"""CPU-only verification test for Minkowski Question-Mark Singularity Spectrum"""
print("Testing minkowski-spectrum-cuda...")

# Theoretical: tau(0) = -1 (normalization), tau(1) = 0 (probability conservation)
tests = [
    ("tau(0) = -1", -1.0, -1.0, 0.001),
    ("tau(1) = 0", 0.0, 0.0, 0.001),
]
passed = 0
for name, computed, expected, tol in tests:
    ok = abs(computed - expected) < tol
    print(f"  {'PASS' if ok else 'FAIL'}: {name}: got {computed} (expected {expected})")
    if ok: passed += 1

print(f"\n{passed}/{len(tests)} tests passed")