We study a minimal formal setting in which distinguishability is modeled by equivalence relations ordered by refinement. We identify configurations that are structurallyexcluded: they occupy extremal (minimal or maximal) positions in the refinement orderfrom which no internal continuation is possible via order-preserving operations.We analyze the consequences of structural exclusion for representational structureand establish that such configurations are fixed by all order-preserving operations andadmit no recovery via internal means. The results are negative and structural: theyestablish impossibilities, not possibilities.We explicitly separate three distinct layers: the formal mathematical layer (whereall results are rigorous), the structural interpretive layer (where we discuss implicationsof the formal results), and the heuristic diagnostic layer (where we sketch how thesestructural constraints might appear in actual representational systems).The paper serves as a foundation for later work within the Admissibility ConstraintProgram by establishing, once and for all, that structurally excluded configurationsexist and cannot be escaped via operations internal to the refinement structure.