Spectral Coherence in Arithmetic Operators

Key Points

• The aim is to distinguish between spectral coherence as an observable feature and as a structural necessity related to the Riemann zeta function.
• Introduced a structural distinction in the context of spectral coherence.
• Analyzed coherence in closed arithmetic intervals and its relationship to the Riemann zeta function.
• Reframed GOE statistics within the context of coherence constraints.
• Established that spectral coherence can serve as a diagnostic tool.
• Suggests that GOE statistics may represent a coherence constraint rather than a universality.