Pulse Core Lexicon

Tension Propagation

Definition

Tension Propagation is the diffusion of accumulated computational stress through the dimensional hierarchy, so that a local perturbation produces a coherent response in every layer of the architecture. The book lists it with Dimensional Memory and Causal Nesting as the three features of the hierarchical dimensional architecture: each new axis joins a network that remembers, spreads tension and nests causes across scales. Tension that builds in one place does not stay there; it spreads, is fed by sources and is absorbed, and the whole stack responds together. In the chapter on null wells, the same process appears as the diffusion term of the collapse equation, where a diffusion coefficient σ [š•ƒĀ²Ā·š•‹ā»Ā¹] for recursive tension propagation balances nonlinear collapse of recursive density. The current lexicon statement gives the unified tension evolution as āˆ‚T/āˆ‚t = D⊹ Ɨ āˆ‡Ā²T + S⟹ āˆ’ A⟸ Ɨ T, where T is the accumulated tension, D⊹ the effective diffusion coefficient, āˆ‡Ā²T its spatial Laplacian, S⟹ the source of new tension and A⟸ the rate at which tension is absorbed. Tension Propagation connects to Accumulated Tension, Dimensional Memory, Causal Nesting, Recursive Tension Dynamics and Null Well Collapse Evolution.

Mathematical Expression

From the book · Chapter 4 · The Architecture of Dimensional Layers

āˆ‚T/āˆ‚t = D⊹(x,t) Ɨ āˆ‡Ā²T + S⟹(x,t) - A⟸(x,t) Ɨ T [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³]

Dimensional analysis:
Where (from the book): T [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā²], D⊹(x,t) [š•ƒĀ²Ā·š•‹ā»Ā¹], āˆ‡Ā²T [š•„Ā·š•ƒā»Ā³Ā·š•‹ā»Ā²], S⟹(x,t) [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³], A⟸(x,t) [š•‹ā»Ā¹], x [š•ƒ], t [š•‹]
Read dimensionally: (T/t) = D⊹(x,t) Ɨ āˆ‡Ā²T + S⟹(x,t) - A⟸(x,t) Ɨ T
([š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā²] Ć· [š•‹]) = [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³]
[š•ƒĀ²Ā·š•‹ā»Ā¹] Ɨ [š•„Ā·š•ƒā»Ā³Ā·š•‹ā»Ā²] + [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] - [š•‹ā»Ā¹] Ɨ [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā²] = [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] + [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] - [š•‹ā»Ā¹] Ɨ [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā²] = [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] - [š•‹ā»Ā¹] Ɨ [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā²] = [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] - [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] = [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³]
[š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] = [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³] āœ“ Valid PulseCore Verified āœ“

Stress spreads, builds, and drains to maintain stability.

Where:

  • T is unified tension field [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā²]
  • D⊹(x,t) is effective diffusion coefficient [š•ƒĀ²Ā·š•‹ā»Ā¹]
  • āˆ‡Ā²T is Laplacian of tension field [š•„Ā·š•ƒā»Ā³Ā·š•‹ā»Ā²]
  • S⟹(x,t) is source terms from Recursive State Evolution [š•„Ā·š•ƒā»Ā¹Ā·š•‹ā»Ā³]
  • A⟸(x,t) is absorption coefficient [š•‹ā»Ā¹]
  • x is spatial position [š•ƒ]
  • t is time [š•‹]

Technical Details

Category Concept

Chapter Chapter 4

Importance

Related Terms