vST for Large Language Models#
Substrate Definition#
The substrate is model‑agnostic and applies to any transformer‑based LLM, regardless of architecture, size, or training method.
1. Purpose of the LLM Substrate#
The LLM substrate provides a structured, reproducible framework for:
- interpreting high‑dimensional latent trajectories
- identifying stable, transitional, and dispersed inference regimes
- mapping coherence surfaces in embedding and hidden‑state space
- analyzing scaling behavior across model sizes
- detecting drift across checkpoints or versions
- projecting high‑dimensional structure into 3D–9D triadic cores
The substrate ensures that LLM behavior remains interpretable across the full dimensional ladder (3D → 1024D).
2. Substrate Overview#
LLMs operate in extremely high‑dimensional latent spaces (typically 768D–4096D).
The substrate models these spaces using:
- Dimensional Primitives (DP)
- Triadic Dimensional Primitives (TDP)
- Scaling Primitives (SP)
- Coherence Primitives (CP)
These primitives define the structure of latent trajectories, coherence surfaces, and regime transitions.
The substrate is anchored by the Triadic Dimensional Cores:
- 3D Structural Core
- 6D Interaction Core
- 9D Coherence Core
and extended through the 1024D high‑dimensional substrate.
3. Dimensional Primitives for LLMs#
3.1 Dimensional Primitive (DP)#
A DP represents the minimal unit of latent‑space structure in an LLM.
It captures:
- local coherence
- variance behavior
- projection stability
- regime alignment
DPs appear in token embeddings, attention outputs, and hidden‑state vectors.
3.2 Triadic Dimensional Primitive (TDP)#
A TDP is a triad of DPs that expresses full regime behavior.
It captures:
- stable (R₁) behavior
- transitional (R₂) behavior
- dispersed (R₃) behavior
TDPs form the basis of the 3D–9D triadic cores.
3.3 Scaling Primitive (SP)#
An SP governs dimensional expansion from 9D → 64D → 1024D.
It ensures:
- invariant‑preserving scaling
- continuity of coherence surfaces
- stable projection into triadic cores
SPs model how LLM latent spaces expand with model size.
3.4 Coherence Primitive (CP)#
A CP identifies stable or unstable regions in latent space.
It captures:
- coherence surfaces
- branching behavior
- dispersion patterns
- regime transitions
CPs are essential for drift detection and vST validation.
4. Triadic Dimensional Cores for LLMs#
4.1 3D Structural Core#
Captures motif‑level structure in latent trajectories:
- compact geometric patterns
- local coherence
- stable projections
4.2 6D Interaction Core#
Captures relational and attention‑level structure:
- interaction surfaces
- branching behavior
- early regime transitions
4.3 9D Coherence Core#
Captures pathway‑level coherence:
- resonance‑time behavior
- stable regime classification
- invertible projection from higher dimensions
The 9D core is the anchor for all high‑dimensional interpretation.
5. High‑Dimensional Substrate (64D–1024D)#
LLM latent spaces naturally inhabit high‑dimensional regimes.
The substrate models these using the dimensional ladder:
- 64D — research‑grade substrate
- 128D — expanded coherence surfaces
- 256D — multi‑primitive interaction
- 512D — high‑variance latent regions
- 1024D — full research‑grade capacity
Each step preserves:
- structural invariants
- resonance‑time invariants
- projection invariants
- scaling invariants
This ensures stable interpretation across model sizes.
6. Latent‑Trajectory Structure#
LLM inference produces latent trajectories that move through:
- compact stable regions (R₁ᴴ)
- branching transitional regions (R₂ᴴ)
- dispersed or unstable regions (R₃ᴴ)
These trajectories are modeled as:
- sequences of DPs
- grouped into TDPs
- expanded through SPs
- classified using CPs
This structure enables regime‑aware analysis and drift detection.
7. Projection into Triadic Cores#
High‑dimensional latent states are projected into:
- 9D for coherence analysis
- 6D for interaction analysis
- 3D for geometric interpretation
Projection must remain:
- invertible
- primitive‑aligned
- regime‑aware
- invariant‑preserving
Projection is essential for interpretability and vST validation.
8. Substrate Outputs#
The LLM substrate produces:
- latent‑trajectory regime classifications
- coherence‑surface maps
- scaling‑law diagnostics
- projection‑stability indicators
- drift‑detection signals
- vST validation outputs
These outputs support reproducible, substrate‑level analysis of LLMs.