Persistent Records and Physical State Spaces

What must a physical theory preserve when it makes a record? A square state space gives a precise test: making a perfect record of one coordinate can erase the other from the entire output. We prove the algebraic obstruction, identify the state directions lost, and derive sharp accuracy bounds for classical records and coherent quantum outputs. A closed, resource-funded square model nevertheless preserves every posted history. It can be attached to a recognition framework while leaving its comparison observable, conserved charge, and realized hierarchy intact. Persistent records and positive accounting therefore leave a specific state-selection premise open: the availability of recordings that preserve distinctions within an already certain outcome. This premise excludes the square, while further composition principles are needed to select the complete quantum matter-and-field structure. Files. The 10-page paper and a sanitized archive containing its complete LaTeX source, reproduction instructions, evidence manifest, change log and license.