The Born Rule as a Theorem, Not a Postulate: Quantum Measurement in the GTE Framework

Quantum mechanics says a particle can be in a superposition — in two states at once. Measurement collapses it to one. The measurement problem is: what causes the collapse, and why do the probabilities follow the formula P(k) = |c_k|^2? Nobody has a satisfying answer from within standard quantum theory. This tutorial explains how the GTE (Generative Triple Evolution) framework derives the Born rule — the law that links quantum amplitudes to measurement probabilities — as a theorem from first principles, requiring no additional postulates. The Born rule emerges necessarily from the arithmetic structure of the GTE substrate.