Transitional Scaling Function

The Transitional Scaling Function is the weighted blend of classical and quantum computational scaling that describes the smooth migration from classical to quantum-dominated computing, with the quantum fraction as the weight. The book uses it to argue that quantum computation continues the historical scaling trajectory rather than breaking it: classical architectures reach their saturation limits, but the underlying scaling framework persists, expressed through a function that shifts weight from classical capacity to quantum acceleration as the sigmoid Quantum Fraction Evolution rises. Classical and quantum computation thus become phases of a single recursive trajectory, which the book calls Classical-to-Quantum Transition Dynamics. S⊶(t) = S●(t) × (1 − f⊡(t)) + S⊡(t) × f⊡(t), where S⊶(t), S●(t) and S⊡(t) are the transitional, classical and quantum scaling functions [𝕋⁻¹], f⊡(t) is the quantum fraction [∅] and t is time [𝕋]. The book checks [𝕋⁻¹] × [∅] + [𝕋⁻¹] × [∅] = [𝕋⁻¹]. It is weighted by Quantum Fraction Evolution and connects to Classical-to-Quantum Transition Dynamics, Quantum Superposition Recursion and Quantum Scaling Laws.