Chapter 52: No Knobs and One Diagram

The Hinge Theorem (the relevant theorem, Ch. 61) proved that the seven-book architecture is derived. The export contracts (Remark [rem:export-contracts-books-iv-vii], Ch. 62) formalised what each downstream book receives. This chapter closes the arc with three inventories and one picture. Section 1 presents the No Knobs Ledger: a table of all inter-sector and self-couplings, each a rational function of ι_τ = 2/(π + e) at a specific primorial depth, and the No Knobs Theorem that all couplings are canonically determined. Section 2 places all eight Millennium Problems on a single enriched bi-square—the Master Schema. Section 3 compiles the complete Results Inventory of τ-effective theorems proved in Parts 0–VII. Section 4 condenses the entire series into one commutative diagram whose vertical axis is enrichment and whose horizontal axis is sector.