Greatest Independent Returns for Statistical Experiments: Spectral Classification and Sharp Gaussian Simulation

This preprint asks what information a statistical experiment can release independently of a prescribed observation. For boundedly complete experiments, compatibility of every pair of binary returns characterizes the existence of a greatest exact return. A uniform partition condition gives a sharp total variation threshold for greatestness at positive tolerance. For interval exponential tilts, the closed additive group generated by the interval lengths determines the greatest common experiment. Hard Gaussian interval observations remove exact return information in the observed directions. With a noisy interval observation, a Gaussian residual can be maximal even when there is no greatest return. For Gaussian simulation of a competing binary return, the paper gives a finite-mean dual formula, an exact logarithmic rate governed by a Paley-Wiener point-evaluation norm, and a sharp testing exponent. In one dimension, two variances force constant exact returns when a sensor event has a nonconstant finite Fourier probability. The files contain the paper PDF, the matching LaTeX source, and a computation supplement.