Σ-Model V3.0+: Schema Coherence Framework for AI Agents

Paper: The Σ-Model: Schema-Coherence Suppression as the Origin of Compositional Generalisation Failure

Status: Preprint (preparing for peer review) | Version: 3.0+ (Full Reconstruction)

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Quick Start

One-Command Docker Setup

docker build -t sigma-model . && docker run --rm -it sigma-model python scripts/mre_sigma.py

Minimal Reproducible Example

pip install -e .
python scripts/mre_sigma.py

Expected output: ✅ ALL CHECKS PASSED (runtime ~0.5s CPU).

Run the Test Suite

PYTHONPATH=code:$PYTHONPATH pytest tests/ -q

Expected: 31 passed in ~2s.

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Abstract

The Σ-Model V3.0+ formalises AI agent knowledge development as a coupled dynamical system centered on schema coherence $\sigma_A(d,t)$ — the degree to which an agent's representations are restructured around deep governing principles rather than surface-statistical regularities.

Core Problem: Current training pipelines optimise parametric depth $\delta_A(d,t)$ without formally targeting schema coherence, producing agents that pass in-distribution evaluation while failing out-of-distribution recombination tasks.

Key Contributions:

• Formal ODE system for schema coherence dynamics (Eqs. 15–28)
• Five-phase training arc with measurable transition conditions (Prop. 3.2–3.4)
• Nine falsifiable predictions distinguishable from depth-only accounts (§9)
• Executable benchmark families for all cognitive faculties (§10)

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Reproducing Results

Hardware Requirements

• Minimum: 16GB RAM, 4 CPU cores
• Recommended: 32GB RAM, 8 CPU cores, GPU (NVIDIA RTX 3080+ or equivalent)
• Benchmark execution: ~2–4 hours on recommended hardware

See HARDWARE.md for detailed specifications and VRAM audit.

Setup

# Create virtual environment (Python ≥3.12)
python -m venv venv && source venv/bin/activate

# Install with dev dependencies
pip install -e ".[dev]"

Validation Experiments

# ODE validation experiment (canonical notebook)
cd experiments
jupyter nbconvert --to notebook --execute h-bar-experiment.ipynb

# Cognitive evaluation benchmark suite
jupyter nbconvert --to notebook --execute h-bar-v3-cognitive-evaluation-benchmark-suite.ipynb

Smoke Test

PYTHONPATH=code:$PYTHONPATH python scripts/smoke_test.py

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Repository Structure

Path	Contents
paper/manuscript.tex	Main manuscript (tmlr, 48 pages)
code/sigma/	Python package (ODE, models, config, benchmarks)
experiments/	Jupyter notebooks and YAML configs
scripts/	Smoke test, MRE, reproducibility scripts
hackathon/	Track definitions and dataset archives
docs/	Claims registry, issue register
tests/	Pytest test suite (31 tests)

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Citation

@misc{basyirin-amsyar2026sigma,
  title={The {$\Sigma$}-Model: Schema-Coherence Suppression as the Origin of
         Compositional Generalisation Failure},
  author={{Basyirin Amsyar Basri}},
  howpublished={Preprint},
  doi={10.5281/zenodo.20714248},
  year={2026}
}

License

MIT