Binary Amplification

Binary Amplification is the growth of data capacity by doubling rather than by linear addition: each completed pulse multiplies total data capacity by two. The Binary Progression {1, 2, 4, 8, 16, …} illustrates it. Because each pulse re-contains all the data of the pulses before it and adds as much again, the amplification factor between successive pulses, A(n) = ℜ(n)/ℜ(n−1), is exactly two at every depth (n ≥ 1) and never tapers. The first count is not an amplification but a genesis: the Zinf's one whole completion, ℜ(0) = 1, from which every doubling follows. Recursive growth is therefore bounded not by any slowing of the doubling but by the substrate's finite capacity. It is distinct from Quadratic Amplification, the growth of structural capacity as a square, developed in Quantum Pulse Theory, whose ratio (n + 1)²/n² tapers toward one. Formally, A(n) = ℜ(n)/ℜ(n−1) = 2 for n ≥ 1, where A(n) is the amplification factor, ℜ(n) the total data capacity after n completed pulses from ℜ(n) = 2ⁿ, and n the count of completed pulses; all [∅]. It connects to Amplification Factor, Amplification Factor Properties, Quadratic Amplification, Substrate Capacity Limit Properties and BPT Foundational Equation.