Why observational completeness is structurally impossible (and why this matters across physics)

This paper demonstrates that observational completeness is a structural impossibility rather than a technological limitation. Using the Theory of Axiomatic Necessity (TNA), we show that any observable domain necessarily presupposes a latent structural support that cannot be recovered from observation alone. A recurring aspiration across physics is observational completeness: the idea that empirical observation can fully determine the structure of a physical theory. We argue that this aspiration is structurally impossible, as any empirically accessible domain (N₀) necessarily relies on a latent structural domain (N₁) required for coherence. This incompleteness is not epistemic but ontological: observation is defined only within a closure that excludes its own structural support. We demonstrate that several theoretical tensions—such as underdetermination and fine-tuning pathologies—are symptoms of attempts to enforce an impossible observational closure. Ultimately, we propose a criterion of "structural honesty, " where theories are judged not by their demand for completeness, but by their explicit acknowledgment of these foundational limits