Predictive Information Loss at Physical Model Interfaces: Sufficient State Transfer and Information-Retention Horizons

Coupled physical models can preserve conserved quantities and a current observable while discarding upstream information needed for future prediction. We formulate this loss relative to a shared information record, an additional record available to the sending module, and a specified future observation. Conditional mutual information gives the irreducible expected logarithmic-score loss of compression; a separate relative-entropy term measures downstream misspecification. A linear– Gaussian specialization yields a fixed-rank state-retention rule. A positive, energy-balanced threereservoir benchmark preserves total energy and instantaneous luminosity while hiding a coordinate that affects later emission. At the declared noise level, a nominal 95 % plug-in interval achieves 29.09 % ensemble coverage near the early loss maximum. Exact marginalization restores ensemble coverage at 3.50 times the width of the state-informed reference; transmitting the extra coordinate removes this interface loss only when it is already available upstream. A model-specific analytic bound guarantees a marginal information-retention interval of at least 0.02736 time units for a tolerance of 0.05 nats, compared with a numerically located first crossing at 0.02820. Joint-target calculations show why cancellation at one forecast time cannot certify an entire curve. Noise sensitivity and correlated-readout tests delimit the numerical claims. The results concern a controlled interface and do not infer an unknown source state or validate a real astrophysical event.