Binary Progression

The Binary Progression is the sequence of total data capacities generated by the BPT Foundational Equation, {1, 2, 4, 8, 16, 32, …}: one at level 0, the first count, and double the previous value at every completed pulse after it. It is what ℜ(n) = 2ⁿ yields when n counts completed pulses from the base at n = 0, where ℜ(0) = 2⁰ = 1: the Zinf's one whole completion, the Prime Pulse, two frames 0 → 1 → 0 carrying two bits (2ᵇ), one per Zinf Rhythm. The First Recursion gives 2; then 4, 8, 16 and onward, each term holding every earlier pulse's data and as much again. The book offers it as the illustration of Binary Amplification: doubling, not linear growth. The difference between successive terms equals the earlier term, by the Binary Increment Law. Written out, ℜ(k) = 2ᵏ for k = 0, 1, 2, …, with ℜ(0) = 1 the first count, giving {1, 2, 4, 8, 16, 32, …}, where ℜ(k) is the total data capacity after k completed pulses and k the count of completed pulses; both are [∅]. It connects to BPT Foundational Equation, Recursive Growth Law, UniSphereal Recursive Growth Relations, Prime Pulse and First Recursion.