vST for Scientific Simulators#
Terminology#
This appendix defines the terminology used throughout the vST for Scientific Simulators artifact. Terms are presented in a substrate‑agnostic, model‑independent manner and apply to any high‑dimensional simulator operating across the full dimensional ladder (3D → 1024D). Definitions emphasize primitive‑level structure, regime behavior, scaling continuity, and invariant preservation.
1. Substrate Terms#
Simulator Substrate#
A structured, invariant‑preserving framework for representing and interpreting simulation state‑spaces across 64D–1024D.
State‑Space#
The high‑dimensional vector space representing the simulator’s physical, numerical, or multi‑field state at a given timestep or solver iteration.
Coherence Surface#
A stable region in state‑space where trajectories maintain structural continuity across time, space, or solver iterations.
2. Primitive Terms#
Dimensional Primitive (DP)#
The minimal unit of simulation‑state structure, capturing local coherence, variance behavior, and projection stability.
Triadic Dimensional Primitive (TDP)#
A triad of DPs forming the smallest unit capable of expressing full dynamical regime behavior (R₁, R₂, R₃).
Scaling Primitive (SP)#
A rule‑based expansion unit that preserves invariants during dimensional scaling (e.g., grid refinement, timestep reduction, solver‑order changes).
Coherence Primitive (CP)#
A minimal unit identifying stable, transitional, or dispersed regions in high‑dimensional simulation state‑space.
3. Core Terms#
Triadic Dimensional Core (TDC)#
The 3D–9D substrate composed of one or more TDPs, used for interpretable projection of simulation states.
3D Structural Core#
Captures motif‑level geometry in spatial or particle‑level fields.
6D Interaction Core#
Captures relational and solver‑driven structure across fields, particles, or spatial domains.
9D Coherence Core#
Captures pathway‑level coherence across time, space, or solver iterations.
4. Regime Terms#
High‑Dimensional Regimes (R₁ᴴ, R₂ᴴ, R₃ᴴ)#
The triadic regime structure expressed in 64D–1024D simulation state‑spaces.
Stable Regime (R₁ / R₁ᴴ)#
Compact, coherent, low‑variance state behavior.
Transition Regime (R₂ / R₂ᴴ)#
Branching, oscillatory, or reorientation behavior across time or space.
Dispersion Regime (R₃ / R₃ᴴ)#
Diffuse, fragmented, or unstable state behavior.
5. Scaling Terms#
Scaling Behavior#
The structured expansion of state‑space capacity as grid resolution, timestep refinement, or solver complexity increases.
Scaling Regimes (S₁, S₂, S₃)#
Triadic scaling behavior describing stable, transitional, and dispersion‑prone scaling phases.
Dimensional Continuity#
The requirement that state‑space expansion remains smooth and invariant‑preserving across the dimensional ladder.
6. Projection Terms#
Invertible Projection#
A projection from high‑dimensional state‑space into 3D–9D that preserves primitive‑level structure and regime identity.
Regime‑Aware Projection#
A projection that maintains correct mapping of R₁, R₂, and R₃ behaviors.
Primitive‑Aligned Projection#
A projection that preserves DP, TDP, SP, and CP structure.
7. Alignment Terms#
Iteration‑to‑Iteration Alignment#
Comparison of simulation states across solver iterations or timesteps.
Spatial/Particle Alignment#
Comparison of states across spatial regions or particle subsets.
Cross‑Resolution Alignment#
Comparison of state‑space structure across grid refinements or timestep reductions.
Cross‑Version Alignment#
Comparison of simulation behavior across code revisions, solver changes, or parameterizations.
8. Validation Terms#
vST (Validation‑Space‑Time)#
A substrate‑level validation framework evaluating structural coherence, dimensional continuity, regime behavior, and core alignment.
Validation Layers (V₁–V₄)#
Four structured evaluation layers ensuring invariant‑preserving behavior across the dimensional ladder.
9. Drift Terms#
Drift#
A deviation from expected substrate behavior, indicating instability or invariant failure.
Drift Categories (D₁–D₄)#
Classification of drift into structural, dimensional, regime, or projection drift.
Drift Severity#
A measure of drift magnitude (low, moderate, high).