Phase-Shift Transport: Geometric Constraints on Wave Phase Manipulation within DOT

This paper derives geometric constraints on phase-based spatial transport within Dimensional Oscillation Theory (DOT). If particles are standing wave convergences whose location is defined by phase relationships across four modes (DOT Postulate P3), then controlled phase manipulation constitutes spatial transport. The paper surveys established physics of wave phase modification — from classical interference to the experimentally confirmed gravitational Aharonov-Bohm effect — then derives the specific geometric requirements any DOT-consistent transport mechanism must satisfy: ring topology with three emitters at 120°, weak-mode precision bottleneck, and a six-parameter address space reducible to three effective dials. The entire argument reduces to a single assumption (P3); every intermediate step is either a proven theorem or an established experiment. The paper explicitly identifies the coupling problem (35 orders of magnitude), quantum uncertainty limits, and discontinuity stability as fundamental obstacles that may be physically impossible to overcome. This document records the mathematical constraints for priority, not an engineering proposal.