Chapter 119: The Logos Sector: Definition and Universal Property

The structural crown jewel of the 2nd Edition. The Logos sector S_L is the unique location in the 4+1 sector decomposition of τ at E₃ where proof-validity and stance-stability coincide — where the diagrammatic register ℝeg_D and the commitment register ℝeg_C produce the same answer. A content is S_L-admissible if and only if its ℝeg_D-validity and its ℝeg_C-stability are mutually witnessing: to prove it is to commit to it, and to commit to it is to have proved it. The sector is named by its universal property, in the same way that a categorical limit is named by its universal property: the name describes the structure, nothing more. The Logos Sector Uniqueness Theorem (VII.T45) shows that S_L is unique up to natural isomorphism.