A control-theoretic diagnostic framework for stability, regime detection, and bounded dynamics in nonstationary systems.
Many complex systems exhibit loss of stability and regime transitions before overt failure or collapse. Traditional approaches emphasize detection after the fact; this repository focuses instead on stability-aware diagnostics characterize when system trajectories approach inadmissible regimes.
The goal is not to predict outcomes or control dynamics directly, but to provide a reproducible, control-compatible diagnostic scaffold that can be applied across domains where dynamics are nonstationary, hysteretic, or path-dependent.
System evolution is represented by a triadic feature state:
- φₛ(t) — instantaneous structural feature (e.g., coherence or state estimate)
- φᵢ(t) — memory / history feature (integral, EWMA, hysteresis state)
- φ_c(t) — constraint / admissible-regime feature (stability envelope or safe-set margin)
The diagnostic operator is defined as:
⎡ φ̇ₛ(t) ⎤
ΔΦ(t) = ⎢ φₛ(t) − φᵢ(t) ⎥
⎣ φ_c(t) − φₛ(t) ⎦
A weighted score
J(t) = wₛ·φ̇ₛ² + wᵢ·(φₛ − φᵢ)² + w_c·(φ_c − φₛ)²
acts as an indicator of instability and regime transition. The formulation is Lyapunov-compatible, emphasizing stability criteria over speculative effects.
Detailed definitions and stability conditions are provided in the core framework files.
AI-Stabilized-Spacetime-Dynamics/
│
├── README.md # Project overview, scope, and usage
├── LICENSE # MIT license
├── CITATION.cff # Citation metadata
│
├── paper/
│ └── delta_phi_framework.md # Canonical research manuscript (Markdown)
│
├── framework/
│ ├── delta_phi.py # ΔΦ operator implementation
│ ├── stability.py # Stability score J(t) and regime logic
│ └── __init__.py # Framework exports
│
├── features/
│ ├── feature_maps.py # φ_S: instantaneous state features
│ ├── memory_models.py # φ_I: memory / history models
│ ├── constraint_models.py # φ_C: admissible regime boundaries
│ └── __init__.py # Feature registries
│
├── pipeline/
│ ├── observer.py # Diagnostic observer (y → ΔΦ → J)
│ ├── config.py # Explicit configuration and locking
│ ├── replay.py # Deterministic replay & audit tools
│ └── __init__.py # Pipeline entry points
│
└── tests/
├── test_delta_phi.py # ΔΦ operator unit tests
├── test_stability_score.py # Stability score behavior tests
└── test_reproducibility.py # Deterministic replay verification
Additional documentation, figures, or illustrative examples may be released in future versions, but are intentionally excluded from the present reference implementation.
- ✓ A deterministic, observer-like diagnostic scaffold
- ✓ Compatible with linear, nonlinear, stochastic, and hybrid systems
- ✓ Designed for stability analysis, admissible regimes, and boundary transitions
- ✓ Reproducible when implementation choices are fully specified
- ✗ A controller
- ✗ A predictive oracle
- ✗ An ontological model of spacetime
- ✗ Unique without explicit specification of features, memory, and constraints
- Input signal → y(t)
- Feature extraction → φₛ(t)
- Memory update (EWMA / integral) → φᵢ(t)
- Constraint estimation (envelope / safe set) → φ_c(t)
- Compute ΔΦ(t), score J(t), and regime flags
Every experiment must explicitly specify:
- the feature map used for φₛ(t)
- the memory operator used for φᵢ(t)
- the constraint model used for φ_c(t)
- sampling rate, windowing, smoothing, and thresholds
Without these disclosures, results are not interpretable or falsifiable.
A triadic structure also appears in the Helix–Light–Vortex (HLV) framework as an organizing principle for coherence and memory channels. This repository does not require or assume that physical layer; the diagnostic framework stands independently as a control-theoretic method.
This framework is intentionally limited to a diagnostic layer. It does not claim:
- an ontological model of spacetime,
- uniqueness of the triadic decomposition, or
- a guaranteed causal mechanism behind regime changes.
The only testable content is the implemented pipeline and its explicitly stated components.
Active development. Current focus: formalizing the minimal mathematical structure and stability criteria. Applications, if any, are secondary to methodological rigor.
MIT
| Symbol | Meaning |
|---|---|
| φₛ(t) | Structural feature (instantaneous state) |
| φᵢ(t) | Memory/history feature (integral, EWMA) |
| φ_c(t) | Constraint/admissible regime feature |
| ΔΦ(t) | Diagnostic operator (triadic vector) |
| J(t) | Weighted instability score |
| wₛ, wᵢ, w_c | Weights for structural, memory, constraint terms |
A control-theoretic lens for understanding system stability and regime boundaries.