How Complex Should an Explanation Be? A Distortion-Rate View of Time Series Attribution

Feature attribution for time series is usually posed as a choice among solution concepts - Shapley, Owen, Banzhaf - estimated as accurately as possible. We argue, and measure, that this framing is mis-specified. First, the attributed object is not a property of the model: the coalition value function depends on a masking baseline and an output scale, and every summary of it on a coalition measure. Across seven trained models these choices move the additive share of the value function by up to 32 points, and on one real model the top-10% attributed cells agree only 32% of the time between a zero and a first-observation baseline; neither values nor rankings survive a change of convention. Second, at a fixed convention the answerable question is how much of the value function an explanation of a given size can carry. Treating an explanation as a lossy code, we measure its distortion against its rate, the numbers it emits per input. On five real models, additive attribution is inefficient even at its own rate, locality is the wrong structure - a lag-1 band buys 3-9 points where a rank-one factorisation buys 21-30 at 2-9x fewer numbers - and the optimal complexity is finite and set by the query budget. Perturbation-based faithfulness metrics do not resolve these distinctions on a game with exact ground truth. Finally, an amortized estimator that emits the coefficients of a structured surrogate ships each explanation with a measured fidelity: it reaches 99% of a 200,000-query per-input fit on one model and fails on two of six, which its audit, whose query cost we price, reports.