Sovereign MOHAWK Protocol V2.1.0

The formal verification architecture of Sovereign Mohawk treats formal methods not as a marketing claim, but as a first-order engineering scalpel applied strictly to proof-critical infrastructure bounds12. Rather than attempting full-program verification, the protocol targets four core domains where undefined behavior or specification bugs lead to catastrophic failure: consensus safety, differential privacy accounting, cryptographic handshakes, and ledger transaction state2more_horiz.1. Lean 4 Formalization Architecture & IntegrityThe Lean 4 proof suite serves as the mathematical source of truth across proofs/LeanFormalization.lean and the proofs/LeanFormalization/ theorem modules5. Zero Placeholder Baselines: The proof tree across proofs/LeanFormalization, proofs/Specification, and proofs/Refinement contains zero sorry placeholders6. The only eight remaining non-proven statements are documented, CI-allowlisted IEEE-754 non-NaN comparison facts in proofs/Refinement/MultiKrum.lean6. Zero Compiler Warnings: Release v2.1.0 resolved all compiler warnings, including exponentiation threshold adjustments and simpa tactic hints7. Claim Traceability: Every protocol assertion is indexed in proofs/FORMAL_TRACEABILITY_MATRIX.md, mapping 15 distinct protocol claims to their Lean module, runtime test evidence, and formal status5. CI Proof Gate: Automated proof validation is enforced on every pull request via .github/workflows/full-validation-pr-gate.yml (full-validation-fast), which compiles the full Lean suite and executes vacuous-theorem lints before merges to main5. Theorem 1 (BFT Resilience): Formally machine-checks the honest-majority composition and a concrete 5/9 profile guard check in proofs/LeanFormalization/Theorem1BFT.lean89. Theorem 4 (Liveness & Straggler Resilience): Models redundant update paths and liveness guards under network stragglers in proofs/LeanFormalization/Theorem4Liveness.lean9. Computable RDP → $(\varepsilon, \delta)$-DP Conversion: Resolves non-computable real logarithm dependencies by implementing a computable two-sided rational bound on $\ln(x)$ in proofs/Refinement/RDPLogBound.lean6. This ensures differential privacy composition bounds are calculated deterministically without floating-point ambiguity6. TransferWithControls Parity: The Lean transferSpec model incorporates absent-account and insufficient-balance guards matching Go's runtime implementation7. Groth16/BN254 Verification: Circuit-derived Groth16 SNARK verification is wired directly into the C-shared Go bridge (pyapi) and hybrid verification pipeline6. Eliminating "Proofs of a Fiction": A formal proof of an abstract algorithm is meaningless if the underlying language runtime exhibits memory corruption10. By pairing a memory-safe Rust/Go execution layer with Lean 4 specifications, the protocol ensures runtime state matches verified mathematical models611. Targeted Proof Scope ("Scalpel over Sledgehammer"): Verification effort is concentrated exclusively on invariants where failure causes systemic risk—preventing two honest nodes from committing conflicting states or preventing privacy budget leakage across federated rounds2more_horiz. Performance tuning and business logic are tested via benchmarks and property tests instead12. Trace Validation & Structural Replay: Through Lean structural replay validators and Go correspondence models (MultiKrum, RDPAccountant, Ledger, Transport), real execution traces generated during runtime are validated directly against Lean structural rules612. Preventing Claim Drift: Machine-checked CI gates replace static, unverified academic papers with living, automated build gates5. Any pull request introducing a proof gap or vacuous