Deterministic Computable Presentation-Dual Objects with Silent Diagnostic Failure

We introduce a class of deterministic computable objects admitting dual presentations—a symbolic (sequential) representation and a geometric (non-sequential) representation—linked by computable inverse maps and defining the same object up to computable isomorphism. We study such objects within data-local diagnostic systems, whose operations depend only on restriction to a finite accessible domain. We establish a structural limitation: if the diagnostic algebra factors through finite data and a non-realizable function admits a realizable shadow, then the two are indistinguishable under all diagnostics. Consequently, diagnostic adequacy is not sufficient for realizability, and membership in the realizable function class is not decidable within the diagnostic system. We provide an explicit deterministic construction of an object with these properties via a computable encoding of symbolic sequences into geometric structures. The induced function is shown to be non-realizable in a standard linear function class by exhibiting a strict separation in representational dimension from that class, verified by explicit finite-dimensional construction, while remaining indistinguishable from a realizable function under all data-local diagnostics. The construction additionally exhibits a witness-dependent hierarchy of representational dimension, where the rank of the encoder on finite witness families stabilizes at a threshold determined by their statistical structure. The construction exhibits two forms of silent diagnostic failure: one due to formal restriction of diagnostics to accessible data, and another due to structural limitations of finite witness families. These results are invariant under change of representation and are independent of probabilistic or asymptotic assumptions. Together, these findings identify a fundamental constraint on data-local diagnostic systems: deterministic computable objects may be internally certified as adequate while remaining globally non-realizable, with no diagnostic means of detecting this discrepancy.