A shared observation shields collective fluctuations while preserving local independence

As a liquid approaches its glass transition, its dynamics turns heterogeneous: mobile and immobile regions coexist, and the four-point susceptibility χ4 that quantifies this heterogeneity grows sharply. However, collective signals such as tracer trajectories, overlap functions, or mean fields are generated by the very particles they monitor. Here, we compute exactly what conditioning on such a shared record does to the population that produced it; the guiding example is a tagged particle and the cage of z neighbors that drives its force history. Using a Girsanov path transformation, we prove that the conditioning multiplies the independent joint law of the z trajectories by exactly one term: a centered-square penalty along the single collective direction the record can see. Any fixed pair of particles stays nearly independent, with covariance falling as O(z−1) and mutual information as O(z−2), the property known as propagation of chaos, yet the z(z − 1) weak pair correlations add coherently into a finite suppression of collective fluctuations, the Schur shield D − C = −C2(aI + C)−1 ⪯ 0. The physical consequence is a calculable baseline for dynamical heterogeneity: conditioning itself contributes a computable, nonpositive amount to the susceptibility of a conditioned ensemble, so the genuine cooperative signal is the excess of a susceptibility measured at fixed record over this baseline rather than over zero. Finally, we provide a concrete protocol to test these predictions on trajectory data, and verify it on simulated trajectories of an exactly solvable Brownian model.