Version 2 — revised in response to an external structural review and an automated critique pass. See "Response to Review" appendix in the PDF for the change log.Large-model systems are evaluated at multiple layers—statistical, algorithmic, systems, and behavioral—yet each layer's evaluation methodology has been developed largely in isolation. This paper identifies a shared structural pattern across these layers: evaluations that are locally valid but globally misleading. Drawing on recent preprints spanning federated learning, LLM inference, causal inference, high-dimensional statistics, latent reasoning, and multi-agent coherence, we offer a *heuristic reading* that a common pattern recurs: a system or estimator satisfies its local objective (loss reduction, throughput, oracle test passage, component-level coherence) while concealing a deeper failure that only manifests at a different scale, composition, or distribution shift. We call this the **local-validity trap**. Specifically, we synthesize evidence that (1) oracle-based testing may miss semantically incorrect but symptom-reducing fixes in AI-assisted development; (2) component-level probabilistic coherence does not guarantee joint coherence in multi-agent LLM systems; (3) measurement error silently biases high-dimensional regression even when penalized estimators converge; (4) asynchronous pipeline parallelism bounds staleness locally but may accumulate convergence error globally; and (5) contribution metrics in federated learning should track optimization trajectories rather than static snapshots to avoid misattribution. We propose that evaluation rigor for large-model systems may benefit from explicit cross-scale consistency checks, analogous to structural constraints studied in the algorithmic and statistical literatures, and outline candidate design principles for building such checks into system pipelines. The "local-validity trap" framing is introduced here as an organizing heuristic; it is not a term used in any cited source, and the cross-domain structural analogy is asserted on the basis of shared vocabulary rather than shared mechanism. ---Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename.Cited arXiv preprints: 2605.29566v1, 2605.29639v1, 2605.29664v1, 2605.29740v1, 2605.29944v1, 2605.30075v1, 2605.30113v1, 2605.30153v1, 2605.30158v1, 2605.30319v1, 2605.30321v1, 2605.30327v1, 2605.30335v1, 2605.30336v1, 2605.30341v1, 2605.30343v1, 2605.30353v1