Extended UniSpheral Dimensional Framework

The Extended UniSpheral Dimensional Framework is the formula for dimensional capacity that multiplies the logarithm of total data capacity by a multiplicity factor and adds a weighted sum of past Data Memory: D(n,k) = k × log₂(ℜ(n)) + Σᵢ₌₁ⁿ ↁ𝓜(i)/2ⁱ. Dimensional capacity grows further when multiplicity and history are included: dimensional emergence then reflects both current recursion depth and the cumulative record of past states, each earlier level's Data Memory weighted down by 2ⁱ. The book presents it as integrating binary expansion, logarithmic dimensional indexing and historical accumulation into one law of emergence, by which higher-dimensional architectures stabilize and refine physical law. Its base term, log₂(ℜ(n)), equals n, so with k = 1 and no history it reduces to one axis per completed pulse. Formally, D(n,k) = k × log₂(ℜ(n)) + Σᵢ₌₁ⁿ ↁ𝓜(i)/2ⁱ, where D(n,k) is the extended dimensional capacity after n pulses with multiplicity k; k the dimensional multiplicity factor; ℜ(n) = 2ⁿ the total data capacity, so log₂(ℜ(n)) = n; the sum runs over historical levels i = 1 to n; ↁ𝓜(i) is the Data Memory at level i; and 2ⁱ the exponential weighting factor. All are [∅]. It connects to UniSpheral Dimensional Capacity, Dimensional Multiplicity Factor, Historical Dimensional Contributions, Data Memory Definition and Extended Dimensional Formula.