Boundary Conditions at Measurement Extremes

This paper specifies boundary conditions governing the interaction between continuous system resolution and discrete measurement. It shows that mismatches between resolution rate and sampling rate necessarily produce observable artifacts, such as apparent discontinuity under undersampling and apparent stasis under oversampling. These effects arise from measurement limits rather than from scale-dependent ontology. The analysis is pre-theoretical and pre-interpretive. It defines invariant constraints, along with minimal constructs such as cores and shells, that persist across measurement regimes and must be respected by any downstream measurement formalism. The paper does not propose modifications to existing theories; it establishes structural limits within which such theories must operate.