Measuring captured predictive information in manufacturing control: a value-of-information bound, its non-Gaussian and high-dimensional corrections, and which claims survive a fair test

Industry 4.0 metrics (OEE, throughput, scrap) are aggregate and ex post; none measures how well a system can predict, and so pre-empt, its own future. This paper defines a manufacturing system's captured predictive information (I_pred) as the mutual information between its world model and its own future waste-relevant state, and establishes the Predictive Organization Bound: the fractional reduction in expected waste achievable by any control policy is upper-bounded by I_pred, independent of actuation capacity. The bound is presented honestly as a specialisation of the established information-theoretic limits of control (Touchette–Lloyd; the Nair–Evans data-rate theorem) and rate–distortion theory — not a new inequality.

It is extended to non-Gaussian disturbances via an entropy-power factor g, to multivariate waste via an effective dimension (a participation ratio), and across a control hierarchy via a coherence-throttled composition law, and tested across eleven seeded, reproducible computational pilots (with multi-seed bootstrap confidence intervals) and one real recorded series.

Key results: the naive Gaussian / ambient-dimension ceilings are reliably beaten (rates 0.25, 0.66) while the corrected entropy-power / effective-dimension forms are never beaten (0.00); Net Predictive Organization peaks then declines with model capacity; a controller can hold predictive information it cannot use; control reach tracks the predictive horizon (slope-1, R² = 0.999); and usable foresight is throttled by the weakest cross-layer link.

Reported as a falsified hypothesis, not omitted: the marketable claim that a forward index beats conventional activity metrics does not survive a fair baseline (+0.013 R², 53% of seeds), nor an early-warning reformulation (R² = 0.07).

This is a candid methods-and-bound contribution; all results are simulation- and proxy-scale, and a physical line remains the decisive test. The broader, explicitly speculative programme it instantiates (the Predictive Reality Hypothesis) is developed separately and is not relied upon for any claim here. Code and figures: see the supplementary archive.