vST for Multi‑Model Alignment#
Substrate Definition#
This document defines the substrate used to perform multi‑model alignment within the Validation‑Space‑Time (vST) framework and the 1024D dimensional substrate. It establishes the primitives, alignment invariants, cross‑architecture mapping rules, and projection‑compatible structures required to compare heterogeneous models in a stable, invariant‑preserving manner.
The substrate is architecture‑agnostic and applies to LLMs, PLMs, diffusion models, VAEs, flow models, simulators, robotics policies, embedding stores, and hybrid systems.
1. Purpose of the Multi‑Model Alignment Substrate#
The multi‑model substrate provides a structured, reproducible framework for:
- aligning latent spaces across architectures and modalities
- mapping regime behavior (R₁/R₂/R₃) across heterogeneous inference systems
- comparing scaling behavior across model families
- projecting high‑dimensional states into 3D–9D cores for cross‑model interpretability
- detecting drift across architectures, checkpoints, or training runs
- establishing a unified dimensional grammar for all model types
Multi‑model alignment requires a substrate that is neutral, invertible, and invariant‑preserving across all architectures.
2. Substrate Overview#
The multi‑model substrate models heterogeneous latent spaces using:
- Dimensional Primitives (DP)
- Triadic Dimensional Primitives (TDP)
- Scaling Primitives (SP)
- Coherence Primitives (CP)
- Alignment Primitives (AP)
These primitives define the structure of cross‑model alignment, regime mapping, and projection behavior.
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. Alignment Primitives#
3.1 Alignment Primitive (AP)#
The AP is the minimal unit of cross‑model comparability.
It captures:
- local geometric compatibility
- variance‑aligned structure
- regime‑consistent mapping
- projection‑stable correspondence
APs allow two heterogeneous latent states to be compared without requiring architectural similarity.
3.2 Cross‑Architecture TDP (TDP‑X)#
A TDP‑X is a triad of APs that expresses full cross‑model regime behavior.
It captures:
- stable alignment (R₁ ↔ R₁)
- transitional alignment (R₂ ↔ R₂)
- dispersed alignment (R₃ ↔ R₃)
TDP‑X is the backbone of multi‑model regime mapping.
3.3 Cross‑Model Scaling Primitive (SP‑X)#
SP‑X governs dimensional expansion across architectures.
It ensures:
- invariant‑preserving scaling
- compatibility between different latent dimensionalities
- stable projection into triadic cores
- consistent scaling‑law interpretation across models
SP‑X is essential for aligning models with different latent sizes (e.g., 4096D LLM ↔ 1024D diffusion ↔ 256D PLM).
3.4 Cross‑Modality Coherence Primitive (CP‑X)#
CP‑X identifies stable or unstable regions in cross‑model alignment.
It captures:
- coherent alignment regions
- transitional alignment regions
- dispersed or incompatible regions
- cross‑modality regime transitions
CP‑X is essential for drift detection and vST validation.
4. Triadic Dimensional Cores for Multi‑Model Alignment#
4.1 3D Structural Core#
Captures motif‑level geometry shared across models.
Used for:
- cross‑modality motif comparison
- alignment of stable regimes
- low‑variance structural mapping
4.2 6D Interaction Core#
Captures relational structure across architectures.
Used for:
- cross‑model interaction surfaces
- alignment of transitional regimes
- sampler‑ or decoder‑dependent reorientation
4.3 9D Coherence Core#
Captures pathway‑level coherence across heterogeneous inference systems.
Used for:
- cross‑model coherence mapping
- alignment of inference trajectories
- invertible projection from higher dimensions
The 9D core is the anchor for all cross‑model alignment.
5. High‑Dimensional Substrate (64D–1024D)#
The multi‑model substrate spans the dimensional ladder:
- 64D — minimal cross‑model substrate
- 128D — expanded alignment surfaces
- 256D — multi‑primitive interaction
- 512D — high‑variance cross‑architecture regions
- 1024D — full research‑grade alignment substrate
Each step preserves:
- structural invariants
- resonance‑time invariants
- projection invariants
- alignment invariants
- scaling invariants
This ensures stable alignment across architectures and modalities.
6. Cross‑Model Alignment Structure#
Cross‑model alignment is modeled as:
- sequences of APs
- grouped into TDP‑X
- expanded through SP‑X
- classified using CP‑X
This structure enables:
- regime‑aware alignment
- cross‑modality comparison
- cross‑architecture drift detection
- unified scaling‑law interpretation
7. Projection into Triadic Cores#
High‑dimensional states from different models are projected into:
- 9D for coherence alignment
- 6D for interaction alignment
- 3D for geometric alignment
Projection must remain:
- invertible
- primitive‑aligned
- regime‑aware
- architecture‑neutral
- invariant‑preserving
Projection is essential for cross‑model interpretability.
8. Substrate Outputs#
The multi‑model substrate produces:
- cross‑model regime maps
- alignment surfaces
- scaling‑law diagnostics
- projection‑stability indicators
- drift‑detection signals
- vST validation outputs
These outputs support reproducible, substrate‑level alignment across architectures, modalities, and inference systems.