When Have We Learned Enough Physics? Target-Relative Sufficiency for PDE Operator Discovery

Equation discovery is often declared complete when the selected support, fitted coefficients, or validation error appears stable. Those criteria describe the behavior of an estimator. They do not answer the scientific question: could another operator that is still compatible with the evidence behave differently in the regime that matters? We define completion through the version set of all data-compatible operators. A target state envelope, declared before the unknown future response is observed, induces a target-action diameter on this set. This diameter measures the scientific ambiguity that remains after the completed experiments. We prove an exact conditional ambiguity law and show that the realized diameter cannot increase as valid experiments are added. Under a common one-sided stability bound, we further transfer operator ambiguity to unseen-trajectory ambiguity and obtain a monotone stopping rule. Validated derivative error and bounded model discrepancy enter through explicit uncertainty inflation. On public $R{e}_{\tau }\approx 1000$ turbulent-channel DNS from JHTDB, two acquisition blocks reduce normalized target-action ambiguity from 0.418 to 0.282 for an outer-layer target and from 0.434 to 0.313 for a near-wall target. Pressure and viscous multiplier coordinates nevertheless continue to span their declared prior intervals. We make no trajectory-stopping claim for this turbulent case because no useful validated global one-sided stability constant is available for the declared regime. For an analytically controlled reaction–diffusion system, both the invariant target envelope and the stability constant are certified. The locked conservative trajectory certificate first crosses its predeclared tolerance at experiment 6. Across 100 independent noise realizations, 99 runs certify by experiment 8, the median stopping step is 6, every certificate path is monotone, and no operational false stop occurs among the 99 stopped runs. The central distinction is therefore between finding a plausible equation and having enough evidence to declare the scientific uncertainty resolved.