Prime Phase Interference Spectroscopy of Riemann Zeros: Multiscale Interaction Hierarchy, N-Body Decoupling, and Spectral Rigidity

### OverviewThis release provides the complete manuscript, numerical execution pipelines, raw observation datasets, and high-resolution diagnostic plots for the Prime Phase Interference Spectroscopy of Riemann zeros. By mapping prime numbers to unitary logarithmic oscillators (omega_p = ln p), the squared modulus of the prime Dirichlet series resolves into an invariant ground-state self-energy baseline P(2) = sum p^{-2} approx 0.452247 and an off-diagonal pairwise cross-coupling lattice M_{pq}(t) = 2/(pq) * cos(t ln(p/q)). This research reframes non-trivial Riemann zeros along Re(s)=1/2 as microscopic resonance nodes and establishes a bottom-up effective field theory framework for prime phase dynamics. --- ### Key Numerical & Theoretical Findings1. Infrared Potential Basin & Heavyweight Monopoly: Surveying 499,500 prime pairs across the first 200 Riemann zeros reveals that prime pairs p, q <= 7 account for 85.50% of Rank-1 destructive leaders, driven by the hyperbolic amplitude envelope A_{pq} = 2/(pq).2. Macroscopic Resonance Trenches (Selberg Corridor): Grounded in Selberg's central limit approximation ln|zeta(1/2+it)| approx -sum p^{-1/2} cos(t ln p), an unconstrained 1-body projection autonomously generates deep phase suppression trenches (< -2.2) spanning the critical zero coordinates.3. Dynamic Dephasing & GUE Level Repulsion: The analytical dephasing cycle Delta t_{cycle} = pi / |ln(q/p)| accounts for an empirical 67.84% hegemony switching rate between consecutive zeros. As zero spacing narrows, coupling to high-frequency modes (q >> p) scales as pi / ln q, providing a dynamical foundation for Montgomery-Odlyzko level repulsion.4. Composite-Prime Harmonic Couplings (pq vs. r): Quadratic composite harmonics operate as dense secondary phase tuners, producing near-perfect anti-phase alignments (cos approx -0.995) against low-lying prime bases.5. Exact N-Body Algebraic Bound & 5-Body EFT Decoupling: Generating polynomial convolutions over 100 primes establish that N-body phase entanglement decays strictly as prod p^{-1/2}, plunging to 1.4568e-110 at order k=100. Interaction orders k <= 5 saturate 99.8718% of total coupling energy, validating truncation to an effective 5-body field theory.6. Macro-Baseline Calibration: High-precision calibration using the classical Riemann-Siegel formula Z(t) verifies zero coordinates with a mean absolute error of 3.2932e-04 (O(t^{-3/4}) boundary residual decay), enabling unbiased microscopic phase profiling. --- ### Execution & ReproducibilityAll numerical scripts are written in standard Python 3.Requirements: numpy, scipy, matplotlib, mpmath, pandas Run sequence:- python k_protocol_master.py- python prime_resonance_radar.py- python k_protocol_spectral_profiler.py- python k_protocol_100th_zero_nbody.py Repository: https://github.com/CitizenKorea/k-protocol-riemann-zeros