Proving Sovereign Mohawk with Lean4

1. Architectural Foundation: Eliminating "Proofs of a Fiction"A formal proof of an abstract algorithm is meaningless if the underlying runtime exhibits memory corruption or undefined behavior4. If a runtime contains a use-after-free or a data race, the system's mathematical proofs end up proving properties of a fiction4.Sovereign Mohawk addresses this by coupling machine-checked proofs with a memory-safe execution stack56: Memory Safety by Construction: Rust components eliminate buffer overflows, null pointer dereferences, and data races in the hot path without garbage collection pauses56. Data Isolation: In federated learning, a data race in the gradient aggregation layer can cause client gradients to bleed into another client's update—a privacy violation that no amount of differential privacy can retroactively fix56. Bounded Primitives: Lock-free SPSC (single-producer, single-consumer) ring buffers provide allocation-free, bounded communication between inference stages6more_horiz. Zero sorry Baseline: The proof tree across all Lean modules contains zero sorry placeholders910. The eight remaining non-proven statements in proofs/Refinement/MultiKrum.lean are documented, CI-allowlisted IEEE-754 non-NaN comparison facts rather than open proof gaps910. Zero Compiler Warnings: The v2.1.0 release eliminated all compiler warnings, resolving exponentiation threshold bounds and simpa tactic hints11. Proof Tree Sanitization: Draft or unsound proofs were quarantined in proofs/quarantined/ with explanatory READMEs detailing why each draft failed its claims, while unclaimed or vacuous files (e.g., Specification/Byzantine.lean, Theorem2RDP_Enhanced) were completely removed10. Theorem 1 (BFT Resilience): Formally models honest-majority composition and machine-checks a concrete 5/9 profile guard check in proofs/LeanFormalization/Theorem1BFT.lean12more_horiz. Theorem 4 (Straggler Liveness): Models redundancy paths and liveness guards under network stragglers in proofs/LeanFormalization/Theorem4Liveness.lean1314. Computable RDP → $(\varepsilon, \delta)$-DP Conversion: Closed issue #174 in proofs/Refinement/RDPLogBound.lean by constructing a computable two-sided rational bound on $\ln(x)$10. This removes the dependency on non-computable real logarithms, ensuring Rényi Differential Privacy (RDP) budget composition is calculated deterministically at runtime without floating-point ambiguity10. TransferWithControls Ledger Parity: Updated Lean’s transferSpec formalization to explicitly model absent-account and insufficient-balance guards, achieving 1:1 specification parity with Go’s runtime implementation11. Groth16/BN254 Circuit Verification: Wired real circuit-derived Groth16 BN254 SNARK verification into pyapi C-shared bridge exports (VerifyZKProof, BatchVerifyProofs) and the hybrid verification engine10. Correspondence Models: Located in proofs/Refinement/, formal models establish structural equivalence between abstract Lean specifications and Go runtime logic for MultiKrum, RDPAccountant, Ledger, and Transport10. Trace Replay & Validation: Execution traces generated by the Go node agent are validated against Lean structural rules via dedicated trace validators for RDPAccountant and HierarchicalBFT alongside a Lean structural replay validator1015. Traceability Matrix: All 15 protocol claims are indexed in proofs/FORMAL_TRACEABILITY_MATRIX.md, mapping each claim to its Lean module, runtime test evidence, and verification status914. Mandatory CI Proof Gate: Merges to main require a green build from .github/workflows/full-validation-pr-gate.yml (full-validation-fast), which compiles the entire Lean 4 proof