TaoCore

A systems-level abstraction layer for reasoning about stability, coherence, and dynamics in complex systems.

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Why TaoCore?

Modern ML systems operate in a black box—predict, classify, recommend—but rarely explain their behavior or guarantee stability. When you ask:

"Will this system stay within acceptable bounds?"

"Are these state transitions coherent?"

"What equilibrium will this converge to?"

...you get silence.

TaoCore provides answers.

It's a domain-agnostic layer that sits above ML models, data pipelines, and agent systems to analyze:

• Stability – Does the system reach equilibrium?
• Coherence – Are transitions smooth and directional?
• Balance – Do values stay within operating bounds?
• Structure – How are components organized and connected?

Unlike optimization frameworks, TaoCore doesn't tell systems what to do—it observes and analyzes what they actually do.

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Quick Start

Installation

pip install taocore

Or from source:

git clone https://github.com/yourusername/taocore.git
cd taocore
make install

30-Second Example

from taocore import EquilibriumSolver, StateVector, ConvergenceReason
import numpy as np

# Define system dynamics
def damping_rule(state):
    return StateVector(state.array * 0.9)

# Find equilibrium
solver = EquilibriumSolver(tolerance=1e-6)
result = solver.solve(
    initial=StateVector(np.array([10.0, 5.0])),
    update_rule=damping_rule
)

# Analyze results
if result.converged:
    print(f"✓ Equilibrium reached in {result.iterations} iterations")
    print(f"  Stability score: {result.stability_score:.3f}")
else:
    print(f"✗ {result.convergence_reason.value}")
    if result.oscillation_detected:
        print("  System is oscillating—conflicting dynamics")

Output:

✓ Equilibrium reached in 65 iterations
  Stability score: 0.847

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Core Concepts

1. Equilibrium as First-Class Abstraction

Instead of asking "what's the answer right now?", TaoCore asks:

"What does this system settle into when signals interact?"

Equilibrium represents consensus, resistance to noise, and stable interpretation.

from taocore import EquilibriumSolver, StateVector

# System with competing forces
def weighted_average(state):
    # Move 30% toward target [5, 5]
    target = np.array([5.0, 5.0])
    return StateVector(0.7 * state.array + 0.3 * target)

solver = EquilibriumSolver()
result = solver.solve(StateVector(np.array([0.0, 10.0])), weighted_average)

print(f"Converged to: {result.state.array}")
# Output: Converged to: [5.0, 5.0]

2. Metrics Without Objectives

TaoCore provides descriptive metrics, not prescriptive loss functions:

• BalanceMetric – Are values within acceptable bounds?
• FlowMetric – How coherent are state transitions?
• ClusterMetric – How is the system organized?
• HubMetric – What components are most influential?

from taocore import BalanceMetric

# Define operating regime
metric = BalanceMetric(bounds={
    "cpu": (0, 80),      # %
    "memory": (0, 90),    # %
    "latency": (0, 200)   # ms
})

# Evaluate system health
score = metric.compute({
    "cpu": 65,
    "memory": 70,
    "latency": 120
})
print(f"Balance: {score:.2f}")  # 1.00 = perfect balance

3. Graph Analysis

Analyze system structure and relationships:

from taocore import Graph, Node, Edge, HubMetric, ClusterMetric

# Build service dependency graph
graph = Graph()
for service in ["api", "db", "cache", "auth"]:
    graph.add_node(Node(service))

graph.add_edge(Edge("api", "db"))
graph.add_edge(Edge("api", "cache"))
graph.add_edge(Edge("api", "auth"))

# Find critical services
hub_metric = HubMetric(method="pagerank")
importance = hub_metric.compute(graph)
print(f"Most critical: {max(importance.items(), key=lambda x: x[1])}")

# Detect communities
cluster_metric = ClusterMetric(algorithm="modularity")
clusters = cluster_metric.compute(graph)
print(f"Found {clusters['num_clusters']} service groups")

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Features

Primitives

• Node – Entities with numeric features
• Edge – Weighted relationships
• Graph – Topology with traversal and filtering
• StateVector – Dual dict/array representation

Metrics

• BalanceMetric – Bounded stability analysis
• FlowMetric – Temporal coherence (volatility, directionality)
• AttentionMetric – Similarity and relevance scoring
• ClusterMetric – Community detection (components, modularity, distance)
• HubMetric – Centrality measures (degree, betweenness, eigenvector, PageRank)
• CompositeMetric – Weighted metric combinations

Solvers

• EquilibriumSolver – Fixed-point iteration with:
  • Multiple convergence criteria (tolerance, stability window)
  • Oscillation detection (2-cycle, 3-cycle, general)
  • Comprehensive diagnostics (stability score, convergence reason)
  • Failure mode reporting

Extensions (RFC-1)

• Temporal primitives – Timestamps, decay rates, expiration
• Graph queries – k-hop neighbors, shortest paths, subgraphs

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Real-World Use Cases

1. Service Mesh Health Monitoring

from taocore import BalanceMetric, FlowMetric, StateVector, CompositeMetric

# Define health metrics
balance = BalanceMetric(bounds={
    "error_rate": (0, 0.05),
    "latency_p99": (0, 500),
    "cpu_usage": (0, 80)
})

flow = FlowMetric(mode="volatility")

# Combine metrics
health_metric = CompositeMetric(
    metrics=[balance, flow],
    weights=[0.7, 0.3],  # Prioritize balance
    aggregation="weighted_sum"
)

# Monitor system
current_state = {"error_rate": 0.02, "latency_p99": 350, "cpu_usage": 65}
history = [...]  # Previous states

health_score = health_metric.compute(current_state, history)

if health_score < 0.6:
    trigger_alert("System health degraded")

2. Multi-Agent Consensus

# Agents updating beliefs based on neighbors
def agent_update(agent_id):
    def update_belief(state):
        neighbors = graph.neighbors(agent_id)
        neighbor_beliefs = [agents[n].belief for n in neighbors]
        # Move toward average
        avg = np.mean(neighbor_beliefs, axis=0)
        return StateVector(0.7 * state.array + 0.3 * avg)
    return update_belief

# Find equilibrium for each agent
solver = EquilibriumSolver(stability_window=5)
for agent_id, agent in agents.items():
    result = solver.solve(
        StateVector(agent.initial_belief),
        agent_update(agent_id)
    )
    agent.consensus_belief = result.state

3. Photo Memory Analysis (Temporal Graph)

from taocore import Node, Graph, AttentionMetric

# Build memory graph with temporal decay
memories = []
current_time = time.time()

for photo in photos:
    node = Node(
        id=photo.id,
        features=photo.embedding,
        timestamp=photo.timestamp,
        decay_rate=0.01  # Decay over time
    )
    memories.append(node)

# Query relevant memories
attention = AttentionMetric(mode="composite")
query = {"joy": 0.8, "outdoor": 0.9}

scores = attention.compute(
    query=query,
    target=memories,
    current_time=current_time
)

# Filter expired or weak memories
relevant = [m for m, score in scores.items()
            if score > 0.5 and not memories[m].is_expired(current_time)]

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Architecture

┌─────────────────────────────────────────────────────────────┐
│                         Applications                         │
│  (Service monitoring, agent systems, memory analysis, ...)  │
└────────────────────────────┬────────────────────────────────┘
                             │
┌────────────────────────────┴────────────────────────────────┐
│                        TaoCore Layer                         │
│                                                              │
│  ┌──────────────┐  ┌──────────────┐  ┌──────────────┐     │
│  │   Metrics    │  │   Solvers    │  │   Policies   │     │
│  │              │  │              │  │              │     │
│  │  Balance     │  │  Equilibrium │  │  Decider     │     │
│  │  Flow        │  │  Convergence │  │  Decision    │     │
│  │  Attention   │  │  Oscillation │  │              │     │
│  │  Cluster     │  │  Diagnostics │  │              │     │
│  │  Hub         │  │              │  │              │     │
│  └──────────────┘  └──────────────┘  └──────────────┘     │
│                             │                               │
│  ┌──────────────────────────┴─────────────────────────┐   │
│  │              Primitives                              │   │
│  │  Node │ Edge │ Graph │ StateVector                  │   │
│  └──────────────────────────────────────────────────────┘   │
└──────────────────────────────────────────────────────────────┘
                             │
┌────────────────────────────┴────────────────────────────────┐
│                    ML Models & Data                          │
│  (Neural networks, embeddings, feature extractors, ...)     │
└──────────────────────────────────────────────────────────────┘

TaoCore sits between your models and your application logic, providing:

• ✓ Stability analysis for model outputs
• ✓ Structural analysis of system relationships
• ✓ Equilibrium finding for multi-agent dynamics
• ✓ Quality metrics without optimization objectives

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Design Philosophy

What TaoCore Is

• Descriptive, not prescriptive – Analyzes what systems do, doesn't tell them what to do
• Domain-agnostic – Works with any numeric state representation
• Explicit and inspectable – All behavior is observable
• Minimal and composable – Few primitives, powerful combinations

What TaoCore Is Not

• ❌ Not an ML framework – No training, no gradient descent
• ❌ Not an optimization library – No loss functions, no objectives
• ❌ Not a control system – No feedback loops, no actuation
• ❌ Not domain-specific – No assumptions about what data represents

Core Principles

1. Equilibrium over optimization – Seek stable states, not optimal solutions
2. Stability over prediction – Measure coherence, not accuracy
3. Structure over semantics – Analyze relationships, not meanings
4. Diagnostics as data – Failure modes are signals, not errors

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Documentation

• RFC-1: Core Systems Layer – Primitives, metrics, equilibrium
• RFC-2: Advanced Metrics – Clustering, hubs, composition
• RFC-3: Enhanced Equilibrium – Oscillation detection, diagnostics
• Testing Guide – Comprehensive testing documentation
• Publishing Guide – PyPI release process
• Docker Guide – Container deployment

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Development

Requirements

• Python: 3.9, 3.10, 3.11, 3.12, 3.13
• Dependencies: NumPy ≥ 1.24.0 (≥ 1.26.0 for Python 3.13)

Setup

# Clone repository
git clone https://github.com/yourusername/taocore.git
cd taocore

# Install dependencies
make install

# Install dev dependencies
make dev

Testing

# Run tests
make test

# Run with coverage
make coverage

# Test across Python versions
make tox-all

# Run linting and type checking
make tox-lint
make tox-type

Current metrics:

• 115 tests passing
• 92% code coverage
• Supports Python 3.9-3.13

Code Quality

# Format code
make format

# Type checking
make tox-type

# Linting
make tox-lint

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Examples

Comprehensive examples in examples/:

• rfc1_verification.py – Core primitives and metrics
• rfc2_verification.py – Graph analysis features
• rfc3_verification.py – Enhanced equilibrium solver

Run examples:

uv run python examples/rfc1_verification.py
uv run python examples/rfc2_verification.py
uv run python examples/rfc3_verification.py

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Contributing

We welcome contributions! See CONTRIBUTING.md for guidelines.

Areas for contribution:

• Additional metrics (spectral clustering, information-theoretic measures)
• Performance optimizations (sparse matrices, GPU acceleration)
• Visualization tools (trajectory plots, graph rendering)
• Integration examples (with popular frameworks)
• Documentation improvements

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Citation

If you use TaoCore in your research, please cite:

@software{taocore2026,
  title = {TaoCore: A Systems-Level Abstraction Layer for Stability and Coherence Analysis},
  author = {TaoCore Contributors},
  year = {2026},
  url = {https://github.com/yourusername/taocore},
  version = {0.1.0}
}

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License

MIT License

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Roadmap

v0.2.0 (Q1 2026)

• Adaptive solvers with auto-tuning
• Stochastic equilibrium analysis
• Performance benchmarks

v0.3.0 (Q2 2026)

• Visualization toolkit
• Multi-attractor analysis
• Integration examples (LangChain, AutoGen, etc.)

v1.0.0 (Q3 2026)

• Production-ready API freeze
• Comprehensive documentation site
• Community governance model

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Community

• Issues: GitHub Issues
• Discussions: GitHub Discussions
• Twitter: @taocore_dev

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Built with ❤️ by the TaoCore team

Seeking equilibrium in complex systems, one fixed point at a time.