Local perception operators and classicality: new tools for old tests

Quantum nonlocality is often judged by violations of Bell-type inequalities for a given state. The computation of such violations is a global task, requiring evaluation of global correlations and subsequent testing against a Bell functional. We ask instead: when is a given state local (classical)? We formalize this question via local perception operators (LPOs) that compress global observables into locally accessible statistics, and we derive two complementary witnesses - one implementable by a single party with classical side information, one intrinsically two-sided. These tools revisit familiar Bell scenarios from a new operational angle. We show how the witness leads to state-aware constraints that depend on local marginals and measurement geometry, with natural specializations to canonical scenarios. The resulting criteria are built from first moments and standard projective measurements and provide a way to certify compatibility with local hidden variable explanations for the LPO-processed data in regimes where conventional Bell violations may be inconclusive.