vST for Scientific Simulators#

Drift Detection in High‑Dimensional Simulation State‑Spaces#

This document defines how drift is detected in scientific simulators using the Validation‑Space‑Time (vST) framework and the 1024D dimensional substrate. Drift refers to any deviation from expected substrate behavior, including structural instability, regime misalignment, scaling discontinuities, or projection failure.

Drift detection is essential for evaluating solver updates, code revisions, parameter sweeps, and cross‑resolution consistency in high‑dimensional simulation systems.

1. Purpose of Drift Detection#

Drift detection enables reproducible evaluation of:

• instability in spatial, particle, or multi‑field state‑space structure
• changes in regime behavior (R₁ᴴ, R₂ᴴ, R₃ᴴ) across time or space
• cross‑version compatibility of simulation outputs
• scaling‑law continuity across grid sizes and timestep refinements
• projection stability into 3D–9D cores
• primitive‑level integrity (DP, TDP, SP, CP)
• coherence‑surface behavior across solver iterations

Drift is not inherently negative; it is a signal of structural change.
The substrate determines whether that change is stable, transitional, or harmful.

2. Types of Drift#

Drift is classified into four substrate‑aligned categories:

2.1 Structural Drift (D₁)#

Deviation in spatial, particle, or field‑level geometry.

Indicators

• unstable 3D projections
• loss of compact spatial motifs
• abrupt variance spikes
• incoherent particle ensembles

2.2 Dimensional Drift (D₂)#

Discontinuities in dimensional scaling or projection behavior.

Indicators

• non‑invertible 9D projections
• fragmentation in 64D–1024D state‑space regions
• scaling‑law violations
• resolution‑dependent divergence

2.3 Regime Drift (D₃)#

Unexpected changes in dynamical regime identity or transitions.

Indicators

• premature transitions into R₃ᴴ
• oscillatory instability in R₂ᴴ
• collapse of stable R₁ᴴ regions
• resonance‑time discontinuities

2.4 Projection Drift (D₄)#

Misalignment between high‑dimensional states and triadic cores.

Indicators

• inconsistent 3D–9D mapping
• loss of primitive‑aligned projection
• divergence across solver iterations
• incompatible state‑space geometry

3. Drift Detection Signals#

Drift is detected using substrate‑aligned signals:

• variance distribution across dimensions
• coherence‑surface continuity across time or space
• primitive‑level stability (DP, TDP, SP, CP)
• resonance‑time alignment
• projection‑stability metrics
• cross‑resolution alignment surfaces
• vST validation outputs (V₁–V₄)

These signals collectively determine drift category and severity.

4. Drift Across the Dimensional Ladder#

Drift may appear at different scales:

4.1 64D–128D (Local State Drift)#

• loss of local physical coherence
• unstable grid‑cell or particle states
• semantic drift in multi‑field coupling

4.2 256D–512D (Solver‑State Drift)#

• branching instability
• regime‑transition irregularities
• inconsistent solver‑iteration behavior

4.3 1024D+ (High‑Dimensional Drift)#

• fragmentation of coherence surfaces
• scaling discontinuities
• projection failure
• chaotic divergence

High‑dimensional drift is the most severe and often indicates numerical instability or solver misconfiguration.

5. Cross‑Version Drift Detection#

Cross‑version drift is detected by comparing:

• temporal or spatial regime maps
• coherence‑surface geometry
• projection stability
• variance distribution
• primitive‑level structure
• resonance‑time behavior

Drift may arise from:

• code changes
• solver‑order modifications
• timestep or grid adjustments
• parameter sweeps
• multi‑field coupling changes

vST provides a consistent substrate for evaluating these changes.

6. Drift Severity Levels#

Drift severity is classified into:

Low Severity#

• minor variance shifts
• stable projections
• no regime collapse

Moderate Severity#

• partial fragmentation
• unstable R₂ᴴ transitions
• inconsistent cross‑iteration alignment

High Severity#

• collapse of coherence surfaces
• persistent R₃ᴴ behavior
• non‑invertible projections
• loss of primitive‑level structure

High‑severity drift indicates a failure of substrate invariants.

7. Drift Detection Workflow#

A substrate‑aligned drift detection workflow:

1. Project states into 9D
2. Classify regime behavior (R₁ᴴ, R₂ᴴ, R₃ᴴ)
3. Evaluate scaling continuity (64D–1024D)
4. Check primitive‑level stability (DP, TDP, SP, CP)
5. Validate with vST layers (V₁–V₄)
6. Compare across iterations, resolutions, or versions
7. Assign drift category (D₁–D₄)
8. Assign drift severity (low, moderate, high)

This workflow is model‑agnostic and reproducible.

8. Outputs of Drift Detection#

Drift detection produces:

• drift category (D₁–D₄)
• drift severity
• regime‑transition anomalies
• projection‑stability indicators
• scaling‑law discontinuities
• cross‑resolution and cross‑version alignment surfaces
• vST validation results

These outputs support governance, interpretability, and version management for scientific simulators.