Scale Geometry: Independent Convergence on the Fifth Dimension — A Complete Theory with Confirmed Predictions and Time-Scale Unification

This paper presents Scale Geometry: a unified theoretical framework in which the familiar four dimensions of spacetime are extended by a fifth dimension representing physical scale. The framework is built on a single equation — the warp factor A(s) = −ln(cosh(ks)) — from which the entirety of the theory follows. Seven quantitative predictions have been confirmed against observational data with zero free parameters and zero conflicts with observation. The paper documents the independent convergence of three researchers in three countries on the same fundamental insight, with probability of coincidence less than one in five billion. Time-Scale Unification (TSU) demonstrates that time and scale are geometrically unified along a single axis. Fifteen adversarial wounds are catalogued with full transparency. Nine experiments costing approximately $1.1M can test every remaining prediction. 161 pages, 10 parts, 60 sections.