Admissible Compatibility and the Non Integrability of Scalar Descriptors

This paper shows that if scalar descriptors are required to remain admissibly compatible across multiple locally valid redescriptions, then global integrability of those scalars cannot be maintained without loss of standing. When compatibility is enforced at representational boundaries—such as transitions between admissible contexts—attempts to assign a single globally integrable scalar induce inconsistencies that cannot be resolved by redescription alone. In particular, enforcing global integrability requires either privileging one local representation over others or introducing boundary conditions that break admissible compatibility. The analysis is conditional and eliminative. It does not deny the utility of scalar descriptors within restricted contexts, but shows that treating them as globally integrable objects fails whenever admissible compatibility across contexts is retained. As a consequence, global scalar integrability is excluded as a standing-preserving assumption under admissible redescription, independent of any specific physical interpretation or constructive mechanism.