This volume extends the Universal Rigid Compiler framework to clinical neurology. We demonstrate that neurological and psychiatric pathologies can be understood as compilation errors in the algebraic structure of the brain. Each Brodmann area implements a specific operator of the 0-Hecke monoid H0(Ã2), and lesions or dysfunction correspond to violations of braid relations, loss of idempotence, or collapse of λ = −1. We present the first Algebraic Clinical Cases in medical history, redefining diagnosis from symptomatic description to compilation failure analysis. Keywords: Neural pathology; algebraic diagnosis; Brodmann areas; Hecke braid relations; compilation errors; λ = −1; Kashiwara crystal; gamma oscillations