Research-Stack/4-Infrastructure/shim/VERIFICATION_PROTOCOL.md

F01-F12 Verification Protocol

Layer 1: Mathematical Verification (Wolfram Alpha)

Every equation verified against Wolfram Alpha:

Input: 121.567 * 65536
Wolfram: 7,967,421.952
Rounded: 7,967,422
Q16.16: 0x0079.9120

Required for each F01-F12:

• Closed-form solution where available
• Numerical test with 3+ input sets
• Edge cases (zero, infinity, singularities)
• Document Wolfram query in comment

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Layer 2: Computational Verification (Lean 4)

Every def requires:

def encodeWavelength (λ : Q16_16) : Q16_16 := ...

#eval encodeWavelength (Q16_16.ofFloat 121.567)
-- Expected: 0x0079.9120
-- Wolfram verified: 121.567 * 65536 = 7,967,422

Every def requires theorem:

theorem encodeWavelength_total (λ : Q16_16) : 
  ∃ result, encodeWavelength λ = result := by 
  simp [encodeWavelength]

Build must pass:

cd 0-Core-Formalism/lean/Semantics && lake build

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Layer 3: Determinism Verification

Test: Same inputs → Same outputs (always)

def test_determinism():
    for i in range(1000):
        result = f01_encode(121.567)
        assert result == 0x0079.9120

Failure modes:

• Non-deterministic: Reject
• Undefined behavior: Reject
• Platform-dependent: Reject

---

Layer 4: Symbolic Stripping Verification

Test: Remove all semantic content, verify computation

Original: encode_hydrogen_wavelength(λ)
Stripped: N_7 = floor(N_0 * 65536 + 32768) / 65536

Test: N_0 = 121.567 → N_7 = 0x0079.9120
Pass: Computation identical with/without names

Required: 100% pass rate on adversarial stripping test.

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Layer 5: Property-Based Testing

QuickCheck-style random testing:

theorem encode_roundtrip (λ : Q16_16) (h : λ ≥ 0) :
  |decode (encode λ) - λ| < 0.0001 := by 
  -- Property: encode then decode ≈ original

Test properties:

• Roundtrip (encode→decode ≈ original)
• Monotonicity (x < y → f(x) < f(y))
• Boundedness (output in valid range)
• Idempotence (f(f(x)) = f(x) where applicable)

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Layer 6: Cross-Implementation Verification

Two independent implementations:

1. Lean 4 (canonical): 0-Core-Formalism/lean/Semantics/
2. Python (reference): 4-Infrastructure/shim/validation/

Verify bit-identical outputs:

def test_cross_impl():
    for input_val in test_vectors:
        lean_result = lean_call(input_val)
        py_result = python_call(input_val)
        assert lean_result == py_result  # Bit-identical

---

Layer 7: Statistical Verification (6.5σ)

For claims with statistical component:

Claim: Compression ratio > baseline
Test: 1000 random inputs
Mean: μ, Std: σ
Achieved: x = 6.5σ above baseline?
Required: Yes for 6.5σ claim

Standard: 6.5σ = 99.999999992% confidence
Minimum: 5σ = 99.9999427% confidence
Below 5σ: REJECT

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Verification Checklist per FXX

Layer	Test	Pass Criteria	Status
1	Wolfram Alpha	3+ numerical cases verified	☐
2	Lean #eval	All public functions have #eval	☐
3	Totality theorem	Every def has totality proof	☐
4	Determinism	1000 iterations, identical outputs	☐
5	Symbolic stripping	Passes adversarial test	☐
6	Property tests	Roundtrip, monotonicity, bounds	☐
7	Cross-impl	Bit-identical with Python shim	☐
8	Statistical	6.5σ where applicable	☐
9	Lake build	lake build passes	☐
10	No sorry	Zero sorry in code	☐

All 10 must pass for VALIDATED status.

---

Automated Verification Script

#!/bin/bash
# verify_fxx.sh

FXX=$1

echo "Verifying $FXX..."

# Layer 2: Lean build
cd 0-Core-Formalism/lean/Semantics
if ! lake build; then
    echo "FAIL: lake build"
    exit 1
fi

# Layer 4: Adversarial stripping
if ! python3 4-Infrastructure/shim/adversarial_symbolic_stripping.py --test $FXX; then
    echo "FAIL: symbolic stripping"
    exit 1
fi

# Layer 6: Cross-implementation
if ! python3 4-Infrastructure/shim/cross_verify.py --lean $FXX; then
    echo "FAIL: cross-implementation"
    exit 1
fi

echo "PASS: $FXX verified"

---

Best Verification: Compositional

Verify components, compose to system:

F01 verified + F02 verified + ... + F12 verified
    ↓
Compose: F01∘F02∘...∘F12
    ↓
Verify composition: Master equation

Do not: Verify only final output
Do: Verify each FXX independently, then verify composition

---

Summary

Best verification = 10-layer compositional checking:

1. Wolfram Alpha (math)
2. Lean #eval (compute)
3. Totality theorems (total functions)
4. Determinism (1000 iterations)
5. Symbolic stripping (no semantic deps)
6. Property-based (random testing)
7. Cross-implementation (bit-identical)
8. Statistical (6.5σ)
9. Lake build (compiles)
10. No sorry (proven correct)

10/10 required for publication.

Current F01-F12 status: 0/10

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Document ID: VERIFICATION-PROTOCOL-2026-05-06
Standard: 10-layer compositional verification
Target: 100% pass rate for all F01-F12
Current: 0% — blocked on F01-F12 formalization