Local Completion Is Not Transportability

This work studies a finite representation problem in which a representation may be exactly sufficient for one operational architecture while failing to preserve distinctions required after a change in the operational equivalence regime. The paper distinguishes three notions that are often conflated: generative truth, operational completion, and transportability. On the complete finite history space H = {0,1}^12, it defines a fixed coarse present quotient, architecture-specific continuation functions, induced operational equivalence relations, and exact re-identification budgets. A central construction shows that a representation can be globally uninformative about a privileged historical residue while becoming fully informative conditional on the quotient. The same representation can exactly complete one architecture while leaving others unresolved. The study also proves constructively that greater retained conditional information does not necessarily increase transportability. Additional retained distinctions can increase H(R|Q) without preserving the distinctions required by a different future architecture. The exact finite-domain layer was independently reconstructed by both investigators. Historical learner results affected by implementation or provenance asymmetries are retained for transparency but are not treated as part of the exact evidential core. The conclusion is deliberately narrow: local operational sufficiency does not imply transportability, and retained conditional information does not by itself identify which distinctions remain relevant under a changed operational equivalence regime.