AlphaFold Substrate Alignments#

Example: Dimensional‑Core Projection#

The goal is to provide a clear, reproducible example of dimensional‑core projection in practice.

1. Input Overview#

For this example, we assume:

• a fixed protein sequence
• an AlphaFold‑class model producing:
  • predicted 3D coordinates
  • residue‑pair embeddings
  • attention‑map structures
  • multi‑stage inference outputs
• stable inference‑cycle behavior

These inputs provide the structural and latent‑space signals required for dimensional projection.

2. Step 1 — Identify High‑Dimensional Structures#

Extract high‑dimensional inference signals, including:

• pairwise‑embedding tensors
• attention‑map coherence regions
• latent‑space orientation vectors
• track‑level folding‑pathway signals

These structures typically exist in 32D–128D latent spaces.

3. Step 2 — Prepare Substrate‑Aligned Signals#

Before projection, align signals to substrate axes:

• S‑axis: structural geometry
• I‑axis: latent‑space orientation
• R‑axis: inference‑cycle behavior

This ensures that dimensional projection preserves substrate invariants.

4. Step 3 — Project into Dimensional Cores#

4.1 3D Structural Projection#

Project structural geometry into the 3D core to evaluate:

• backbone shape
• motif‑level structure
• local geometric coherence

Interpretation:
Stable motifs appear as compact, coherent 3D structures.

4.2 6D Interaction‑Core Projection#

Project interaction‑level signals into the 6D core to evaluate:

• residue‑pair relationships
• interaction‑pattern stability
• latent‑space alignment

Interpretation:
Stable interaction patterns form smooth, low‑variance surfaces in 6D space.

4.3 9D Pathway‑Core Projection#

Project folding‑pathway signals into the 9D core to evaluate:

• pathway coherence
• regime‑transition structure
• resonance‑time alignment

Interpretation:
Stable folding pathways appear as continuous, coherent trajectories in 9D space.

5. Step 4 — Identify Regime Behavior#

Dimensional projections reveal regime identity:

• R₁ (Stable):
  Compact, coherent projections in all cores.

• R₂ (Transition):
  Branching or oscillatory projections, especially in 6D and 9D.

• R₃ (High‑Uncertainty):
  Dispersed projections with weak motif‑level structure.

Regime identification supports interpretability and drift detection.

6. Step 5 — Validate Dimensional Projections#

Apply vST validation layers:

• V₁: structural coherence in 3D
• V₂: latent‑space stability in 6D
• V₃: resonance‑time regime behavior
• V₄: dimensional‑core alignment in 9D

Validation confirms that projections preserve substrate invariants.

7. Step 6 — Interpret Projection Results#

A successful projection yields:

• stable 3D geometry
• coherent 6D interaction surfaces
• continuous 9D pathway trajectories
• predictable regime transitions
• preserved substrate invariants

If projections fail validation, drift detection is triggered.

8. Summary#

This example demonstrates:

• how to extract high‑dimensional inference signals
• how to align them to substrate axes
• how to project them into 3D–9D dimensional cores
• how to classify regime behavior
• how to validate projections using vST
• how to detect drift when invariants fail

Dimensional‑core projection provides a stable, interpretable substrate for analyzing AlphaFold‑class inference systems.