Luck as a Fractal Phase-Shift Phenomenon: A Sparse-Origin Framework for Transformative Human Events

Luck is commonly interpreted as randomness, cognitive bias, or post-hoc narrative construction. This paper proposes a structurally different account: luck as the macroscopic signature of a successful phase transition occurring within a biological system that inherits sparse-origin dynamics from life itself. We begin from the Sparse-Origin Hypothesis, which treats the emergence of life as a near-singular cosmological phase transition requiring extreme boundary conditions. We argue that systems arising from such sparse events may retain the capacity to reproduce analogous phase-shift behavior at reduced scales through fractal correspondence. Under this framework, luck is not an external event nor a probabilistic anomaly, but the visible residue of an internally completed phase transition driven by unconscious computation under critical pressure and stabilized by a biological homeostatic carrier. This model reframes luck as a structural phenomenon that is rare, discontinuous, and conditional, rather than subjective or metaphysical. We outline the core dynamics of this process and derive falsifiable predictions at the human scale.