TheShadow Theorem: An Observational Boundfor the Effective Field Theory of Information Reconstruction (EFIR)

This paper presents a revised and self-contained formulation of the observationalboundarising from the Effective Field Theory of Information Reconstruction(EFIR). It does not presuppose familiarity with earlier drafts. The argumentis built from first principles, and every claim is stated with explicit hypotheses.The paper grew out of a specific intellectual difficulty. The EFIR frameworkcouples three independently motivated mathematical structures: a variationalfield theory, an information-geometric flow, and a Lindblad open-system dynamics. Each structure is well-established in its own domain. The challenge wasto identify a single quantity that unifies all three without artificially combiningtheir equations, and to state a result about that quantity that is both true andnon-trivial.