Pulse Core Lexicon
Recursive Feedback Equation
Definition
The Recursive Feedback Equation is the rule governing feedback-loop dynamics in the substrate: the next feedback state is a transformation of the current feedback state, the current pulse state and the accumulated history, F(n+1) = F_feedback[F(n), P(n), H(n)].
This is the book's older notation. In the book's current notation the same rule is the Recursive Pulse Feedback Equation, ⇄(n+⧖) = ☫⇄[⇄(n), ①(n), ↁ𝓜(n)], in which F(n) becomes the feedback state ⇄(n), P(n) the pulse state ①(n), H(n) the Data Memory ↁ𝓜(n), and the step is one Time Crystal duration.
It connects to Recursive Pulse Feedback Equation, Feedback State, Phase-Synchronized Pulse Sequences and Classification of Feedback Loop Types.
Mathematical Expression
From the book · Chapter 1 · Pulse Feedback Dynamics and Emergent Order
⇄(n+⧖) = ☫⇄[⇄(n), ①(n), ↁ𝓜(n)]
Where:
- ⇄(n+⧖) [∅] – feedback state at next Time Crystal step; evolved feedback configuration
- ⇄(n) [∅] – feedback state at iteration n; current self-reinforcing pattern
- ☫⇄ [∅] – UniSpheral feedback transformation function; recursive evolution operator
- ①(n) [∅] – Pulse state at iteration n; current binary transition input
- ↁ𝓜(n) [∅] – Data Memory at iteration n; accumulated historical state vector
- n [∅] – iteration index; discrete computational step counter
- ⧖ [𝕋] – Time Crystal duration; fundamental temporal step increment
Technical Details
Category Concept
Chapter Chapter 1
Importance