Intent-Tensor-Theory

Glyph-Space Mechanics

Chapter 3: Glyph-Space Entropy Mechanics

The Dynamics of Drift, Lock, and Divergence in Field Evolution

3.1 Overview

While Chapter 2 established entropy as a recursive functional, this chapter unpacks the micromechanical source of drift: the misalignment and memory incoherence in Glyph Space.

In ITT, entropy is not statistical but geometric and semanticβ€”arising from mismatch between intention and memory, fold and re-fold.

3.2 Glyph Space Definition

Glyph Space is the configuration space of the ITT field stack:

𝒒 = {(Ξ¦, Ci, β„³ij) | Ξ¦ ∈ ℝ, Ci ∈ ℝ³, β„³ij ∈ ℝ3Γ—3sym}

Dimensionality: 1 (scalar) + 3 (vector) + 6 (symmetric tensor) = 10 degrees of freedom per spatial point.

3.3 The General Drift Equation

π’Ÿ(x,n) = Ξ±M β€–βˆ‚n β„³ijβ€–F + Ξ±Ξ¦ β€–βˆ‚n βˆ‡Ξ¦β€–2

Term Symbol Meaning
Memory rate β€–βˆ‚n β„³ijβ€–F Frobenius norm of tensor change
Intent rate β€–βˆ‚n βˆ‡Ξ¦β€–2 Euclidean norm of gradient change
Memory weight Ξ±M Coupling constant for memory
Intent weight Ξ±Ξ¦ Coupling constant for intent

3.4 Misalignment Curvature

Entropy is influenced by misalignment curvatureβ€”how sharply alignment varies across space:

σθ(curv) = β€–βˆ‡π’œ(x,n)β€–Β²

Physical interpretation: Entropy increases where alignment breaks down sharply across space.

3.5 Memory Drift Contribution

The non-coherent update of the memory tensor contributes to entropy:

σθ(mem) = Tr([βˆ‚n β„³ij]drift)

Decomposition:

  • Aligned component: Changes parallel to Ci (coherent evolution)
  • Drift component: Changes perpendicular to Ci (entropic loss)

3.6 Total Entropy Source

Combining drift and curvature:

σθ(x,n) = π’Ÿ(x,n) Β· (1 βˆ’ β„’(x,n)) ∝ β€–βˆ‡π’œβ€–Β² + Tr([βˆ‚n β„³ij]drift)

Key insight: Entropy density arises where alignment degrades AND memory fails simultaneously.

3.7 The Curvent as Entropy Director

The curvent field Ci determines which directions in glyph space are “coherent”:

[βˆ‚n β„³ij]aligned = ProjCi(βˆ‚n β„³ij)

Entropy is generated by components orthogonal to Ci.

3.8 Entropy Hotspots

Locations of maximum σθ are entropy hotspots:

These occur where:

  1. Drift is maximum: β€–βˆ‚n β„³ijβ€– + β€–βˆ‚n βˆ‡Ξ¦β€– is large
  2. Lock is minimum: β„’ β†’ 0
  3. Alignment gradient is steep: β€–βˆ‡π’œβ€– is large

Physical examples:

  • Black hole horizons (high memory load, alignment stress)
  • Cosmic voids (low lock, diffuse intent)
  • Phase boundaries (sharp π’œ gradients)

Key Takeaways

  1. Glyph Space is the 10-dimensional configuration space of ITT fields
  2. Drift decomposes into memory and intent components
  3. Misalignment curvature β€–βˆ‡π’œβ€–Β² contributes to entropy
  4. Memory drift Tr([βˆ‚n β„³ij]drift) generates unbinding
  5. The curvent defines coherent directions in glyph space
  6. Entropy hotspots occur where lock fails and drift peaks

Next: Chapter 4 β€” Ceilings and Information Erasure

Back: Chapter 2 β€” Formal Derivation