Chapter 121: Mediator Fixed-Point Basin

The Logos sector is the mediator of the 4+1 decomposition: the unique sector through which all four registers factor. This chapter proves that the D–C coincidence at S_L forces E–P convergence there as well, so that all four readout functors produce the same answer on S_L-admissible content. The Logos sector is then characterised as a fixed point of the register-crossing dynamics, with a basin of attraction containing exactly those contents stable under all four readout functors. The master constant ι_τ factors through S_L; its ubiquity across seven books is a structural shadow of this factorization. The chapter closes by connecting the E_3 instantiation to the abstract mediator-sector template of Book III.