Cohesion: A Unified Field Theory of Matter and Motion

This paper develops a unified field framework in which the observable universe ismodelled as a pressure-bound domain embedded within a larger scale hierarchy. Asingle axiom — that the universe is under pressure from the next higher scale — generatesintrinsic motion, scale invariance, intrinsic rotation, surplus flow, collapse, and recursivestructure formation. These consequences are formalised through a universal OperatorSystem and three coupled field equations: Surplus Continuity, Collapse/Momentum,and Continuance. Version 2 added the funneled-spring geometry and its connection tothe golden angle and fine-structure constant. Version 3 adds four further developmentsestablished in the series: (1) the binary recursion toggle — only two stable polaritystates exist for the funneled-spring recursion, hexapolar (n = 6) and bipolar (n = 2),with all others geometrically excluded; (2) matter formation as trapped recursion —matter forms when the stability index Φ > 1 and the recursion cannot escape itscoherence volume; (3) the infinite asymmetric cascade — the fine-structure constantis the coupling between adjacent levels of a hierarchy with no top and no bottom;and (4) the variable-c boundary condition — all calculations in this series use c = cE,the Earth-density propagation rate, valid within the solar system density layer; thepropagation rate is density-dependent at cosmological scales. No operator definitionsare altered.