Part VI. Certificate discovery, approximation and sequential evidence
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A signal model must distinguish a representation that preserves probability from a representation that predicts the observed process accurately. Part V gave an exact curved certificate and a way to recognize a supplied operator template. It also made the polynomial-degree assumption explicit. This block advances both boundaries without identifying them with each other.
The first development is a restricted discovery procedure. It recovers an ellipsoidal probability domain from fitted polynomial operators, without a supplied template, matrix embedding or hidden generator. The second is a positive approximation theorem for operator densities outside a finite polynomial class. The third is sequential evidence under dependent observations, including the cost of action coverage. Together they separate structural validity, approximation error and observable disagreement.
The invariant-form and quadratic-certificate ingredients belong to classical systems theory [R8, R13]. Positive polynomial averaging uses the classical Bernstein–Durrmeyer kernel [R19]. The sequential argument is an elementary martingale confidence sequence, not a new concentration principle [R20]. The contribution of this block is their connection to the large signal model's explicit representation contracts and to independently replayable examples. Propositions 62–70 have proofs below. No proof kernel or production training system is invoked.