UniSpheral Memory Structure

The UniSpheral Memory Structure is the set that makes up Data Memory at level n: the union of all pulse states so far, all recursive states and all looping states, ↁ𝓜(n) = {①₁ … ①ₙ} ∪ {ℜ₁ … ℜₙ₋₁} ∪ {⌘₁ … ⌘ₙ₋₁}. It formalizes the genesis of Systemic Memory, the moment the substrate stops being a sequence of isolated pulses and starts preserving its own history. Each new pulse is both an event and an addition to a growing record that unites pulses with their recursive transformations and closed loops. This memory is written at the recursion as each loop closes, the record of the trip, and is intrinsic to the substrate rather than external storage, 'the UniSphere's first hard drive'; it does not live in the Pre-Pulse Field ∅, which carries no information. The book treats it as the substrate's method of self-continuity and the ground for causality and law. Memory grows by UniSpheral Data Accumulation, ↁ𝓜ₙ₊₁ = ↁ𝓜ₙ ∪ {①ₙ₊₁, ℜₙ, ⌘ₙ}, which builds a hierarchical information architecture. In the book's notation, ↁ𝓜(n) is the data memory structure at level n, ①ᵢ are pulse states, ℜᵢ recursive states, ⌘ᵢ Data Looping states, ∪ is set union and n is the level index; all are [∅]. The cardinality is |ↁ𝓜(n)| = 3n − 2, counting n pulses and n − 1 each of recursions and loops. The analysis reads [∅] = {[∅]} ∪ {[∅]} ∪ {[∅]} = [∅]. It connects to Data Memory Definition, Systemic Memory, Loop-to-Recursion Binding, UniSpheral Recursive Pulse Development Framework and The Pre-Pulse Field.