The Minimal Sufficient Spectral State for Decision and Risk
Unreviewed draft. This paper has not been human-reviewed.
Mathematical claims may be unverified. Use with appropriate caution.
Abstract
Decision systems often carry excessive state, obscuring both theory and implementation. We define and characterize the minimal sufficient spectral state needed to preserve optimal decision value and calibrated risk estimation. The main theorem gives necessary and sufficient conditions under which a reduced spectral state is information-complete for a target decision class.
Length
1,793 words
Claims
3 theorems
Status
Draft
Novelty
Lifts COS-coefficient CDF approximation guarantees (URRT) to decision-functional and risk-measure preservation, giving a tight necessary-and-sufficient mode count K* for lossless spectral compression relative to a Lipschitz risk class.