Kepler's Rhythm in Turbulence: Toward a Conserved 1:2:3 Law via Recursive Gradient Processing

This paper reports reproducible evidence of a conserved 1:2:3 frequency ratio in turbulent probe data, uncovered using a fully automated Recursive Gradient Processing (RGP) pipeline interrogating the Johns Hopkins Turbulence Database (JHTDB). Unlike equation-based approaches to turbulence (Navier–Stokes and their neural-operator surrogates), RGP bypasses PDEs entirely and extracts conserved rhythms directly from nature’s record. The finding—reminiscent of Kepler’s harmonic laws—emerges consistently across independent probes and acquisition windows. It is predicted by RGP’s first principles: • Zeroth Law: gradients as causal primacy, the “unmoved mover” of natural change. • First Law: a least-divergence extremum principle that favors alignment and harmonic locking. • Second Law: entropy-driven unity–disunity cycles. • PoLA: the Principle of Least Action reframed as least divergence. The pipeline enforces rigor through full archival of raw CSVs, metadata, JSON analyses, and machine-written YAML pulses, whether runs succeed or fail. This design prevents fabrication and ensures reproducibility. We emphasize that the present evidence, though compelling, is still fragile. It must be validated on additional datasets and probe geometries. Yet even at this stage, the simplicity, reproducibility, and falsifiability of the observed 1:2:3 law suggest a paradigm shift: turbulence may be governed not by unsolved PDEs but by conserved recursive rhythms. This paper is part of the Φ-Mesh fossil trail, documenting the progressive development of RGP as an alternative framework for turbulence, coherence, and complex systems.NotebookLM podcast about this paper here.