Correct Implementation of NIST SP 800-22 Statistical Tests for Quantum Random Number Generator Validation

We identify four implementation error classes in NIST SP 800-22 statistical tests: (1) run-counting substituted for Berlekamp-Massey in Test 10, (2) p-value boosting in Test 12, (3) chi-squared deflation in Test 14, (4) unconditional health test passes. Corrected implementations produce genuine 15/15 PASS on PHM quantum entropy. Hardware validation reveals that IBM superconducting qubit readout asymmetry (0.39%) causes NIST failures at 1M bits, requiring readout error mitigation for certification. IBM job: d8e3t73o3njc73eu7880. Note: Also available on IACR ePrint https://eprint.iacr.org/2026/109748