Date: 2026-05-20 | Session: DS6a | Status: SPECIFIED — BUILD QUEUED
Use the Lean 4 compiler from WSL2 Ubuntu to formally verify the mathematical claims in the Proving Ground submissions, then wire the compiled proof artifacts into the HTML as cryptographically verifiable evidence.
# Install Lean 4
wget -q https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh
bash elan-init.sh -y
source ~/.bashrc
# Verify installation
lean --version
# Create a test proof and compile
echo 'theorem t : True := by trivial' > test.lean
lean test.lean
# Should output nothing (success) or error if failed
# Compile the OE Lean4 proofs
cd /home/idor/oe-local/lean4
lake build
Integration Points
1. Compile OE's Existing Lean4 Proofs
lean4/Axioms/Peano.lean — 6 theorems
lean4/Axioms/NumberTheory.lean — 9 theorems
lean4/SAL/Yoneda.lean — 1 theorem
lean4/SAL/Basic.lean — Adjoint Triple definitions
Output: .olean compiled binaries + verification status
Wire into HTML: each proof shows "✅ Verified by Lean 4 kernel" or "❌ Failed" with error message
2. Compile AI-Submitted Lean4 Proofs
Each AI submission includes Lean4 proof files
Extract the Lean4 code from submissions
Compile via lean command
Capture output: success (exit 0) or failure with error lines
Wire into convergence table as verifiable column
3. Proof Hash Anchoring
SHA-256 hash of each .lean source file
SHA-256 hash of compiled .olean binary
Both hashes embedded in HTML
Any auditor can recompile and verify hashes match
4. Glass-Box Auditor Integration
Gate 4 auditor currently runs in JavaScript (simulated checks)
With Lean4 compiler available, auditor can perform REAL formal verification
Check: does the submitted Lean4 proof actually compile?
Check: does the compiled proof establish the claimed theorem?
Output: Tuple[bool, ProofObject] with compiler exit code and hash
5. Proving Ground Submission Validation
When an AI submits Lean4 code, validate it through the compiler
If compilation fails, submission is rejected (falsifies_if triggered)
Compiler output becomes part of the audit trail
HTML Wiring
Each Lean4 proof in the convergence table gets a "Compile" button
Button triggers a visual indicator: "Compiling..." → "✅ Verified" or "❌ Failed: [error]"
Compiled proofs get a green border. Uncompiled proofs get a yellow border.
SHA-256 of source and compiled binary displayed
Dependencies
WSL2 Ubuntu with Lean 4 installed via elan
OE repo Lean4 files in lean4/ directory
AI-submitted Lean4 code extracted from Proving Ground submissions
*Checkpoint: 2026-05-20 — Session DS6a*
Prior: Proving Ground HTML deployed. ChatGPT Row 1. Live tools queued.
Next: Install Lean4 in WSL2. Compile OE proofs. Wire compiler output into HTML.
---
## Gemini Engineering Review (Added 2026-05-20)
### Critical Compiler Behaviors Identified
1. **Import Path Management:** Standalone `lean file.lean` fails if code imports Mathlib or external dependencies. Fix: require pure Core/Init proofs for standalone gates, or use `lake env lean` from within Lake project directory.
2. **Error Stream Capture:** Lean 4 outputs errors to stdout (not stderr) while still returning exit code 1. Fix: capture both streams:
```bash
lean submission_gate1.lean > compile_output.log 2>&1
STATUS=$?
Browser Sandbox Bridge: HTML/JS cannot execute local shell commands. Fix: lightweight Python server (Flask/FastAPI) on localhost:5000. HTML sends fetch request, Python writes temp file, calls lean, returns JSON response with compiler output.
Strengths Confirmed
Visual Compile State Matrix (Yellow/Green/Red borders) approved
Double-Hash Anchoring (.lean + .olean) approved as exceptional security
Core Math Validation (Peano, NumberTheory, Yoneda) approved as foundational
Overall spec rated "Production-Grade Execution"
Build Requirements Updated
Python-to-WSL bridge script needed for HTML "Compile" button
Flask/FastAPI server bound to localhost:5000
Lake project initialization for dependency management
Stdout+stderr capture for error parsing
*Engineering review by Gemini, 2026-05-20. Build cleared for DS6a execution.*