Part VIII. Data-supported domains and smaller repairs
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The preceding block certified a perturbed operator family after mixing it with a center reset. Its all-horizon validity guarantee was exact, but its error bound became trivial at horizon eight. It also kept deterministic coefficient boxes separate from statistical confidence sets. This block addresses both limitations in declared sectors rather than weakening either distinction.
First, the same fitted family and previously proposed geometry admit a smaller, independently checked repair. Second, a self-normalized martingale argument produces operator uncertainty sets from a dependent trajectory when the predictive state is an accessible, fixed observable. A nonlinear three-coordinate example connects those sets to a curved domain without a reset correction. Its geometry and feature dictionary are specified in advance. This is not a solution to discovering an unknown hidden state from the same data.
The sequential-regression result is a classical self-normalized concentration theorem [R23], proved here in the form used by the signal model. The contraction argument uses standard Markov-kernel and total-variation ideas [R24]. The new block's contribution is the explicit sequence of assumptions, finite witnesses, structured uncertainty, observation-measure distinctions and executable examples connecting these tools to the realization calculus. Proposition counts are not historical-novelty counts.