Chapter 69: The Bridge Axiom

The preceding chapters diagnosed ZFC as an E₂ virtual machine (Ch. 64), catalogued the five forbidden moves (Ch. 65), and identified incompleteness as an E₂ boundary marker (Ch. 66). This chapter formalises the bridge itself. Section 1 defines the Bridge Axiom (III.D71): a structure-preserving functor satisfying four properties. Section 2 introduces shadow diagrams (III.D72): images of T-internal diagrams under the bridge, preserving commutativity but incurring degeneracies. Section 3 develops the three-layer template that every bridge claim must satisfy. Section 4 applies it to the Riemann Hypothesis as model case (III.T45). Section 5 previews the extension to the remaining seven problems.