Theory of the Intersection of Fields — A Structured Exposition

A geometric framework in which the masses, charges and coupling constants of physics are not free parameters but consequences of the geometry of a codimension-one interface where three equivalent fields meet. From a small set of measured densities — the vacuum energy density and the nuclear saturation density — together with geometry, the framework derives the fine-structure constant (to 0.3%), the Weinberg mixing angle (sin²θ_W = 3/8 at unification), the galactic acceleration scale a₀ without dark matter, and the algebra of the three forces (u(1) ⊕ su(2) ⊕ su(3)). It makes falsifiable predictions, each with its judge and its expiry date: primordial helium Y_p = 63/256 = 0.2461 (+0.2σ), the vacuum share Ω_Λ = 2/3, an absolutely stable proton, a minimum black-hole mass of 1.1×10²² kg, and the switch-off of gravity below 16.9 μm. Every claim carries an explicit status — derived, candidate, or debt — and the framework names what it does not yet derive. This document is a structured exposition; A companion French version is included.