Status: Active research system — validation and kernel integration in progress
NEXAH reconstructs structure, transitions, and stability
directly from system dynamics.
Complex systems are not random.
They evolve within structured fields that constrain motion, transitions, and outcomes.
NEXAH connects continuous dynamics with discrete transition structure across regimes.
NEXAH transforms time-series data into a structured representation of system behavior:
dynamics → structure → field → transitions → navigation
This enables:
- detection of transition regions (gates, boundaries)
- identification of stable regimes (basins)
- reconstruction of system geometry
- simulation of motion within learned structure
Traditional approaches model:
state → next state
NEXAH instead models:
motion within a structured field
Where:
- stability = alignment with field structure
- instability = drift into low-density or conflicting regions
- transitions = movement across structured regions
The demonstrator provides a minimal, reproducible implementation of the core pipeline
and serves as the recommended entry point.
It includes:
- field construction from trajectories
- Gate Operator (continuous instability field)
- Transition Structure (discrete sheet dynamics)
- Navigation Kernel (geometry-aware motion)
👉 Start here:
👉 Core components:
gate_operator.mdtransition_structure.mdnavigation_kernel.md
System motion follows a constrained flow field — transitions occur only along admissible paths.
Control emerges from alignment with system geometry rather than external forcing.
📂 APPLICATIONS/power_systems/VALIDATION_LAYER/
Observed behavior:
- early warning up to 40–50 time units before collapse
- instability appears as geometric deviation
- transition behavior becomes visible in motion metrics
NEXAH_CORE/
Implements:
- field reconstruction
- transition detection (gates, basins)
- probabilistic instability modeling
- structure-aware trajectory analysis
NEXAH_DEMONSTRATOR/
- minimal working system
- reproducible experiments
- empirical validation layer
NEXAH integrates:
Field (continuous)
↔ Geometry (structure)
↔ Graph (transitions)
↔ Control (trajectory shaping)
Interpretation:
- field → defines motion
- geometry → defines constraints
- graph → encodes transition structure
- control → shapes trajectories within these constraints
✔ field reconstruction from data
✔ stability as spatial structure
✔ transition detection (gates, basins)
✔ probabilistic transition modeling
✔ trajectory simulation within learned fields
❌ no unified runtime kernel
❌ limited large-scale validation
❌ early-stage control integration
❌ not production-ready
pip install -e .
# or
pip install -r requirements.txt
python run_nexah_demo.pyStability is not a scalar value.
It is a region within a structured field.
A system does not fail randomly.
It moves through structured transition regions
that constrain what outcomes are possible.
Thomas K. R. Hofmann · NEXAH · 2026