Research Notebook: Discrete Scale Invariance, RG Dynamics, and ϕ-Scaling in Gravity

We investigate a hypothesis of self-organizing, phase-conjugate, fractal compression of charge,termed “implosive coherence”—through a discrete scaling law*. We construct a continuous field-theoretic extension exhibiting discrete scale invariance (DSI). This leads to a modified gravitational potential withlog-periodic corrections. We develop a relativistic scalar–tensor theory encoding this structure,derive observable consequences, and propose a gravitational wave detection strategy based onlog-frequency phase modulation. *Our 1st Physics paper_ 'A scalar–tensor gravity theory with discrete scale invariance (DSI)', which behaves like: GR at leading order RG limit-cycle corrections at subleading order oscillatory vacuum energy in cosmology.