Self-bootstrapping mathematical civilization via MDL compression

A society of agents that, under compression pressure alone, discovers mathematical structure, verifies self-modifications through a cryptographic proof market, and derives the Chinese Remainder Theorem without being told what it is.

Mathematical structure (modular arithmetic, the Chinese Remainder Theorem) emerges from compression pressure. Agents are never shown the rules. MDL pressure causes them to discover the rules because the rules are the shortest description of the data.

git clone <repo>
cd ouroboros_project
python3 -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt && pip install -e .

# Full pipeline: ~30 minutes
python scripts/run_full_pipeline.py

# Quick test: ~3 minutes
python scripts/run_full_pipeline.py --quick

# Individual phases
python experiments/phase1/landmark_experiment.py    # Figure 1
python experiments/phase2/self_modification_experiment.py
python experiments/phase3/crt_landmark_experiment.py  # The CRT result

Phase 1: MDL Compression ObservationEnvironment → SynthesisAgent (BeamSearch + MCMC) → ProtoAxiomPool (consensus) → Proto-Axiom AX_00001 Phase 2: Proof Market SelfModifyingAgent → ProofMarket (commit-reveal) → OODPressure → Approved modifications → Convergence in ~8 rounds Phase 3: Causal Theory TheoryAgent (multi-scale) → CausalTheory → JointEnvironment → CRT landmark experiment

1. Mathematical Structure Emergence in MDL-Optimal Agent Societies → docs/papers/paper1_mathematical_emergence.md Target: NeurIPS / ICLR

2. Adversarial Self-Modification via Commit-Reveal Proof Markets → docs/papers/paper2_proof_market.md Target: ICML / NeurIPS

ouroboros/ ├── core/ config, phase1_runner, phase2_runner, phase3_runner ├── environment/ 6 observation environments + joint_environment ├── compression/ MDL engine, beam search, MCMC, hierarchical MDL ├── agents/ BaseAgent → SynthesisAgent → HierarchicalAgent │ → TheoryAgent → SelfModifyingAgent ├── proof_market/ commit_reveal, counterexample, market, ood_pressure └── emergence/ proto_axiom_pool, scale_axiom_pool, causal_theory, crt_detector

• Rissanen, J. (1978). Modeling by shortest data description.
• Schmidhuber, J. (2003). Gödel machines: Fully self-referential optimal agents.
• Grünwald, P. (2007). The Minimum Description Length Principle.
• Hoel, E.P. et al. (2013). Quantifying causal emergence.
• Li, M. & Vitányi, P. (1997). An Introduction to Kolmogorov Complexity.