Shadow-Certified Reporting and Monodromy Obstructions (A Mathematical Foundations Note)

To formalize observation, we introduce a report map defined on the covering space. A harmonic example demonstrates that specific parameters admit rational projections, yielding exactly representable outputs despite the underlying multivalued structure. Using Non-Standard Analysis, we construct hyperfinite internal grids and analyze the stability of these projections under infinitesimal perturbations. A shadow stability lemma shows that differentiability of the report map suffices to preserve the standard value. In particular, we establish that a hyperfinite parameter with standard part 17/617/617/6 produces a report whose shadow equals 1/21/21/2. This provides a concrete instance in which topological multivaluedness collapses into a stable rational output under projection.