On the Spectral Stability of the Riemann Zeta Function's Remainder Term: An Analysis of Von Koch's Estimate.

MokraBela Spectral Project (v2.0): High-Precision Analysis Major Update (April 18, 2026):This version (v2.0) provides a massive-scale numerical verification of the spectral framework. By analyzing 100,000 real Riemann zeros (sourced from Odlyzko's tables) at a scale of N = 2,000,000, we establish a high-precision analysis of von Koch's estimate (1901). The results confirm a stable energy density C ≈ 0.045 and a near-critical spectral decay law with an exponent α ≈ -0.94. Foundational Manuscript (v1.0):This manuscript, originally submitted for peer review on April 04, 2026, establishes a breakthrough in number theory by proposing a predictive spectral law for the summatory function of primes Ψ(K). For the first time, it introduces the scaling C(K) ~ K³/² √ln K, allowing for the prediction of prime sums fluctuations without prior knowledge of individual primes. This work serves as the precursor to the MokraBela Spectral Project, providing the physical-mathematical basis for the energy flux constants S and λ. Legal Note & Priority Claim:This manuscript was originally submitted to the International Journal of Number Theory (IJNT) on April 04, 2026. This DOI (v2.0) maintains and extends the global priority of the initial spectral discovery. Included in this record (v2.0): Technical Manuscript (PDF): Detailed 9-page structural analysis. Numerical Dataset (Excel): High-precision data for 100,000 zeros. Python Source Code: Core algorithm for spectral projection. Diagnostic Plots (PNG): Visual proof of spectral stability. Note to Editorial Board: This revised and expanded version is submitted to IJNT as per the editor's request for metadata update and large-scale validation (Manuscript ID: IJNT-S-26-00222).