Probability as Topological Entropy: A Monadic Worldline Model of Quantum Reality

This paper presents a novel framework deriving quantum statistics, particle masses, and spacetime curvature from a single braided worldline embedded in ordinary 3+1 dimensional spacetime. Building upon Wheeler's "one-electron universe" conjecture, we develop a rigorous mathematical formalism where all Standard Model excitations emerge as local manifestations of a single cosmic strand. The key innovation is a topological action that weights different knot configurations by a complexity function combining crossing number and Jones polynomial evaluation. This approach transforms the infinite configuration space of possible worldline embeddings into a convergent partition function. Born probabilities naturally emerge as normalized counts of topological configurations, offering a geometric interpretation of quantum uncertainty. Our framework reproduces the charged lepton mass hierarchy with remarkable precision using a single parameter fit, derives Einstein's field equations from coarse-grained knot density, and explains black hole entropy through worldline crossing saturation at the event horizon. The approach unifies quantum statistics, mass generation, gravity, and information theory through a consistent topological framework while maintaining spacetime realism. The paper makes several falsifiable predictions testable at current and near-future facilities, including specific heavy-lepton resonances at 8-18 TeV, modified Higgs decay rates, precise energy shifts in Rydberg atomic states, and modifications to vacuum birefringence in strong electromagnetic fields.