Dimensional Capacity

Dimensional Capacity is the number of geometric degrees of freedom available after n completed pulses, the measure of how much dimensional structure recursion can support: D(n) = log₂(ℜ(n)) = n. Chapter 1 derives it from the Recursive Growth Law as the logarithm of total data capacity, so each doubling of capacity unlocks one further dimensional axis, starting from D(0) = 0 at the base; the Dimensional Growth Formula writes the same quantity ◉(n). No cap is placed on it; the 3 + 1 dimensions observed at our depth are not derived, and a binding rule on dimensional capacity is an open question. Chapter 6 ties dimensional structure to Null Mass: an emergent universe's maximum dimension count is set by the ratio of its Null Mass to the Planck mass, d⥣ = floor(½·log₂(M_n/M_P)) + 3, with one dimension reserved for temporal evolution, d☐ ≤ d⥣ − 1. In D(n) = log₂(ℜ(n)) = n, D(n) is the dimensional capacity, ℜ(n) = 2ⁿ the total data capacity and n the count of completed pulses, all [∅]. In the Null Mass form d⥣ is [∅], M_n and M_P are [𝕄], and [∅]([∅]([𝕄] ÷ [𝕄])) + [∅] = [∅]. It connects to UniSphereal Dimensional Capacity, Dimensional Growth Formula, Extended UniSphereal Dimensional Framework, Dimensional Emergence and Null Mass (M_n).