Paraxiom Research

Coherence-preserving architectures for distributed intelligence

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Mission

Paraxiom develops theoretical foundations and practical implementations for coherence-preserving distributed systems. Our work bridges mathematical physics, machine learning, and distributed consensus to create architectures that maintain internal consistency under adversarial conditions.

Research Areas

• Hamiltonian Machine Learning — Geometric constraints for stable AI reasoning
• Post-Quantum Cryptography — SPHINCS+ signatures for quantum-resistant infrastructure
• Distributed Consensus — Physics-based alternatives to game-theoretic mechanisms
• Spectral Graph Theory — Efficient algorithms on structured topologies

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Publications (December 2025)

Paper	Topic	DOI
ERLHS	Hamiltonian framework for coherence-preserving ML	10.5281/zenodo.17928909
Karmonic Mesh	O(N log N) spectral consensus on toroidal manifolds	10.5281/zenodo.17928991
Proof of Coherence	QKD-based distributed consensus mechanism	10.5281/zenodo.17929054
Toroidal Mesh	10K TPS with SPHINCS+ via parallel verification	10.5281/zenodo.17931222
Toroidal Governance	Defensive publication — Tonnetz manifold governance	10.5281/zenodo.17929091
Augmented Democracy	Coherence-constrained democratic infrastructure with epistemic gates	Preprint
Conservation-Constrained Aggregation	Doubly-stochastic normalization for distributed trust networks	Technical Note

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Implementation

The QuantumHarmony blockchain implements concepts from these papers:

• SPHINCS+-256s post-quantum transaction signatures
• Coherence-based validator selection
• Distributed proof-of-coherence consensus

Testnet Status: Running (Alice, Bob, Charlie validators)

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Citation

@misc{cormier2025erlhs,
  author    = {Cormier, Sylvain},
  title     = {ERLHS: A Hamiltonian Framework for Coherence-Preserving Machine Intelligence},
  year      = {2025},
  doi       = {10.5281/zenodo.17928909},
  publisher = {Zenodo}
}

@misc{cormier2025karmonic,
  author    = {Cormier, Sylvain},
  title     = {Karmonic Mesh: Spectral Consensus on Toroidal Manifolds},
  year      = {2025},
  doi       = {10.5281/zenodo.17928991},
  publisher = {Zenodo}
}

@misc{cormier2025poc,
  author    = {Cormier, Sylvain},
  title     = {Proof of Coherence: QKD-Based Distributed Consensus},
  year      = {2025},
  doi       = {10.5281/zenodo.17929054},
  publisher = {Zenodo}
}

@misc{cormier2025augmented,
  author    = {Cormier, Sylvain},
  title     = {Augmented Democracy as a Coherence-Constrained Control System},
  year      = {2025},
  note      = {Preprint},
  publisher = {Paraxiom Research}
}

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Contact

Sylvain Cormier Paraxiom Research sylvain@paraxiom.org

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_{All publications are timestamped via Zenodo DOI for prior art establishment.}