vST for Large Language Models#

Terminology#

This appendix defines the terminology used throughout the vST for Large Language Models artifact. Terms are presented in a substrate‑agnostic, model‑independent manner and apply to any transformer‑based LLM operating across the full dimensional ladder (3D → 1024D). Definitions emphasize primitive‑level structure, regime behavior, scaling continuity, and invariant preservation.

1. Substrate Terms#

LLM Substrate#

A structured, invariant‑preserving framework for representing and interpreting LLM latent‑space behavior across 64D–4096D.

Dimensional Ladder#

The ordered sequence of dimensional regimes used for projection and scaling analysis:
3D → 6D → 9D → 64D → 128D → 256D → 512D → 1024D.

Coherence Surface#

A stable region in latent space where trajectories converge and maintain structural continuity.

2. Primitive Terms#

Dimensional Primitive (DP)#

The minimal unit of latent‑space structure, capturing local coherence and variance behavior.

Triadic Dimensional Primitive (TDP)#

A triad of DPs forming the smallest unit capable of expressing full regime behavior (R₁, R₂, R₃).

Scaling Primitive (SP)#

A rule‑based expansion unit that preserves invariants during dimensional scaling.

Coherence Primitive (CP)#

A minimal unit identifying stable, transitional, or dispersed regions in high‑dimensional latent space.

3. Core Terms#

Triadic Dimensional Core (TDC)#

The 3D–9D substrate composed of one or more TDPs, used for interpretable projection.

3D Structural Core#

Captures motif‑level geometry and compact latent structure.

6D Interaction Core#

Captures relational and attention‑driven structure.

9D Coherence Core#

Captures pathway‑level coherence and resonance‑time behavior.

4. Regime Terms#

High‑Dimensional Regimes (R₁ᴴ, R₂ᴴ, R₃ᴴ)#

The triadic regime structure expressed in 64D–1024D latent space.

Stable Regime (R₁ / R₁ᴴ)#

Compact, coherent, low‑variance latent behavior.

Transition Regime (R₂ / R₂ᴴ)#

Branching, oscillatory, or reorientation behavior.

Dispersion Regime (R₃ / R₃ᴴ)#

Diffuse, fragmented, or unstable latent behavior.

5. Scaling Terms#

Scaling Behavior#

The structured expansion of latent‑space capacity as model size increases.

Scaling Regimes (S₁, S₂, S₃)#

Triadic scaling behavior describing stable, transitional, and dispersion‑prone scaling phases.

Dimensional Continuity#

The requirement that latent‑space expansion remains smooth and invariant‑preserving.

6. Projection Terms#

Invertible Projection#

A projection from high‑dimensional latent space into 3D–9D that preserves primitive‑level structure and regime identity.

Regime‑Aware Projection#

A projection that maintains correct mapping of R₁, R₂, and R₃ behaviors.

Primitive‑Aligned Projection#

A projection that preserves DP, TDP, SP, and CP structure.

7. Alignment Terms#

Layer‑to‑Layer Alignment#

Comparison of latent trajectories across transformer layers.

Token‑to‑Token Alignment#

Comparison of latent states across positions in a sequence.

Cross‑Version Alignment#

Comparison of latent‑space structure across model versions or checkpoints.

Cross‑Model Alignment#

Comparison of latent‑space geometry across different architectures or model families.

8. Validation Terms#

vST (Validation‑Space‑Time)#

A substrate‑level validation framework evaluating structural coherence, dimensional continuity, regime behavior, and core alignment.

Validation Layers (V₁–V₄)#

Four structured evaluation layers ensuring invariant‑preserving behavior across the dimensional ladder.

9. Drift Terms#

Drift#

A deviation from expected substrate behavior, indicating instability or invariant failure.

Drift Categories (D₁–D₄)#

Classification of drift into structural, dimensional, regime, or projection drift.

Drift Severity#

A measure of drift magnitude (low, moderate, high).