Chapter 21: The Coherence Programme

In the relevant chapter we previewed the Master Schema: boundary determines interior determines spectral invariants. In the relevant chapter we completed the spectral algebra foundation. We now possess earned infrastructure to address the Millennium Problems as instances of one structural pattern.

This chapter frames the coherence programme: a uniform checklist applied to every millennium problem in Parts IV–VI and IX. Each problem receives (i) a Mutual Determination formulation, (ii) an admissibility predicate, (iii) an enrichment-level placement, (iv) a conjectural bridge to orthodox statements, and (v) a 4-tier scope grade. Part IV demonstrates the pattern at enrichment level E₀ (RH, Poincar'e); Parts V and VI scale to E₁ and the E₁ → E₂ bridge; Part IX addresses P vs NP at E₂.