The Holographic Circlette: Part 12 — Topological Origin of the Fine-Structure Constant and Discrete Vacuum Polarization

WITHDRAWAL NOTICE (18 October 2026). This paper is withdrawn and should no longer be cited as a result. It is built on a lattice geometry — the 4.8.8 tiling ("circlette") — that the framework retired between June and September 2026. The theorems and mechanisms tied to that geometry were withdrawn [G81, G84]. Its dressed fine-structure value (137.035999077) was a fit and has been superseded, and the framework's later value does not agree with experiment on its own geometry [K5, K13, G88]. The research programme was concluded in October 2026; its review found the framework's Standard-Model content assigned rather than derived. The original description is kept below for the record. Original description (kept for the record): We derive alpha to 3 parts per billion from discrete topological invariants. The bare coupling alpha_0=1/137 follows from 136 confined microstates plus 1 emission pathway. 1-loop and 2-loop vacuum polarisation yield alpha^{-1}~137.035999077 via a discrete Dyson-Schwinger equation. The 4-point trace evaluates to -240, matching the E8 root vectors.