The Applications Layer is where NEXAH methods meet concrete systems.
The non-authoritative NEXAH Evidence Atlas provides claim-level navigation to selected application results and limits. Application protocols and their owning evidence remain authoritative.
It contains runnable demonstrations, system-specific research programs, integration tools, conceptual models, and experimental navigation prototypes. These are not finished products. They are working environments for asking:
Which parts of a dynamical system can be reconstructed, compared, and navigated using structural field methods?
In NEXAH, an application can be:
- a runnable tool that produces an analysis or visualization
- a reference system used to test a method
- an applied research program with experiments and evidence
- an adapter that translates another system into a NEXAH representation
- an experimental prototype exploring a possible future capability
- a conceptual model describing how a class of systems might be represented
The status of each area matters. A runnable script is not automatically a validated method, and a promising experiment is not automatically a deployable application.
| You want to… | Start with |
|---|---|
| Run the verified visual reference pipeline | NEXAH Demonstrator |
| Orient a declared network and compare its structure | network_orientation/ |
| Explore a compact Lorenz application | demos/lorenz_demo/ |
| Study Lorenz field and geometry analysis | dynamical_systems/lorenz/ |
| Compare a different chaotic flow | dynamical_systems/halvorsen/ |
| Explore the most developed applied program | power_systems/ |
| Study governed orientation over fixed public knowledge sources | Orientation Translation |
| Connect another system to NEXAH | adapters/ |
| Inspect experimental navigation tools | navigation/ |
| Understand the conceptual model families | models/dynamical_models/ |
If you are completely new to NEXAH, begin with the repository front door before entering an application program.
| Area | What it offers | Current status |
|---|---|---|
| Network Orientation | Typed graph topology, reachability, structural comparison, five read-only probes, and V1/V2 fixtures | Verified illustrative application |
| Orientation Translation | Source-bounded public-knowledge pilots, Reflections, Neighborhoods, comparisons, methodological studies, and reviews | Applied methodological research; reader effect not yet tested |
| Power Systems | Current IEEE benchmark geometry/replay plus historical exploratory warning, prediction, recovery, scaling, and control programs | Bounded benchmark evidence / historical research lineage |
| Lorenz Research | Density, FTLE, Lyapunov, separatrix, regime, and navigation analysis | Active reference system |
| Halvorsen Research | Distributed transport, transition graphs, residue models, reachability, and policy experiments | Experimental research |
| Lorenz Demo | Compact visual pipeline for geometry and transport structures | Runnable demonstration |
| Lorenz Core Demos | Historical progression from pattern detection to navigation and meta-control | Reference / legacy series |
| Adapters | Interfaces and examples for Lorenz, Kuramoto, grids, traffic, and supply chains | Experimental integration layer |
| Navigation | Mod-77, drift quantization, Phi-Split, and IEEE9 navigation prototypes | Legacy / experimental prototype |
| Dynamical Models | Stability, gradient, drift, and regime model documents | Theoretical reference |
| Datasets | Synthetic JSON system descriptions | Reference data; documentation incomplete |
| Archive | Superseded prototypes and former root demos | Archived |
Orientation Translation is a non-canonical applied research program investigating how fixed public representations can be separated, compared, navigated, explained, and bounded while preserving provenance and explicit evidence limits.
It remains physically part of Applications, participates conceptually in Research, and does not define Orientation Language semantics or Kernel behavior. Meta Review 01 requires limited review before further use, while Method Archaeology 01 provides only a provisional candidate-action inventory for future Reader-Test design. Reader effect has not yet been established.
Current demonstrated scope: reproducible IEEE benchmark computation, failure-aware geometry extraction, unchanged IEEE-9→IEEE-14 method transfer, structural replay and bounded Orientation Brief generation. Prospective warning, prediction, risk, stability forecasting, causal precursors, operational control and universal scaling are not established. Historical experiments remain preserved as research lineage.
APPLICATIONS/power_systems/ is currently the most developed applied research program in NEXAH.
It investigates whether simulated and benchmark power-system states can be organized into structural representations containing:
- operating regions and basin-like territories
- transition corridors
- warning and critical regimes
- recovery pathways
- candidate anchors and bottlenecks
- atlas-guided intervention concepts
Primary environments include:
| Environment | Role |
|---|---|
| FIELD_NAVIGATION_VALIDATION/ | Main atlas, prediction, recovery, and reconstruction experiment series |
| VALIDATION_LAYER/ | Quantitative indicators and validation experiments |
| ieee_xray_pipeline/ | Feature and geometry reconstruction pipeline |
| nexah_ieee9/ | Compact IEEE9 navigation and control environment |
| nexah_ieeeX/ | Scaling studies across larger IEEE benchmark networks |
| stability_field_dynamics/ | Broad stability-field and IEEE experiment archive |
Current questions include:
- Do warning regimes appear before simulated collapse?
- Which structural indicators remain stable across IEEE network sizes?
- Can recovery trajectories be grouped into recurring archetypes?
- How much of an atlas can be reconstructed from historical simulation artifacts?
- Which proposed control actions survive comparison with established power-system methods?
- What changes when repository experiments are tested against operational data?
This work uses IEEE benchmark models and repository-generated simulation archives. It should not yet be interpreted as operational grid validation or a production control system.
For detail, use the Power Systems README and Power Systems Index. The maintained public-use path is the completed IEEE Geometry V1 Showcase, with a 90-second map, a ten-minute replay, a research path, and reproducible figures governed by the Phase V evidence and outcome testkit.
Network Orientation is the first maintained, graph-native application of the typed Orientation Layer. It turns declared nodes and directed edges into an evidence-bound structural report containing paths, reachability, components, bottlenecks, missing information, and explicit uncertainty.
Its Supply Chain and Ecosystem inputs are illustrative fixtures. Their authored regime, risk, action, and shock fields are excluded. The application is designed for learning how maps and paths change, not for issuing control commands.
The Dynamical Systems area provides reference systems for developing and comparing NEXAH methods.
dynamical_systems/lorenz/ contains the broadest non-power-system analysis environment:
- attractor and density reconstruction
- FTLE and Lyapunov analysis
- filament and separatrix extraction
- regime and switching maps
- flow-field visualization
- exploratory navigation
Lorenz is the main reference system for recognizable switching behavior and well-known chaotic geometry.
dynamical_systems/halvorsen/ provides a contrasting flow geometry with distributed rotational transport. It contains:
- transition and coarse-graining experiments
- graph connectivity and reachability
- candidate gate and policy studies
- residue-flow comparisons
- Lorenz/Halvorsen visual comparisons
The comparison asks which observed NEXAH structures depend on the system and which recur across different representations.
NEXAH currently has several demo layers with different roles:
| Demo | Role |
|---|---|
| PROTO_CORE/NEXAH_DEMONSTRATOR | Canonical, verified hands-on entry |
| demos/lorenz_demo | Compact application-level Lorenz visualization |
| core_demos/lorenz | Historical development series and visual archive |
The existence of several Lorenz areas reflects the development history. New users should choose the canonical demonstrator first.
The Adapter Layer explores a minimal translation boundary between an external system and a structural NEXAH representation.
Examples currently cover:
- Lorenz
- Kuramoto
- power-grid abstractions
- supply chains
- traffic systems
- synthetic energy grids
These adapters are useful prototypes and starting points for contributors. They are not yet a stable public integration API.
Questions for this layer:
- What is the minimum information a system must expose?
- Which state, transition, phase, or graph representation is appropriate?
- Can different domains share one adapter contract without losing essential dynamics?
- How should uncertainty and measurement noise enter the representation?
The navigation/ directory contains an earlier experimental navigation line based on Mod-77 state spaces, drift quantization, Phi-Split events, and an IEEE9-style prototype.
It is preserved because it contains executable ideas and useful research questions. It is not the canonical NEXAH navigation layer and is not integrated with every current application.
The Dynamical Models documents describe a conceptual progression:
stability landscape
→ gradient dynamics
→ drift dynamics
→ regime transitions
The datasets/ directory contains synthetic JSON descriptions
for energy grids, supply chains, ecosystems, and server clusters. The shared
nodes/edges subset used by the Supply Chain and Ecosystem fixtures now has a
typed consumer in Network Orientation V1. Other
metadata and datasets remain historical reference material with inconsistent
schemas.
This layer intentionally exposes open work. Useful contributions include:
- reproducing an experiment in a clean environment
- comparing structural indicators against standard baselines
- connecting a new system through an adapter
- documenting a synthetic dataset and its schema
- testing Lorenz-derived methods on another dynamical system
- evaluating IEEE results with power-system expertise
- replacing simulated archives with appropriate operational or public data
- separating representation artifacts from system-invariant behavior
- improving statistical treatment and uncertainty reporting
The goal is not to present every question as solved. The goal is to make the current tools, evidence, and open problems inspectable.
| Status | Meaning |
|---|---|
| Runnable demonstration | A documented script or pipeline can be executed |
| Active applied research | Ongoing system-specific experiments and evidence |
| Experimental | Promising implementation with limited validation |
| Theoretical | Conceptual model or proposed mechanism |
| Legacy / reference | Historical work retained for context or reuse |
| Archived | Superseded material outside the current entry path |
Runnable does not mean validated. Experimental does not mean ineffective. The labels tell readers what kind of evidence and maintenance level to expect.
The Applications Layer does not yet provide:
- a unified application API
- production deployment guarantees
- comprehensive real-world operational validation
- one reproducibility command for every historical experiment
- stable interfaces across all adapters and navigation prototypes
- independent validation of the major application claims
These are collaboration opportunities, not hidden assumptions.
- Repository Overview
- Research Portal
- Validation Portal
- Findings Portal
- Architecture
- NEXAH Demonstrator
NEXAH Applications
Systems · Tools · Evidence · Open Questions