Three continents. Post-quantum. Live now.

AI your auditors
can trust.

Agent-agnostic trust infrastructure. Any agent, any model — every action signed, verified, and provable. Post-quantum security from day one.

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Published on
Zenodo crates.io PyPI HuggingFace GitHub
Architecture
Securing the trust chain from wire to decision.

One integrated architecture. Five layers. You deploy what you need.

TL

Transport Layer

Post-quantum encrypted communications. Drop-in replacements for SSH and TLS, plus a QKD-compatible transport gateway — all patent-free, all formally verified.

  • QSSH — quantum-safe SSH
  • QSSL — quantum-safe TLS
  • PQTG — post-quantum transport gateway
  • Satellite QKD integration
  • NIST-standardized algorithms
Complete
AL

Attestation Layer

AI governance that works. Coherence Shield sits between your platform and any LLM. Every response is signed, constrained, and attested on-chain. If the AI said it, there's a cryptographic receipt.

  • Coherence Shield — OpenAI-compatible proxy
  • Toroidal logit-bias for hallucination reduction
  • Falcon-512 post-quantum signatures
  • Immutable on-chain audit trail
  • Responsible AI governance
Deployed
IL

Inference Layer

Lightweight AI that runs at the edge. Ternary quantization, toroidal attention, and spectral filtering — 20x model compression, CPU-native, no cloud required.

  • SMDR — Sparse Meta Distributed Representations
  • 1.5 J per query (1300x more efficient than cloud)
  • Runs on battery-powered field hardware
  • Hallucination-resistant by design
  • Air-gappable, zero outbound traffic
Active R&D
CL

Consensus Layer

QuantumHarmony — a post-quantum Layer 1 blockchain purpose-built for attestation. Toroidal mesh topology. Byzantine fault tolerant. The immutable backbone behind every Paraxiom product.

  • SPHINCS+ post-quantum signatures
  • Proof of Coherence consensus
  • Multi-continent validator network
  • Self-healing resilient mesh
  • 649 formally verified theorems (Lean 4)
Live Network
AP

Application Layer

Drista — post-quantum encrypted field communications. Triple Ratchet forward secrecy, zero-knowledge message verification, designed for contested environments.

  • ML-KEM-1024 key exchange
  • PQ Triple Ratchet protocol
  • STARK zero-knowledge proofs
  • Forward secrecy on device capture
  • Runs on standard mobile devices
Complete
How It Works
Three steps to provable AI.

Deploy Coherence Shield in front of any LLM. No model changes required.

Connect your AI

Point your application at Coherence Shield instead of your LLM provider. OpenAI-compatible API — one line of code to switch.

Every response is signed

Each AI output is cryptographically signed with post-quantum algorithms and recorded on QuantumHarmony. Tamper-proof, timestamped, permanent.

Audit with confidence

Every response has a verifiable receipt. Regulators, auditors, and compliance teams get cryptographic proof of what the AI said and when.

Trust Architecture
Safe. Verified. Quantum-ready.

Every component is mathematically proven correct — not tested, proven. The same level of assurance as aircraft flight control software.

Mathematically Proven

Every critical component carries formal mathematical proofs of correctness. Not test coverage — total coverage. Every input, every edge case, every adversarial scenario.

Post-Quantum Security

All cryptography uses NIST-approved post-quantum algorithms. Your audit trail, signatures, and encryption survive the arrival of quantum computers. Patent-free.

On-Chain Attestation

Every AI response is Falcon-512 signed and recorded on QuantumHarmony — a formally verified, post-quantum L1. No classical crypto to break. No single point of failure. The audit trail survives quantum computers.

Solutions
Built for regulated industries.

Where AI accountability isn't optional.

Σ

Financial Services

Auditable AI for banking, insurance, and capital markets compliance.

Δ

Government & Defence

Sovereign AI infrastructure aligned with national defence strategies.

Ω

Healthcare

Verifiable AI outputs for clinical decision support and diagnostics.

Λ

Legal & Notarial

Quantum-safe document attestation and chain-of-custody proofs.

About
Founded in 2023. Built in Montréal.

Paraxiom Technologies Inc. was founded by Sylvain Cormier to build sovereign post-quantum trust infrastructure for Canada and its allies. 20+ years of engineering at the intersection of mathematics and systems. 649 formally verified theorems. Nine production systems. Zero compromises.

Sylvain Cormier

Sylvain Cormier

Founder

20+ years building systems that bridge mathematics and infrastructure. Every Paraxiom product is formally verified and running in production.

Pricing
Start free. Scale when ready.

Every product is open-source or API-accessible. Enterprise support when you need it.

Open Source

Free

MIT & Apache 2.0 licensed
  • QSSH — quantum-safe SSH
  • QSSL — quantum-safe TLS
  • PQ Transport Gateway
  • Drista — PQ encrypted chat
  • QuantumHarmony node
  • Toroidal Logit Bias
  • All Lean 4 formal proofs
View on GitHub
Hosted API

Usage-based

Pay per request. No minimums.
  • Coherence Shield API
  • TAO Signal data feeds
  • QuantumHarmony attestation
  • PQ-signed audit logs
  • 99.9% uptime SLA
Get API Access
Enterprise

Custom

Tailored to your infrastructure.
  • On-prem PQ infrastructure
  • QKD gateway integration
  • Migration & threat modelling
  • Custom Lean 4 verification
  • Private blockchain deployment
Contact Us
Open Source
Built in the open.

45 repositories, 18 peer-reviewed publications, formally verified with 649+ Lean 4 theorems.

QuantumHarmony

Post-quantum L1 blockchain. SPHINCS+ signatures, Proof of Coherence consensus, 950 tests.

Rust Lean 4

QSSH

Quantum-safe SSH replacement. Falcon + SPHINCS+ + ML-KEM, QKD-compatible. 132 tests.

Rust Lean 4

QSSL

Patent-free post-quantum TLS. 12 cipher suites, 100 formal theorems. 40 tests.

Rust Lean 4

PQ Transport Gateway

Post-quantum networking gateway. Transparent PQ upgrade for existing infrastructure.

Rust

toroidal-noise

Quantum noise channels with density matrix simulation. Spectral gap dephasing. 31 tests.

crates.io

pennylane-toroidal-noise

PennyLane plugin for toroidal dephasing channels. Gradient-compatible. 15 tests.

PyPI

Publications

Research on Zenodo. All defensively published as prior art.

TitleYearDOI
Post-Quantum Authentication for QKD Control Channels (PQTG) 2026 10.5281/zenodo.18786526
Toroidal Geometry of LLM Representations: Karmonic-Guided Alignment 2026 10.5281/zenodo.18746144
162 Lean 4 Theorems — Three-Tier Formal Verification (QTS, QSSH, QH) 2026 10.5281/zenodo.14805498
Topological Constraints for Coherent Language Models (v6, 23pp) 2026 10.5281/zenodo.14584587
Topological Coherence — Rust Implementation 2026 10.5281/zenodo.14805498
Defensive Technical Disclosure — 4 Embodiments 2026 10.5281/zenodo.18595753
Toroidal Logit Bias — Multi-Model TruthfulQA (+2.8pp) 2026 10.5281/zenodo.18516477
Prompt Injection as a Control Problem: Topological Constraints 2026 10.5281/zenodo.14805498
Decentralized Quantum Randomness: Kirk Network + PQ-VRFs 2026 10.5281/zenodo.14805498
Toroidal Mesh Topology for Post-Quantum Blockchain (v2) 2025 10.5281/zenodo.14805498
Augmented Democracy — Technical Appendices 2025 10.5281/zenodo.14805498
Augmented Democracy as a Coherence-Constrained Control System 2025 10.5281/zenodo.14805498
Toroidal Mesh Topology for Post-Quantum Blockchain 2025 10.5281/zenodo.14805498
Paraxiom Harmonic Toroidal Governance Layer (Defensive Patent) 2025 10.5281/zenodo.14805498
Proof of Coherence: QKD-Based Consensus Mechanism 2025 10.5281/zenodo.14805498
Karmonic Mesh: Spectral Foundations for Hyperfluid Consensus 2025 10.5281/zenodo.17928991
ERLHS: Hamiltonian Framework for Coherence-Preserving ML 2025 10.5281/zenodo.17928909
Quantum Nanotube Lattice Optics — CNT Arrays for QKD 2025 10.5281/zenodo.14805498
Integrate
Connect any agent in minutes.

OpenAI-compatible API. One line to switch. Your agent gets post-quantum signing and on-chain attestation automatically.

Discovery

Point your agent at /.well-known/agent.json to discover capabilities, endpoints, and attestation details.

Connect

Swap your LLM base URL to paraxiom.org/shield/ and add your bearer token. Standard OpenAI SDK works out of the box.

Verify

Every response comes with a Falcon-512 signature and an on-chain receipt on QuantumHarmony. Query the audit trail anytime.

Ready to make AI
accountable?

Deploy post-quantum AI trust infrastructure today.

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