This manuscript introduces and proves the Minimal Interference Law for Rotational Systems, a standalone mathematical result characterizing the structural conditions under which interference in irrational rotations is minimized. A baseline-corrected weighted near return functional is defined for rotations on the circle, and a two sided limsup excess objective is used to quantify deviation from universal behavior. An exact identity reduces the functional to averaged prefix discrepancy, enabling a complete and self-contained analysis. The paper proves that bounded type (badly approximable) rotations are the unique optimizer class of the minimal-interference objective. Bounded type is shown to yield logarithmic envelopes via Denjoy–Koksma and Ostrowski expansions, while unbounded type is shown to produce unavoidable super logarithmic discrepancy spikes through an explicit fixed-center staircase mechanism tied to continued-fraction partial quotients. The result establishes a sharp selection principle without reliance on probabilistic averaging, translation freedom, or window axioms. All arguments are constructive and independent of external frameworks. The manuscript is intended as a standalone contribution to ergodic theory, discrepancy theory, and extremal selection principles, and may serve as a foundation for extensions to higher-dimensional systems and other interference-minimization problems.
Kearon Allen (Fri,) studied this question.