Platonic Projection Structures-Based Information Dynamics (PPS-ID): Recursive Transformation of Observable Information

Recursive AI processes transform and reuse observable information across successive stages. Platonic Projection Structures (PPS) describes how latent information becomes observable at a single stage. We introduce PPS-Based Information Dynamics (PPS-ID) to extend this perspective to recursive information evolution, described by O(t+1)=Pi(t)(O(t)) where Pi(t) is a potentially time-dependent observation map and an idempotent projection is a special case. PPS-ID evaluates observable trajectories through state discrepancies and changes in a task-dependent preservation functional Q. This separates the magnitude of observable change from the loss, gain, or preservation of a specified informational property. Cumulative degradation records stepwise decreases in Q, including intermediate losses obscured by later gains or recovery. We instantiate the framework through five generations of recursive knowledge distillation on CIFAR-10, compared with fixed-teacher distillation across five paired random seeds, using the same architecture throughout. Recursive classification accuracy initially improves before declining in later generations. At generation five, fixed-teacher accuracy exceeds recursive accuracy in every seed, with a mean paired difference of 1.542 percentage points. In every recursive run, successive-generation Jensen--Shannon discrepancies decrease while discrepancies from the initial model increase. Positive cumulative degradation also occurs in runs whose final accuracy remains at or above its initial value. These findings demonstrate how trajectory evaluation supplements endpoint evaluation: smaller successive changes can coexist with increasing departure from the initial state, and favorable final performance can conceal intermediate losses. PPS-ID provides a framework for jointly analyzing observable-state evolution and changes in the properties that recursive processes are intended to preserve.