The Registration Framework: Deriving Physical Structure from a Single Axiom

The Registration Framework derives core features of physical reality — dimensional structure, topological stability, quantum mechanics, thermodynamics, and a parameter-free formula for the fine structure constant — from a single axiom: that existence requires registration. Without postulating space, time, particles, or forces, the framework derives: (1) an irreversible generative process manifesting as temporal ordering; (2) the Lorentzian signature from structural asymmetry between irreversible and reversible degrees of freedom; (3) that exactly three spatial dimensions uniquely support topologically stable matter; (4) the Born rule from self-relational structure; (5) the uncertainty principle from finite registration capacity; (6) the fine structure constant α₀ ≈ 1/136.14 from topological invariants of the minimal stable knot, within 0.7% of the measured value with no free parameters. Version 4.0. Working paper.