Frontier Inference Under Repeated Partial Reporting

Public performance records often reveal only the leaders at each reporting time. In such archives, the inferential target is not merely the identity of the current best system, but the unobserved frontier: how much headroom remains, and when the gap to an operational threshold becomes negligible. We study repeated top-$k$ reporting as an observability setting for selection-aware frontier inference. We define time-to-near-plateau, $T_g$, as a functional of a latent frontier-gap path, and use this formulation to separate what can be learned from repeated snapshots from what is lost in terminal-only archives. The resulting identification boundary is sharp: repeated selective snapshots can constrain a common frontier trajectory, whereas a terminal top-$k$ record need not identify pre-terminal timing. In a 25-trajectory selection-heavy study, a coupled dynamic model improves recovery of the latest frontier gap and finite $T_g$ relative to reduced baselines, while retaining strong latest-gap performance in cross-regime robustness checks. The evidence is not uniformly favorable, because full-path recovery and interval calibration remain weak, so our claim is intentionally limited. Repeated selective records can contain recoverable information about frontier timing that terminal archives may lose, but reliable uncertainty quantification for that timing remains unresolved.