Global identification of real symmetric 4×4 matrices from four static configurations of two fixed perturbations: Sufficiency and optimality of the seventh moment

This preprint investigates the global identification of real symmetric 4×4 matrices from a finite set of observed moments. Two fixed symmetric perturbations and four static configurations are considered. The study presents a proof, partly supported by exact computer-assisted certificates, that moments through order seven uniquely identify every matrix in the prescribed class, whereas moments through order six are insufficient for the same protocol. The analysis covers all observed-rank profiles, including degenerate cases, and provides supplementary computational certificates and reproducibility materials. Foundational perspective. The study originates from the premises of the Unitary Field (Campo Unitario) and their possible interpretative consequences. Within this framework, Reality refers to the foundational domain, while measurement concerns a representation arising through local execution. E4 constitutes a mathematical advance within this perspective by investigating the conditions under which a represented structure becomes uniquely identifiable through finite observations. The manuscript is released as a research preprint. Independent peer review has not been completed, and bibliographic novelty has not been definitively established. Foundational reference: https://doi.org/10.5281/zenodo.23645830