Layer Capacity

Layer Capacity is the structural capacity available after completing layer n, which scales as the square of the layer index, C(n) = n²: the organizational potential, combinatorial or area-like, within which substrate pulses organize into nested architectures. It is the Meso Law of structural layering, developed in Quantum Pulse Theory (Chapter 2, Structural capacity: the square of the binary), with the Odd-Number Increment Rule C(n+1) − C(n) = 2n + 1 as its increment: the increments run through the odd numbers {1, 3, 5, 7, …} and the capacity through the perfect squares {1, 4, 9, 16, …}. Binary Pulse Theory keeps of it only the note that structural capacity is the square of the binary capacity, (2ⁿ)² = 2²ⁿ (Part 1.5), distinct from the data capacity ℜ(n) = 2ⁿ of the Recursive Growth Law. The same quadratic family appears in Chapter 3 as R(n) = (n + 1)² and in Chapter 7 as P(n) = (n + 1)², indexed so that the base n = 0 has capacity 1; which indexing the law carries is one law written two ways, and the book has not yet chosen. The editorial rule stands: C(n) times nothing. It characterizes structural capacity, not the passage of time, which follows the binary dilation law Pₙ = (2f)ⁿ · P₀. The book writes C(n) = n², where C(n) is the structural capacity after completing layer n [∅] and n the layer or recursion index [∅]: [∅] = [∅]. It connects to Odd-Number Increment Rule, Perfect-Square Sequence, The Recursive Growth Law, Harmonic Frequency Scaling and Substrate Time Relation.