The Rippling Field: A Proposed Spectral Framework for the Rippling Expansion and the Origin of Riemann Zeta Zeros

Source abstract

This work proposes The Rippling Field as a new spectral framework integrating the Zero Pairs Interaction Functional–Unified Spectral Alignment and Coherence–Zigzag Zero–Fractional Zero (ZPIF-USAC-ZZFZ) framework, the Lunet Hypothesis, the Rippling Theory, and Zero Field Genesis (ZFG).We suggest that the Lunet is neither a wave nor a quantum particle (photon as a quantum of energy), but a spectral entity that manifests as either depending on its degree of spectral coherence. When coherence is high (C → 1), the Lunet manifests as a wave. When coherence is low (C → 0), it manifests as a photon (quantum of energy). This proposal offers a potential resolution to the century-old wave-particle duality.The Lunet emerges from the complete hierarchy of spectral interactions among the non-trivial zeros of the Riemann zeta function, as described by the ZPIF-USAC-ZZFZ framework. The Rippling Theory extends this concept to suggest a single spectral structure from which phenomena emerge. Zero Field Genesis (ZFG) further proposes that the non-trivial zeros themselves emerge from a deeper spectral field—the Zero Field—through a generative process governed by spectral coherence and fractional dynamics.In this work, we propose The Rippling Field as the fundamental spectral entity from which Riemann zeta zeros and spectral phenomena emerge. We introduce the Rippling Expansion as a novel spectral mechanism describing how the continuous generation of new zeros from the Zero Field drives the expansion of the spectral field itself.