Ordered Absorption Reveals Green--Kubo Memory Hidden from Survival Curves

Can a binary survival measurement reveal dynamical memory? We prove that every stationary survival curve generated by a fixed state-dependent absorber is identical for a process and its time reverse. Two ordered pulses remove this obstruction: their joint survival probability gives an exact finite-amplitude lagged covariance, pulse reversal exposes the time-antisymmetric component, and the resulting Bernoulli probabilities bound path irreversibility. Spanning profiles reconstruct finite-state Markov dynamics. A held-out retrospective reanalysis of 20 independent optical-trap records shows a robust experimental time-antisymmetric correlation and recovers its bounded-profile counterpart from virtual survival probabilities. An independent two-state single-molecule model supplies a reversible null and finite-count reconstruction benchmark. These tests use experimental trajectories but emulate the proposed removals; direct physical pulse validation remains open.