Scarcity Estimates for logarithmic Prime Resonances

This paper develops preliminary heuristic estimates for logarithmic resonance scarcity among prime numbers. Motivated by spectral approaches to arithmetic structures, the work studies quantitative bounds for near-resonant logarithmic prime interactions of the form ∣log⁡p−log⁡q∣<δ.|log p - log q| < δ.∣logp−logq∣<δ. The analysis suggests that deep logarithmic resonances are strongly suppressed, supporting interpretations related to arithmetic rigidity and spectral stability. The work is exploratory and heuristic in nature and does not claim a proof of the Riemann Hypothesis. Parts of the conceptual development, verification workflow, and manuscript refinement were conducted through collaborative interaction with AI-assisted systems.