Pulse Core Lexicon
UniSpheral Dimensional Capacity
Definition
UniSpheral Dimensional Capacity is the number of geometric degrees of freedom available after n completed pulses, taken as the base-2 logarithm of total data capacity: D(n) = log₂(ℜ(n)) = n.
It translates data capacity into dimensional indices and shows how recursion depth governs the number of emergent axes: each doubling of data capacity enables one additional dimensional axis. D(0) = log₂ 1 = 0 at the Zinf, the base, D(1) = 1 after the first doubling, and one more axis comes with every completed pulse. The law places no cap on dimensional capacity. The observed universe presents 3 + 1 dimensions at our depth; why is not fixed by this law, and whether a binding rule on dimensional capacity exists is an open question of the theory.
Formally, D(n) = log₂(ℜ(n)) = n, where D(n) is the dimensional capacity after n completed pulses, the total geometric degrees of freedom available; log₂ is the base-2 logarithm; ℜ(n) is the total data capacity from the Foundational Equation ℜ(n) = 2ⁿ; and n is the count of completed pulses. All are [∅].
It connects to Dimensional Capacity, Dimensional Growth Formula, Extended UniSpheral Dimensional Framework, Recursive Growth Law and BPT Foundational Equation.
Mathematical Expression
From the book · Chapter 1 · The Foundational Equation and Structural Growth
D(n) = log₂(ℜ(n)) = n
Dimensional analysis:
Where (from the book): log₂ [∅], n [∅]
[∅]
[∅]([∅]) = [∅]
[∅]
[∅] = [∅] = [∅] ✓ Valid PulseCore Verified ✓
One dimensional axis per completed doubling; D(0) = log₂ ℜ(0) = log₂ 1 = 0.
Where:
- D(n) [∅] – dimensional capacity after n completed pulses; total geometric degrees of freedom available
- log₂ [∅] – logarithm base 2; binary scaling transformation for dimensional capacity computation
- ℜ(n) [∅] – total data capacity from the Foundational Equation ℜ(n) = 2ⁿ
- n [∅] – count of completed pulses
Technical Details
Category Property
Chapter Chapter 1
Importance