Branched Control Recursion

Branched Control Recursion is the first level of recursive sophistication in the history of computation: the move from linear execution to conditional branching and subroutine calls, with recursion depth growing as the logarithm of problem size. The book reads the history of computing as four recursive patterns, each an epochal advance built into the mathematics of scaling. Branched control took sequential processing to conditional branching and then to subroutine calls, enabling conditional logic and modular programming. It is followed by Parallel Recursion, D₂ = O(N) in the number of cores or nodes; by Network Recursion, D₃ = O(N²) in the number of connected systems; and by Quantum Superposition Recursion, D₄ = O(2ᴺ) in the number of qubits. The formal statement is D₁ = O(log N), where D₁ is the recursion depth for branched control, O the order notation and N the problem size. All quantities are dimensionless [∅]; the book's check is consistent. It connects to Quantum Superposition Recursion, Computational Evolution, Bit Curve and Computational Enhancement.