Five peer-reviewed preprints on Prime Harmonic Modulation — connecting quantum cryptography to the Riemann zeta function, prime gap theory, and IBM Quantum hardware validation.
Establishes that PHM wavefunction amplitude coefficients A_p = 1/√p are the Dirichlet series coefficients of the Riemann zeta function evaluated on the critical line Re(s) = 1/2. Proves normalizability boundary at the critical line. States the PHM-GUE conjecture with numerical evidence from N=500 and N=2000 prime spectra.
Proves the first closed-form security parameter for PHM QKD: F_k = cos²(πg_k / 2p_kp_{k+1}), where g_k is the prime gap. Under the Cramér conjecture, adversary advantage vanishes superpolynomially. The adaptive prime ladder provides post-quantum forward secrecy independent of computational hardness assumptions.
PHM energy levels E_p = p²·Ry, fitted with a single scale factor, match 84% of atomic spectral transitions across H, He, Li, C, N, O, Na, Fe, and Xe from the NIST Atomic Spectra Database. He, C, Na, and Xe achieve 100% match within 10% relative error. The value E_{p=1} = 13.6 eV equals the hydrogen ionization energy exactly.
Identifies four implementation error classes in NIST SP 800-22 tests. Corrected implementations produce genuine 15/15 PASS on PHM quantum entropy. IBM hardware validation on 1,048,576 real quantum bits reveals systematic readout asymmetry (0.39%) requiring mitigation for QRNG certification.
First experimental confirmation of F_k = cos²(πg_k/2p_kp_{k+1}) on real IBM quantum hardware. Single-qubit state tomography on IBM Fez confirms the formula within 2.49% for all 6 patent primes. Bloch angles match π/p within 0.66° mean error. Six IBM Quantum jobs executed with publicly verifiable job IDs.
All experiments executed May 31, 2026. Job IDs publicly verifiable at quantum.ibm.com
1,048,576 bits generated — Shannon H = 0.9999
PCT/US25/39370 · Filed July 2025 · Attorney: Todd E. Zenger
4 U.S. provisional priority dates (Feb–Mar 2025) · Covers PB-QKD, PB-QFT, PB-QEC, Prime Hamiltonians, Symbolic IR
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