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Shadow Theory

Research edition 9 October 2026

Abstract and publication identity

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Abstract

We construct an exact smooth split–copy–return protocol for a Gaussian writer and a finite bank of retained position archives. Its complete guidance endpoint map is an area-preserving deformation of a baker map. At every finite separation, a singular archive population, or an exactly retained copy of an initial archive coordinate, can preserve the writer's full fine information: writer-only regularity does not imply conditional preparation. We prove a positive alternative using weak physical relative scores of the complete original conditional law. Sectional bounded-variation estimates and explicitly charged actual tails give quantitative averaged conditional readiness jointly with all final archive coordinates, without a density cap or finite quantile Fisher information. A finite 102102-coordinate example gives readiness below 1.0052×10−51.0052\times10^{-5} and, using one common initial box, the same ceiling for a subsequent labelled projective instrument with an arbitrary finite internal reference. A distinct receiver copies the earlier writer event and retains its sign under the specified holding dynamics. Uniform full conditional writer-score bounds also yield finite-resource existence as the archive bank grows. The results use a declared controlled canonical-current parent; independent material control and preparation-law warrant remain separate hypotheses.