Persistence of Informational Structure Under Projection: An Entropy-Based Analysis of Weak Gravitational Lensing

Persistence of Informational Structure Under Projection: An Entropy-Based Analysis of Weak Gravitational Lensing Description This paper investigates whether global informational structure persists under severe observational projection by analyzing weak gravitational lensing data through an entropy-based framework. Weak lensing provides a uniquely challenging test case: three-dimensional matter distributions are projected into two-dimensional shear fields, heavily filtered by line-of-sight integration, noise, and reconstruction procedures. Using scale-dependent entropy analysis across arbitrary spatial decompositions, this study tests for the presence of a scale-invariant informational plateau—an indicator of global informational coordination—within weak lensing observables. The analysis explicitly distinguishes between intrinsic informational structure and artifacts introduced by projection, smoothing, and inversion. The results demonstrate that while projection suppresses and partially erases informational observability, statistically significant remnants of the invariant persist under specific conditions. These findings establish that informational structure can survive extreme dimensional reduction, but only within constrained regimes, clarifying when and how global informational constraints remain observable in projected cosmological data. This work extends prior entropy-based analyses applied to the cosmic microwave background, large-scale structure, and 21 cm cosmology, completing a progression of tests across increasing levels of observational degradation. The results provide a falsifiable framework for distinguishing physical informational constraints from reconstruction-induced artifacts and establish weak gravitational lensing as a critical boundary case for informational observability. More broadly, the paper contributes evidence for the existence of a global informational constraint governing physical systems, while explicitly identifying the conditions under which that constraint becomes hidden, distorted, or erased by observation itself.