Individual patient data (IPD) are the gold standard for secondary analyses of time‑to‑event outcomes, yet they are seldom made available. Reconstructing IPD from a published Kaplan‑Meier (KM) curve would greatly expand the utility of existing evidence. Current approaches all claim high fidelity, but each is judged by the particular agreement metric it happens to achieve and each returns a single dataset, ignoring the fact that the mapping from a figure to data is not bijective.\ \ We define fidelity explicitly: (1) the dataset must reproduce the risk table exactly; (2) the digitized points must follow the KM curve within the image resolution; (3) the printed median, confidence interval, and total event count must be respected. A dataset satisfying all three constraints is called admissible.\ \ Based on this definition, we propose StochIKM, a stochastic algorithm. It first employs a vision‑capable language model to digitize the KM figure with high precision, then generates a set of admissible IPD collections by random sampling under the fidelity constraints. A solution is guaranteed to exist whenever the figure has been read correctly; a failure therefore indicts either the published figure or its digitization.\ \ In both simulation studies and an empirical test on 79 arms from published oncology trials, StochIKM reproduces the published risk tables and medians more closely than the LLM‑enhanced IPDfromKM method, a high‑impact alternative.\ \ Review