Project T Volume XXXVI : The Collapse Hierarchy Multi-Level Schur Complements, Generalized Mass Ladder, and Depth-Dependent Asymptotic Freedom

We compute Schur complements for all six embeddings in the chain S3 ⊂ S4 ⊂ S5 ⊂ S6, spanning collapse depths m = 1, 2, and 3. The Generalized Mass Ladder is established: L(Sn)|Sₖ = L(Sk) + (n−k)·I, where the mass shift equals exactly the number of collapsed dimensions. Palindromic degeneracy is preserved at every collapse depth, and asymptotic freedom holds universally with a systematic dependence on m: the IR coupling grows linearly with collapse depth (reaching μ/λ = 3.02 at m = 3), while the UV coupling remains bounded near 1. Mass is additive: the triple collapse S3 ⊂ S6 (m = 3) produces the same mass as three sequential single collapses (1 + 1 + 1 = 3). The collapse lattice is complete, consistent, and parameter-free.