Post-Quantum Consensus meets First-Order Logic Proving
Paraxiom × ModulusZK Partnership Discussion
ModulusZK's arithmetization — how logic becomes math
Based on Dr. Murdoch Gabbay's polynomial semantics. A predicate compiles to a polynomial — verification = evaluate at random point, check if zero.
Key insight: FOL is the arithmetization. The polynomial commitment scheme underneath determines quantum resistance.
We use Winterfell STARKs — hash-based, quantum-resistant
FRI Commitments Hash-based No trusted setup
Consensus upgrades automatically as quantum hardware becomes available
Note: SPHINCS+ is a signature algorithm (Level 2+), not the consensus itself. Proof of Coherence is the consensus mechanism.
Clear separation of concerns in the post-quantum architecture
| Algorithm | Type | Purpose | Quantum Safe |
|---|---|---|---|
| SPHINCS+ | Hash-based signature | Validator account signatures (extrinsics) | ✓ Yes |
| Falcon1024 | Lattice-based signature | Coherence vote signing (finality gadget) | ✓ Yes |
| Winterfell STARKs | Hash-based ZK proof | Quantum measurement verification | ✓ Yes |
| Triple Ratchet | Key agreement protocol | Encrypted P2P vote broadcasting | ✓ Yes |
| BLAKE3 / SHA-3 | Hash function | Commitments, Merkle trees, FRI | ✓ Yes |
The entire stack is post-quantum secure — no elliptic curve dependencies in the critical path.
Each quantum entropy share carries a STARK proof of measurement authenticity
A stateful adversarial testing framework for consensus systems
Multi-epoch test scenarios with network partitions, Byzantine validators, timing attacks, entropy manipulation
WASM runtime coverage, consensus state machine edges, STARK verifier branches, economic paths
Safety (no double-finalize), Liveness (bounded progress), Compliance (proof acceptance), PoC (coherence)
Deterministic sandbox, seedable PRNG, virtual clock, snapshot rollback — minimal repro traces
Key question: Can FOL proofs integrate with our existing Winterfell-based verification pipeline, or do they require a separate verifier?
FOL is the arithmetization. The polynomial commitment scheme determines quantum resistance.
| Commitment Scheme | Based On | Quantum Safe? |
|---|---|---|
| KZG | Elliptic curve pairings | No |
| FRI (what we use) | Hash functions | Yes |
| IPA / Bulletproofs | Elliptic curves | No |
"FOL is your arithmetization. What polynomial commitment scheme sits underneath — hash-based like FRI, or curve-based like KZG?"
"Can your proofs integrate with Winterfell verification, or do we need a custom FOL verifier pallet?"
"Your Polkadot support — parachain-level or direct Substrate solo chain integration?"
"How does Layer X relate to L1 finality? Proof coordination, or its own settlement?"
Q1 determines everything. If curve-based, it contradicts our post-quantum thesis.
| Model | Structure | When to Use |
|---|---|---|
| Model A | ModulusZK as Proof Provider | They generate compliance proofs, we verify through STARK gate |
| Model B | CCAE as Service | We run their proof system through CCAE, deliver threat model + regression suite |
| Model C | Joint Ecosystem Grant | Polkadot Treasury or other ecosystem funding |
| Model D | Strategic Alignment | Token swap or equity arrangement for long-term integration |
Current stage: Technical scoping first, then determine which structure creates real value for both sides.
Clarify polynomial commitment scheme — hash-based (compatible) or curve-based (incompatible with our thesis)
Share proof format documentation to assess Winterfell integration path
Sample proofs to run through CCAE harness for initial coverage analysis
Define specific compliance predicates to target (policy proofs, audit attestations)
Contact: sylvain@paraxiom.org