Source Readout Non-Equivalence: Descent and Equivariant Reconstruction Obstructions

This is Paper I of the seven-paper Shadow Theory foundational series. The paper develops a rigorous framework for distinguishing a realization source from an exact readout of that source. Starting only after declared gauge, coordinate, and other physical redundancies have been removed, it proves that an exact quotient presentation of readout data does not imply equivalence with the reduced source structure. Two reconstruction obstructions are developed. First, a physically meaningful source relation is recoverable from readout data exactly when it is constant on readout fibers; variation within a fiber prevents that relation from descending to the readout level. Second, when source and readout carry compatible group actions, an equivariant deterministic representative can be selected exactly when every readout stabilizer fixes a point in its fiber. The paper distinguishes representative selection from recovery of the realized source state, and invariant probability ensembles from deterministic reconstruction. The framework is illustrated with a finite marked-carrier occupation model and the Hopf fibration, where equivariant and topological obstructions are kept logically separate. The results are mathematical and conditional: they provide criteria for a specified model with an identified reduced source space, readout map, and physically meaningful fiber distinctions. They do not claim an unconditional empirical or ontological proof that our universe is a source projection. Paper I supplies the source/readout and reconstruction-obstruction foundation for the subsequent papers on completion, minimal completion, geometric realization, observable quotients and projected dynamics, identifiability, and an RS2 bulk-to-brane physical witness.