vST for Scientific Simulators#

Validation‑Space‑Time Framework for High‑Dimensional Simulation Systems#

This artifact defines a substrate‑level framework for analyzing, validating, and comparing scientific simulators using the Validation‑Space‑Time (vST) system and the 1024D dimensional substrate. It provides a structured, invariant‑preserving method for interpreting simulation state‑spaces, regime transitions, scaling behavior, and cross‑version drift in computational physics, climate models, molecular dynamics, agent‑based systems, and other high‑dimensional simulators.

The goal is to offer a reproducible, model‑agnostic substrate for understanding simulation behavior across time, space, and dimensional regimes.

1. Purpose#

Scientific simulators operate in high‑dimensional state spaces (often 10³–10⁶ dimensions) and exhibit:

• stable and unstable dynamical regimes
• transitions between physical or computational phases
• scaling‑law behavior across grid sizes and solver configurations
• drift across code revisions or parameterizations
• projection‑compatible structure for interpretability

This artifact applies the Resonance Substrate Model (RSM) and vST validation layers to:

• classify simulation‑state regimes
• analyze scaling behavior across spatial and temporal resolutions
• detect drift across simulator versions or parameter sweeps
• map coherence surfaces in simulation state‑space
• project high‑dimensional states into 3D–9D triadic cores

The result is a unified, interpretable substrate for scientific simulation behavior.

2. Contents#

This directory contains:

• substrate_definition.md
  Defines the simulation substrate, dimensional primitives, and state‑space structure.

• simulation_regimes.md
  Describes stable, transitional, and dispersed regimes in simulation dynamics.

• dimensional_scaling_simulators.md
  Maps simulation scaling laws onto the 3D–1024D dimensional ladder.

• projection_into_structural_cores.md
  Defines invertible projection from high‑dimensional simulation states into triadic cores.

• validation_layers_vst_sim.md
  Extends vST (V₁–V₄) to simulator‑specific behavior.

• drift_detection_sim.md
  Provides a substrate‑level framework for detecting cross‑version drift.

• examples/
  Demonstrations of state‑trajectory analysis, projection, and drift detection.

• appendix/
  Terminology and references.

Each file is self‑contained and designed for clarity, reproducibility, and cross‑simulator comparison.

3. Scope#

This artifact is:

• model‑agnostic
  Works with any scientific simulator (PDE solvers, MD engines, climate models, N‑body codes, agent‑based systems, etc.).

• architecture‑independent
  Applies to grid‑based, particle‑based, mesh‑free, and hybrid simulation frameworks.

• method‑independent
  Compatible with explicit, implicit, symplectic, stochastic, and hybrid solvers.

• substrate‑aligned
  Uses the same primitives, invariants, and validation layers as the rest of the RSM canon.

4. Intended Use#

This framework supports:

• state‑space analysis
• cross‑version comparison
• drift detection
• scaling‑law evaluation
• regime‑transition mapping
• simulation‑stability diagnostics
• reproducible inference and solver analysis

It is not a performance benchmark or a numerical‑method tutorial.
It is a substrate‑level interpretability and validation framework.

5. Relationship to Other Artifacts#

This artifact extends:

• Dimensional Substrate Structures (3D–1024D substrate)
• Validation‑Space‑Time (vST)
• Triadic Dimensional Cores (3D–9D)

It parallels:

• vST for Large Language Models
• vST for Protein Language Models
• vST for Robotics and Control Policies
• vST for Scientific Simulators (this artifact)
• vST for Multi‑Model Alignment

Each artifact stands alone but shares a common substrate grammar.

6. Citation#

A CITATION.cff file is included for formal citation.
A zenodo.json file is provided for DOI‑ready metadata.

7. License#

Released under the MIT License.