UniSpheral Binary Progression

The UniSpheral Binary Progression is the foundational scaling law of data capacity in Binary Pulse Theory: total data capacity doubles with every completed pulse, so the Prime Pulse opens a sequence of powers of two, ℜ(n) = 2ⁿ. It counts completed pulses from the base. The first count is one, at level 0: the Zinf's one whole completion, the Prime Pulse, two frames 0 → 1 → 0, ℜ(0) = 2⁰ = 1. The First Recursion holds all of level 0 and as much again, ℜ(1) = 2; the Second Recursion, ℜ(2) = 4; then 8 at pattern stabilization and 16 at dimensional expansion. Each pulse re-contains all the data of the pulses before it and adds as much again, so capacity grows by doubling, not linearly, with an amplification of two at every depth that never tapers. It replaces the perfect-square progression, whose square now survives in Binary Pulse Theory only as structural capacity, (2ⁿ)² = 2²ⁿ, developed in Quantum Pulse Theory. Formally, ℜ(n) = 2ⁿ, giving {1, 2, 4, 8, 16, 32, …}, where ℜ(n) is the total data capacity after n completed pulses and n the count of completed pulses; both are [∅]. It connects to BPT Foundational Equation, Recursive Growth Law, UniSpheral Recursive Growth Relations, First Recursion, Prime Pulse and The UniSpheral Perfect Square Progression.