Modern neural networks often achieve near-perfect performance within the training distribution while failing catastrophically under structured distributional shifts. This failure mode is especially prevalent in periodic and cyclic learning tasks, where models may interpolate locally without learning the underlying generative structure. This work introduces the Periodic Generalization Verification Protocol (PGVP), a model-agnostic diagnostic framework designed to distinguish true periodic generalization from spurious in-domain curve fitting. PGVP evaluates trained models under controlled periodic out-of-distribution (OOD) shifts and quantifies the resulting Periodic Generalization Gap using standard regression metrics. Through controlled evaluations, we show that standard multilayer perceptrons frequently exhibit catastrophic periodic OOD failure despite near-perfect in-domain accuracy, while models with explicit periodic inductive bias generalize reliably. The protocol provides a structural validation layer that complements standard train/validation pipelines. PGVP is intended for pre-deployment model validation in applications involving time-series forecasting, signal processing, cyclic feature modeling, and physics-informed learning. Note: Figures included in this work are illustrative and intended to visualize typical behaviors targeted by the PGVP protocol rather than report specific experimental runs. The PGVP framework constitutes original intellectual work by the author. Specific decision thresholds and implementation details are intentionally omitted to preserve proprietary methodology.