No Dice: Deterministic Interference, Exact Branch Counts, and Quantum Measurement from the Fold

Quantum probability is derived here as an exact preimage census, not installed as a primitive continuum lottery. From one machine-checked self-proven theorem, zero axioms and zero fitted parameters, Smithian Fold Theory generates eight observation branches of indivisible weight 1/8 and proves that they partition the One. The same construction produces stationary spacing 1/8, ground share 1/16, exact phase return and deterministic bright-dark interference: maximal mismatch 1/2 is self-antipodal, aligned halves complete to the One, and the optics shares conserve the whole. A binary fibre independently generates the symmetric and antisymmetric exchange classes and proves that no third class exists. The paper connects mathematical derivation, exact execution, independent generated certificates and physical measurement. It argues that opaque predictive reliability is not a substitute for empirical structural proof. Apparent single-event randomness is identified with the self-opacity of a non-invertible fold, while the complete branch relation remains deterministic. Scientific author and publication authority: Maria Smith, Ernos Labs. Open source: Smithian Fold Theory of Everything.