Research initiative based in Vancouver, BC, investigating the mathematical foundations of quantum mechanics and the questions they raise about physical reality.
Website: pacific-quantum-systems.com
Algebraic classification of Kochen-Specker sets in dimension three. Our central result is that generator norm ≤ 2 controls KS-uncolorability — the integer identity 1+1=2, the Peres identity (√2)²=2, and the Eisenstein identity 1+ω+ω²=0 are all manifestations of the same algebraic constraint. Six constructions from algebraic number rings have been identified, including two genuinely new KS sets (Heegner-7 and Golden ratio) not in any prior catalogue.
Tracking the transition to quantum-resistant algorithms. Coverage of NIST standards (ML-DSA/FIPS 204, ML-KEM/FIPS 203, SLH-DSA/FIPS 205), lattice-based cryptography, and blockchain integration — particularly Tezos tz5 addresses based on ML-DSA (Dilithium).
Quantum key distribution protocols (BB84, E91, CV-QKD), the Canadian quantum communications landscape (NRC QUIN, Photonic Inc., TELUS, SFU Q-Van Lab, QEYSSat), and the classical-quantum software interface enabling secure network infrastructure.
Computational methods — SAT solvers, graph algorithms, algebraic search, and integer linear programming — serve as instruments for foundational discovery. Key tools: Python, PySAT (Glucose4), NumPy/SciPy, CVXPY, NetworkX.
| Year | Title | Venue |
|---|---|---|
| 2026 | The Algebraic Landscape of Kochen-Specker Sets in Dimension Three | In preparation (PRA) |
| 2026 | New KS Sets from Algebraic Number Fields with Enhanced Contextual Advantage | In preparation (PRL) |
| 2026 | Graph Universality of CK-31 and the Norm-2 Boundary | In preparation (PRL) |
| 1995 | Kochen-Specker theorem for eight-dimensional space | Phys. Lett. A 198, 1-5 |
| 1994 | Bell-Kochen-Specker theorem for 20 vectors | J. Phys. A 27, L829 |
Static HTML/CSS site deployed on Netlify.
| Page | Content |
|---|---|
index.html |
Landing page with research pillar overview |
research.html |
Quantum contextuality research — six algebraic islands, graph universality, BPQS |
computational.html |
Computational methods — SAT solvers, graph algorithms, algebraic search, AI role |
pqc.html |
Post-quantum cryptography — NIST standards, lattice problems, Tezos tz5 |
quantum-comms.html |
Quantum communications — QKD protocols, Canadian landscape, standards |
about.html |
About PQS, Michael Kernaghan bio, publications, contact |
- Pure HTML + CSS (no JavaScript framework)
- Google Fonts: Inter + JetBrains Mono
- Responsive design with CSS Grid/Flexbox
- Deployed on Netlify
- Contextuality & KS Set Atlas — Companion research site with detailed KS set documentation
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