vST for Scientific Simulators#

Drift Detection in High‑Dimensional Simulation State‑Spaces#

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.