Projection-Observability Diagnostic Framework (PODF): A Method for Distinguishing Structural Boundaries from Observability Limits

This work introduces the Projection–Observability Diagnostic Framework (PODF), a general methodological tool for distinguishing genuine structural boundaries from limits imposed by projection-induced resolution loss. Across many scientific domains, apparent thresholds and critical values are often interpreted as marking fundamental transitions. PODF provides operational diagnostics—based on resolution decay, edge behavior, sign persistence, coherence, and topological indicators—to determine whether such thresholds correspond to true structural changes or merely to the limits of detectability under a chosen projection. The framework formalizes the distinction between existence and observability, emphasizing that structure may persist beyond observational edges even when it becomes inaccessible to specific scalar or low-dimensional measurements. PODF is applied diagnostically to diverse systems including prime gap statistics, spectroscopic resonance data, solar X-ray time series, and holographic bulk–boundary projections in AdS/CFT. In each case, consistent edge behavior is observed, supporting the utility of PODF as a cross-domain diagnostic methodology. This work introduces no new physical laws or constants and does not modify existing theories. Instead, PODF offers a reusable analytical tool for interpreting thresholds with appropriate epistemic caution, helping to avoid conflating observational artifacts with structural discoveries. The framework includes explicit falsification criteria and is intended for broad application wherever projection and observability limits play a critical role.