An optimizer-aware reliability audit for detecting when a locally favorable PINN update deteriorates after the complete finite optimizer step is executed.
PINN optimization is often interpreted through local component-gradient geometry, but real training executes finite, stateful updates shaped by momentum, adaptive scaling, and conflict resolution. This preprint introduces the direction-execution gap: the event in which a component appears locally favorable before an optimizer step but deteriorates after the complete accepted step is executed on the same frozen audit set. Across 111 paired runs over four PDE families and three update rules, the audit exposes failed local-progress claims, identifies directional curvature as the mechanism behind many reversals, and separates directional promise, realized component progress, and solver-level accuracy.
