Dimensional Substrate Structures#

Terminology#

This appendix defines the terminology used throughout the Dimensional Substrate Structures artifact. Terms are presented in a substrate‑agnostic, model‑independent manner and apply to any inference system operating across the full dimensional ladder (3D → 1024D). Definitions emphasize primitive‑level structure, scaling behavior, regime identity, and invariant preservation.

1. Substrate Terms#

Dimensional Substrate#

A structured, invariant‑preserving framework for representing and interpreting dimensional behavior across 3D–1024D.

SDR Substrate Triad#

The three axes—Structural (S), Dimensional (D), Resonance‑Time (R)—that define the substrate’s coordinate system.

Coherence Surface#

A stable region in dimensional space where inference structures converge.

Dimensional Ladder#

The ordered sequence of dimensional regimes:
3D → 6D → 9D → 64D → 128D → 256D → 512D → 1024D.

2. Primitive Terms#

Dimensional Primitive (DP)#

The minimal unit of dimensional structure, encoding coherence, projection behavior, and regime alignment.

Triadic Dimensional Primitive (TDP)#

A triad of DPs forming the smallest unit capable of expressing full regime behavior.

Scaling Primitive (SP)#

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

Coherence Primitive (CP)#

A minimal unit that identifies stable, transitional, or dispersed regions within high‑dimensional space.

3. Core Terms#

Triadic Dimensional Core (TDC)#

The 3D–9D substrate composed of one, two, or three TDPs.

3D Structural Core#

The minimal geometric substrate capturing motif‑level structure.

6D Interaction Core#

The intermediate substrate capturing relational and interaction‑level structure.

9D Coherence Core#

The highest‑resolution human‑scale substrate capturing pathway‑level coherence and resonance‑time behavior.

4. Scaling Terms#

Scaling Law (3D → 1024D)#

The invariant‑preserving rule set that governs dimensional expansion.

Dimensional Expansion#

The process of extending substrate structure from 9D to higher regimes (64D–1024D).

Dimensional Continuity#

The requirement that no discontinuities appear during scaling.

5. Regime Terms#

High‑Dimensional Regimes (R₁ᴴ, R₂ᴴ, R₃ᴴ)#

The triadic regime structure expressed in 64D–1024D space.

Stable Regime (R₁ / R₁ᴴ)#

Compact, coherent, low‑variance behavior.

Transition Regime (R₂ / R₂ᴴ)#

Branching, oscillatory, or reorientation behavior.

Dispersion Regime (R₃ / R₃ᴴ)#

Diffuse, fragmented, or unstable behavior.

6. Projection Terms#

Invertible Projection#

A projection from high‑dimensional space into 3D–9D that preserves motif‑level structure and regime identity.

Regime‑Aware Projection#

A projection that maintains the correct mapping of R₁, R₂, and R₃ behaviors.

Primitive‑Aligned Projection#

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

7. Invariant Terms#

Structural Invariants#

Properties ensuring motif‑level structure remains identifiable across all scales.

Resonance‑Time Invariants#

Properties ensuring regime transitions follow triadic resonance patterns.

Projection Invariants#

Properties ensuring projections remain invertible and coherence‑preserving.

Scaling Invariants#

Properties ensuring dimensional expansion introduces no discontinuities.

8. Validation Terms#

vST (Validation‑Space‑Time)#

A validation framework evaluating structural coherence, dimensional stability, regime behavior, and core alignment.

Validation Layers (V₁–V₄)#

Four structured evaluation layers ensuring invariant‑preserving behavior across the dimensional ladder.

9. Drift Terms#

Dimensional Drift#

A deviation from expected substrate behavior, indicating instability or invariant failure.

Drift Category (D₁–D₄)#

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

Drift Severity#

A measure of drift magnitude, from low to high.