical law. The main confirmed result is methodological: the original shuffled null model was invalid because it shuffled orbital periods within each system and then re-sorted them before computing adjacent ratios, thereby reconstructing the same statistic. A corrected audit shows that the observed period-ratio structure is largely explained by known mean-motion resonance features, including the (3{:}2), (5{:}3), (7{:}4), (9{:}5), and (2{:}1) regions. Smooth-null tests also show that the scanning peak location near (R_P\approx1.78) is generic to the metric for distributions of similar shape, rather than evidence for a special landmark such as (e-1) or (\sqrt{\pi}). The note preserves an exact partition-coordinate reformulation: any positive ratio (R) can be mapped to normalized shares (a=R/(1+R)), (b=1/(1+R)), asymmetry (\chi=(R-1)/(R+1)), and coupling (\mu=R/(1+R)^2). For (R_P\approx1.785), this gives approximately ((a,b)=(0.64,0.36)), (\chi\approx0.28), and (4\mu\approx0.92). This is presented as a descriptive asymmetry--coupling coordinate only, not as a stability law. The broader lesson is that ratios can be useful survey coordinates without being physical constants.