Pulse Core Lexicon

Recursive Pulse Cycle Time

Definition

The Recursive Pulse Cycle Time is the duration of one pulse cycle at recursion depth n, which grows with the square of (n + 1) from the prime pulse duration. It is the book's basic statement of quadratic time scaling in Temporal Drag. Starting from the Prime Pulse, with minimal computational resistance and zero load, each deeper layer carries accumulated load L_n = n(n+1)/2, and processing time, amplified through resonance coupling with the harmonic structure P(n) = (n+1)², stretches the cycle accordingly. The same factor slows the pulse frequency as ν_n = ν_0/(n + 1)² and lengthens processing delays, driving the system toward the Collapse Threshold. The cycle time also sets the causal limit at depth n: information is causally connected only while its delay stays below T_n. The formal statement is T_n = T_0 × (n + 1)², where T_n is the Recursive Pulse Cycle Time at depth n, T_0 the prime pulse duration, n the recursion depth index and P(n) = (n+1)² the pulse density function. Dimensions: T_n and T_0 [𝕋], n and P(n) [∅]; the book's check is valid and verified. It connects to the Prime Pulse, Pulse Frequency Deceleration, Resonance Coupling, Temporal Drag, Causal Disconnection and Form Persistence Time.

Mathematical Expression

From the book · Chapter 7 · Temporal Drag and the Recursive Pulse Clock

T_n = T_0 × (n + 1)² [𝕋]

Where:

  • T_n [𝕋] - Recursive Pulse Cycle Time (G) at depth n
  • T_0 [𝕋] - prime pulse duration
  • n [∅] - recursion depth index
  • P(n) [∅] - pulse density function, equal to (n+1)²
  • [∅] - quantities without physical units, pure numerical ratios or mathematical constants

Technical Details

Category Concept

Chapter Chapter 7

Importance

Related Terms