18.  Convergence of the Projected Geometry

This is the hardest mathematics in the book, and it sits this far back on purpose. It proves that the jump from a grainy substrate to smooth space really works. The rest of the book needs that proof to exist; no reader needs to follow it to understand the physics.

• 18.1. Mosco convergence: theorem and assumptions
• 18.2. The K-uniform rate: proof and three closures
• 18.3. Dirac-operator convergence: a single analytic estimate
• 18.4. Dirac convergence: the L_round and L_comm lemma chain
• 18.5. Summary