Axiom

Sovereign Proof Engine for Molecular Binding

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A neural network that proves its own geometric integrity. Every prediction is spectral-verified. Every proof is immutable.

Table of Contents

• What Is Axiom?
• Core Concepts
• Architecture
• Core Metrics
• Quick Start
• API Endpoints
• Mathematical Framework
• Graph Morphogenesis
• Swarm Guards
• Dependencies
• Documentation
• Research Use
• Related Repositories
• Citation
• License

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What Is Axiom?

Axiom is a neural network system that predicts molecular binding affinities and cryptographically proves the geometric integrity of its own weight manifold. Every prediction carries an immutable proof that the model has not drifted from its verified state.

The system applies concepts from spectral geometry, random matrix theory, and algebraic topology to continuously audit the health of a trained neural network -- then anchors those audits to an append-only ledger.

What Axiom Does

1. Predicts multi-label molecular binding properties from SMILES input (via RDKit ECFP4 featurisation)
2. Proves weight manifold integrity using K3 surface geometry and Wigner-Dyson eigenvalue statistics
3. Anchors sovereign proofs to an immutable ledger (BSV on-chain or local simulation)
4. Guards the manifold with an autonomous swarm of spectral watchdog agents
5. Grows a graph-rewriting automaton seeded by the vessel's own inference, with sparse Lanczos spectral audits

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Core Concepts

Concept	Description
K3 Similarity	Measures how close the weight manifold's spectral density is to a Calabi-Yau (K3) surface. Lower = healthier.
Wigner Gap Variance	Eigenvalue spacing distribution of the Wishart matrix. Tracks convergence toward GUE universality.
Spectral Strength	Composite health score combining K3 and Wigner metrics into a single [0, 1] indicator.
Horizon Entropy	Decision-path entropy ceiling that prevents runaway inference loops.
Forman-Ricci Curvature	Discrete curvature proxy on the weight lattice. Detects topological discontinuities.
Sovereign Status	Achieved when K3 similarity and holdout accuracy simultaneously meet their targets.
Resonance Lock	Ratchet mechanism that freezes peak weights and reduces spectral pressure to prevent accuracy collapse.
Phoenix Restart	Full weight reinitialisation triggered by meso-stagnation, with warmup cooldown.

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Architecture

                        init_sovereign.py
                     (entry point + health check)
                               |
            +------------------+------------------+
            |                  |                  |
        core/              engine/             api/
     model.py           sieve_runner.py     gateway.py
     spectral.py        discovery.py        bot_bridge.py
     signature.py       pytorch_bridge.py   card_generator.py
     weight_loader.py   graph_automata.py   publisher.py
     featuriser.py      fracture_healer.py  static/
     vault.py                                 manifold.html
            |                  |                graph.html
        walls/             swarm/
     logic_wall.py      agent_factory.py
     smooth_wall.py     handoffs.py
                        scout_agent.py
                        registry.py
                        monitor.py
                        protocols.py
                               |
                           ledger/
                        bounty_smart.py
                        chain_interface.py

Walls enforce geometric constraints (entropy ceiling, topological smoothness). Swarm agents autonomously audit K3, Wigner, curvature, and entropy on every round. Engine runs the training/inference loop with spectral pressure, cosine restarts, and resonance capture. Ledger commits cryptographic proof receipts (not raw data) to BSV or a local JSONL file.

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Core Metrics

Metric	Description	Role
K3 Similarity	FFT-based spectral distance to K3 moduli space	Geometric integrity
Wigner Variance	Eigenvalue gap variance (GUE universality)	Spectral health
Spectral Strength	Composite K3 + Wigner score [0, 1]	Overall health
Horizon Entropy	Decision-path entropy ceiling	Halting safety
Forman-Ricci	Discrete curvature proxy	Topological smoothness
Isometry Loss	Chirality + rotation MSE	Symmetry consistency

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Quick Start

# Install core dependencies
pip install numpy scipy pyyaml requests

# Run health check (loads model, spectral analysis, swarm audit)
python init_sovereign.py --model data/sovereign_vessel.json

# Start the REST API
pip install fastapi uvicorn
uvicorn api.gateway:app --host 0.0.0.0 --port 8000

# Predict binding from SMILES (requires RDKit)
pip install rdkit-pypi
python -c "
from engine.discovery import DiscoveryEngine
engine = DiscoveryEngine.from_checkpoint()
print(engine.predict_smiles('CCO'))
"

# Telegram bot
pip install python-telegram-bot
export AXIOM_BOT_TOKEN=your_token_here
python -m api.bot_bridge

# Terminal spectral visualizer
python scripts/spectral_heartbeat.py --demo

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API Endpoints

Method	Endpoint	Description
GET	/health	System health + spectral metrics
POST	/predict	Predict binding from raw features
POST	/sieve	Full sieve pass (predict + proof + ledger)
GET	/manifold	Weight manifold snapshot (quantized + noise)
GET	/visualise	Interactive 3D manifold (Three.js)
GET	/graph	Current graph automaton state
GET	/graph/seed	Generate a fresh trivalent seed graph
GET	/graph/live	Execution era live status
POST	/graph/audit	Sparse spectral audit of graph adjacency
POST	/graph/fractures	Chirality/rotation fracture detection
POST	/graph/proof	Generate + commit graph proof-of-existence

All protected endpoints require an X-Bounty-ID header. See api/middleware/auth_ledger.py for authentication.

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Mathematical Framework

Axiom's verification layer is grounded in three areas of mathematics:

Spectral Geometry (K3 Surfaces)

The weight matrix's 2D FFT power spectrum is compared against the rotational symmetry expected from an SU(2) holonomy on a Calabi-Yau manifold. Proximity to this signature indicates geometric coherence.

Random Matrix Theory (GUE)

The Wishart matrix WW^T's eigenvalue spacings are compared to the Gaussian Unitary Ensemble. Convergence toward GUE statistics signals that the model has learned a "universal" representation rather than memorizing training artifacts.

Discrete Differential Geometry (Forman-Ricci)

A lattice-based curvature proxy detects sharp ridges or discontinuities in the weight landscape that could destabilize the K3 alignment.

These three metrics are monitored continuously by the Worm Swarm and feed into the Phoenix orchestrator's restart/lock decisions.

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Graph Morphogenesis

In the Execution Era (post-training), Axiom grows a trivalent graph automaton:

1. ECFP Projection maps graph neighborhoods into the vessel's input space via a sparse projection matrix
2. Rule Derivation runs each projected neighborhood through the frozen vessel to produce a 16-bit cellular automaton rule
3. Lanczos Spectral Guard audits the graph's adjacency spectrum in O(k*E) time using sparse eigenvalue methods
4. Axiom-Rewire performs topological relaxation by swapping high-curvature neighbors with low-curvature nodes
5. Fracture Detection tests chirality and rotation invariance across neighborhoods

Graph proofs-of-existence are committed to the ledger, linking the graph's spectral health to the vessel's identity.

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Swarm Guards

Four autonomous agents defend the weight manifold:

Guard	Metric	Role
Prime-Guard	K3 Similarity	Geometric integrity watchdog
Quantum-Guard	Wigner Variance	Spectral descent tracker
Smooth-Guard	Forman-Ricci Curvature	Topological smoothness enforcer
Logic-Guard	Horizon Entropy	Halting safety monitor

Each agent independently audits its metric on every round and reports HEALTHY or ALERT status. A full swarm audit produces a consolidated SOVEREIGN / VIOLATION_DETECTED verdict.

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Dependencies

Package	Required	Purpose
numpy	Yes	Core numerics
scipy	Yes	Eigenvalue decomposition, sparse matrices
pyyaml	Yes	Configuration
requests	Yes	BSV chain interface
fastapi + uvicorn	Optional	REST API
rdkit-pypi	Optional	SMILES featurisation (ECFP4)
python-telegram-bot	Optional	Telegram bot
Pillow	Optional	Sovereign Card image generation
crawl4ai	Optional	Autonomous SMILES discovery crawler
torch	Optional	PyTorch autograd training backend

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Documentation

• Specification -- Formal protocol definition
• Architecture -- System design and data flow
• Mathematics -- Theoretical framework and formulas
• API Reference -- REST and Python API documentation
• Swarm System -- Guard agent architecture
• Sieve Loop -- Training loop walkthrough
• Configuration -- config.yaml reference

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Research Use

This codebase is released for research, educational, and evaluation purposes. Researchers can:

• Study the spectral verification framework (K3, Wigner, Forman-Ricci)
• Examine the swarm-based autonomous audit architecture
• Understand the graph morphogenesis and Lanczos spectral guard
• Review the ledger proof-of-existence protocol
• Build on the ECFP4-based molecular featurisation pipeline

For commercial licensing or access to the full unredacted codebase, contact OriginNeuralAI.

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Related Repositories

Repository	Description
DSC-1	Drug-SMILES Classifier: predecessor model
BioPrime	Biological primitive discovery engine
OriginNeuralAI	Organisation profile

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Citation

@software{axiom2026,
  author       = {OriginNeuralAI},
  title        = {Axiom: Sovereign Proof Engine for Molecular Binding},
  year         = {2026},
  publisher    = {GitHub},
  url          = {https://github.com/OriginNeuralAI/Axiom},
  note         = {Spectral geometry + random matrix theory for neural network verification}
}

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License

Copyright 2025-2026 OriginNeuralAI. All rights reserved.

This software is provided for research and educational use only. Commercial use, redistribution, or derivative works require a written license from OriginNeuralAI. See LICENSE for full terms.

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OriginNeuralAI -- Building sovereign intelligence.

The weight manifold doesn't lie.