Space Reduction and Representability of Relational Feasibility : A Short Note on Factorization under Coarsening Maps

Relations are mediated not by objective positions but by recognized categories. When recognition coarsens the position space through a non-injective map ρ: L → Σ, certain relational feasibility patterns cannot be faithfully represented. We prove a factorization theorem: an objective feasibility pattern R* is representable on the recognition space Σ if and only if it is constant on ρ-fibers. When this condition fails, any recognized rule necessarily produces pseudo-cohesion or pseudo-fragmentation. This result complements the author's prior axiomatic theory: whereas that work established structural impossibility at the objective level, the present note isolates a representation-theoretic source of distortion arising from space reduction.