Non-Source Projection and Internal Identifiability

Paper VI of the seven-paper Shadow Theory sequence establishes when an observable readout is, relative to a specified physical model and target, a non-source projection of a larger physically reduced source space.

It proves that a non-gauge distinction within a readout fiber obstructs any deterministic readout-only answer to a target that distinguishes the two source states, and constructs the canonical minimal completion required to retain that target information. It also proves when deterministic source dynamics descend to autonomous observable laws, showing that autonomous closure does not imply source completeness.

The paper develops exact limits on source identification by joint probes, distinguishes deterministic and statistical observation ceilings, and gives the finite-state Markov criterion of strong lumpability for exact projected Markov dynamics. It clearly separates model-internal mathematical results from the additional physical modelling and empirical work required for application, and makes no unrestricted claim about the universe.