Mandelbrot Fold: Spacetime as a Fractal Manifold with Memory

Abstract

Title: Mandelbrot Fold: Gravity as Residual Geometric Memory in a Fractal Spacetime Summary: This paper presents a conceptual heuristic model that reinterprets gravity not as a force or a smooth curvature, but as residual geometric memory (“folds” or “creases”) in a fractal spacetime manifold. Building on Einstein’s general relativity, the model proposes that the familiar smooth metric is a coarse-grained average of a deeper, history-dependent metric structure. Dark matter is reframed as persistent scars of past mass (termed Levadence), dark energy as the progressive deepening of these creases over cosmic time, and redshift as the stretching of light along lengthening fractal paths. The framework requires no new particles or forces and offers a testable prediction of residual metric noise near the Planck scale. The paper is offered as a thought experiment and structural ansatz intended to invite further mathematical development.