vST for Multi‑Model Alignment#

Terminology#

This appendix defines the terminology used throughout the vST for Multi‑Model Alignment artifact. Terms are presented in a substrate‑agnostic, architecture‑neutral manner and apply to any pair or set of heterogeneous models. Definitions emphasize alignment primitives, cross‑architecture compatibility, scaling behavior, and invariant preservation.

1. Substrate Terms#

Multi‑Model Alignment Substrate#

A structured, invariant‑preserving framework for representing and comparing latent‑space behavior across heterogeneous models.

Cross‑Model Latent Space#

The shared representational space in which heterogeneous latent states are projected for comparison.

Alignment Surface#

A geometric manifold representing how two or more models relate across latent spaces, inference pathways, or modalities.

2. Primitive Terms#

Dimensional Primitive (DP)#

The minimal unit of latent‑space structure, used as a baseline for cross‑model comparison.

Triadic Dimensional Primitive (TDP‑X)#

A triad of alignment primitives expressing full cross‑model regime behavior (A₁, A₂, A₃).

Cross‑Model Scaling Primitive (SP‑X)#

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

Cross‑Modality Coherence Primitive (CP‑X)#

A minimal unit identifying stable, transitional, or dispersed regions in cross‑model alignment.

Alignment Primitive (AP)#

The minimal unit of cross‑model comparability, capturing local geometric compatibility and projection stability.

3. Core Terms#

Triadic Dimensional Core (TDC)#

The 3D–9D substrate used for interpretable projection of heterogeneous latent states.

3D Structural Core#

Captures motif‑level alignment geometry.

6D Interaction Core#

Captures relational structure across architectures and modalities.

9D Coherence Core#

Captures pathway‑level coherence across heterogeneous inference systems.

4. Alignment Regime Terms#

Cross‑Model Alignment Regimes (A₁ᴴ, A₂ᴴ, A₃ᴴ)#

The triadic regime structure expressed in 64D–1024D cross‑model alignment spaces.

Stable Alignment Regime (A₁ / A₁ᴴ)#

Compact, coherent, low‑variance cross‑model compatibility.

Transitional Alignment Regime (A₂ / A₂ᴴ)#

Branching, oscillatory, or reorientation behavior across architectures or modalities.

Dispersed Alignment Regime (A₃ / A₃ᴴ)#

Diffuse, incompatible, or unstable cross‑model behavior.

5. Scaling Terms#

Cross‑Model Scaling Behavior#

The structured expansion of alignment capacity as model size, modality diversity, or architectural complexity increases.

Scaling Regimes (S₁ᴹ, S₂ᴹ, S₃ᴹ)#

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

Dimensional Continuity#

The requirement that cross‑model alignment remains smooth and invariant‑preserving across the dimensional ladder.

6. Projection Terms#

Invertible Projection#

A projection from heterogeneous latent spaces into 3D–9D that preserves primitive‑level structure and alignment regime identity.

Regime‑Aware Projection#

A projection that maintains correct mapping of A₁, A₂, and A₃ behaviors.

Primitive‑Aligned Projection#

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

7. Validation Terms#

vST (Validation‑Space‑Time)#

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

Validation Layers (V₁–V₄)#

Four structured evaluation layers ensuring invariant‑preserving behavior across heterogeneous models.

8. Drift Terms#

Drift#

A deviation from expected cross‑model alignment behavior, indicating incompatibility or invariant failure.

Drift Categories (D₁ᴹ–D₄ᴹ)#

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

Drift Severity#

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