Green-Kubo Memory, Irreversibility, and Experimental-Data Tests from Ordered Absorption

What dynamical information can be inferred when an experiment records only whether a system survives controlled absorption? Static state-dependent absorption is exactly blind to stationary time reversal, even when complete survival curves are known. Two ordered pulses recover lagged covariances through an exact finite-amplitude identity; swapping their order exposes time-antisymmetric correlations and gives a Bernoulli-data lower bound on path irreversibility. Spanning profiles identify a finite-state Markov transition matrix, whereas incomplete or ill-conditioned profiles hide modes or amplify noise. We combine these results with finite-count confidence bounds, information-contraction identities, and the static weak-killing Green--Kubo expansion. New held-out retrospective analyses of 20 separately recorded 100-kHz switching optical-trap realizations reveal a robust time-antisymmetric position--force correlation and recover its bounded-profile order contrast from virtual survival probabilities. A two-state HP3 single-molecule model provides a reversible null and finite-count transition-reconstruction benchmark; Hsp90 traces demonstrate a photobleaching/stationarity exclusion gate. The experimental trajectories are real, but the proposed stochastic removals are emulated after acquisition, so direct pulse validation remains open.