Post-Quantum Consensus meets First-Order Logic Proving
Paraxiom × ModulusZK Partnership Discussion
ModulusZK's core innovation: skip the circuit compilation step
Based on Dr. Murdoch Gabbay's polynomial semantics for first-order logic. Complex predicates compile to a single polynomial — verification reduces to evaluating at a random point.
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 (valid proof acceptance), PoC (coherence bounds)
Deterministic sandbox with seedable PRNG, virtual clock, snapshot rollback — minimal repro traces
ModulusZK proofs pass through our STARK gate. Our CCAE harness provides adversarial hardening — coverage feedback they likely don't have internally.
Coverage signals on their proof system running through our consensus
| Signal Class | What We Track | Value |
|---|---|---|
| Verifier Branch Coverage | Which code paths proofs hit during verification | Find edge cases |
| Constraint-Family Hits | C_transition, C_boundary, C_permutation activation | Ensure full coverage |
| Proof Morphology | Size buckets, query counts, FRI depth, transcript length | Guide toward "weird but valid" |
| End-to-End Gating | precheck → verifier → finality pipeline behavior | Find consensus exploits |
Their proofs get hardened by running through our adversarial harness under Byzantine conditions.
Is FOL arithmetization based on hash functions (STARK-like, quantum-safe) or elliptic curves (SNARK-like, quantum-vulnerable)?
Can ModulusZK proofs pass through a STARK-compatible verification gate, or do they require a custom verifier?
Polkadot support — native parachain integration or external bridge? We run Substrate directly.
How does Layer X interact with our finality layer? Does it complement or compete?
| 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 FOL quantum resistance, verification interface compatibility, Substrate integration path
Share proof format documentation to assess STARK gate compatibility
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