0.3 Bott Periodicity and Seven-Layer Truncation

This article proves that the Berry phase of the circuit equals (non-trivial closure), and from this derives the Seven-Layer Truncation Theorem. attempts to return completely to the origin, but brings back a topological phase — the physical world arises precisely from this incomplete closure. The coding map therefore has only 7 layers ; the 8th layer is the 1st layer but with a global rotation. This article starts from KO-theoretic invariants, passes through the transgression of the Chern-Simons 7-form, and gives a complete computation of the Berry phase.