AlphaFold Substrate Alignments#
Dimensional Cores#
1. Purpose of Dimensional Cores#
Dimensional cores serve three primary functions:
- provide a stable geometric substrate for folding interpretation
- preserve motif‑level structure during projection from high‑dimensional latent spaces
- support regime classification and resonance‑time analysis
The cores ensure that folding predictions remain interpretable across inference cycles and model variants.
2. Core Dimensional Structure#
The AlphaFold substrate uses a 3D–9D triadic dimensional core, defined as follows:
2.1 3D Structural Core#
Represents the physical geometry of protein conformations.
Includes:
- backbone coordinates
- side‑chain orientation
- local motif geometry
This core anchors all structural projections.
2.2 6D Interaction Core#
Extends the 3D core to capture interaction‑level structure.
Includes:
- residue‑pair relationships
- orientation‑pair embeddings
- local‑to‑global interaction patterns
This core corresponds to the latent‑space structures used in folding inference.
2.3 9D Coherence Core#
Represents the minimal dimensional substrate required to capture folding‑pathway coherence.
Includes:
- motif‑level stability signals
- regime‑transition indicators
- resonance‑time alignment patterns
The 9D core is the highest‑resolution substrate used for folding interpretation.
3. Projection Principles#
Dimensional projection follows three rules:
3.1 Structure‑Preserving Projection#
Projections from high‑dimensional latent space into 3D–9D cores must preserve:
- motif‑level geometry
- backbone continuity
- residue‑interaction coherence
3.2 Regime‑Aware Projection#
Projection must maintain regime identity:
- R₁ → stable geometric surfaces
- R₂ → transitional structures
- R₃ → dispersed or unstable projections
3.3 Invariant‑Aligned Projection#
Projection must preserve substrate invariants, including:
- resonance‑time patterns
- motif‑level stability
- latent‑space orientation consistency
4. High‑Dimensional Extensions#
Although the core substrate is 3D–9D, AlphaFold’s latent space often operates in higher dimensions (e.g., 32D–128D).
High‑dimensional extensions follow these principles:
- projections must remain invertible at the motif level
- coherence surfaces must remain identifiable
- regime transitions must remain detectable
- substrate invariants must remain stable
These extensions allow the substrate to interpret complex inference behaviors without losing structural clarity.
5. Dimensional‑Core Behavior Across Regimes#
Dimensional cores interact with folding regimes as follows:
- R₁ (Stable): full alignment with 3D–9D cores; projections are compact and coherent
- R₂ (Transition): partial alignment; projections show branching or oscillatory structure
- R₃ (High‑Uncertainty): weak alignment; projections disperse across higher‑dimensional space
This behavior supports regime classification and drift detection.
6. Integration with Substrate Primitives#
Dimensional cores integrate with:
- Structural Axis (S‑axis): geometric projection
- Inference Axis (I‑axis): latent‑space mapping
- Resonance‑Time Axis (R‑axis): regime‑transition interpretation
Together, these axes form the SIR substrate triad used throughout this artifact.
7. Outputs of Dimensional‑Core Analysis#
Dimensional‑core analysis produces:
- stable structural projections
- regime‑aware folding interpretations
- coherence‑surface identification
- high‑dimensional alignment diagnostics
- substrate‑level validation signals
These outputs integrate with vST validation layers and downstream substrate artifacts.