Pulse Core Lexicon

Integrated Temporal Evolution

Definition

Integrated Temporal Evolution is the time-dependence of the pulse duration once Temporal Drag has acted, a sum of a constant term, a linear drag term and a quadratic drag term. It closes the book's account of temporal drag dynamics, where computational resistance is treated by analogy with viscous drag and load-dependent delays compound with the quadratic scaling of recursion depth, as in the Temporal Drag Equation. Integrating those effects gives a pulse duration that grows from its prime value through two contributions: a linear one at roughly Hubble scale and a quadratic one from computation. The formal statement is T(t) = T_0[1 + γt + δt²], where T(t) is the temporal evolution function, T_0 the prime pulse duration, γ the linear drag coefficient, approximately the Hubble constant H_0, t the time variable and δ the quadratic drag coefficient, approximately 10⁻¹⁸ s⁻². Dimensions: T(t) and T_0 [𝕋], γ and H_0 [𝕋⁻¹], t [𝕋], δ [𝕋⁻²]; the book's check is valid and verified. It connects to Temporal Drag, the Temporal Drag Equation, Temporal Drag Force Analog, Hubble Constant Connection and Information Processing Delay.

Mathematical Expression

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

T(t) = T_0[1 + γt + δt²] [𝕋]

Where:

  • T(t) [𝕋] - temporal evolution function dependent on time
  • T_0 [𝕋] - prime pulse duration
  • γ [𝕋⁻¹] - linear drag coefficient, approximately H_0 Hubble constant
  • t [𝕋] - time variable
  • δ [𝕋⁻²] - quadratic drag coefficient, approximately 10⁻¹⁸ s⁻²
  • H_0 [𝕋⁻¹] - Hubble constant
  • 10⁻¹⁸ [𝕋⁻²] - approximate numerical value for quadratic coefficient
  • [∅] - quantities without physical units, pure numerical ratios or mathematical constants

Technical Details

Category Concept

Chapter Chapter 7

Importance

Related Terms