Information limits of prefix calibrated prediction

A predictor can be uniquely fitted and exactly calibrated on an observed prefix while its unobserved continuation remains undetermined. This technical note develops a finite-dimensional account of that distinction. We first separate recovery of a specified target from recovery of every parameter. For an affine trace model with an unknown common offset and an ellipsoidal bound on its remaining coefficients, we give the complete set of continuations consistent with a prefix and its exact Euclidean minimax radius. The formula combines offset elimination, minimum-norm interpolation, and the unobserved nullspace. It also yields an exact update after one additional measurement and shows why the choice of a centering weight cannot change the information in an unchanged prefix. Counterexamples distinguish residual calibration from slope identification and scale equivariance from extrapolation guarantees, including smooth positive equivariant rules that agree on every member of an arbitrary finite reference set but disagree at a new prefix. The recovery principles are classical; the contribution is a self-contained synthesis for prefix-calibrated prediction, not a claim of new optimal-recovery theory or empirical validation. Self-contained mathematical technical note. No empirical dataset is used. Editable LaTeX and synthetic arithmetic checks accompany the manuscript. Chien-Tung Lin is the first and corresponding author ([email protected]). Sheng-Ye Yu is the second author. This is a technical-note preprint, not a peer-reviewed journal article.