Structural Reduction: Working Outline

• Local Growth (LG) model class: precise hypotheses and the boundary bookkeeping layer
• Boundary descriptors and equivalence: definitions and the target finiteness mechanism
• Finite descriptor bound: a finite state space for boundary compression
• Induced boundary operator cocycle: boundary evolution as a finite-template operator family with bounds
• Quantitative mixing / Doeblin blocks: a bounded-time criterion that yields finite projective diameter and Birkhoff contraction
• Reduction interface: the final statement that packages the reduced objects and the conditions they satisfy

Additional modules (when you want tooling and certification, not only theorems)

• Certification pipeline: payload objects, checks, and failure modes on the reduced finite system
• Periodic approximation at the minimum: what can be proved or certified via periodic structure
• Projective regularity on minimizers: how optimality selects a contracting projective section on the minimizing support
• Related-work anchors: where this fits relative to transfer-matrix methods, PF/projective metrics, random products/Lyapunov exponents, and symbolic dynamics