Certifying Learned Variables

Machine learning can discover variables that predict the large-scale behavior of physical systems, but prediction alone does not establish that they belong to the system's effective physics. I argue that a learned variable is certified when there is warrant that its governing relationship remains invariant across an independently specified range of irrelevant variations. When the variable is physically opaque, certification must proceed externally, through the learning process or the variable's behavior across that range. The learned Ising coarse-graining can be certified in this way; softness in glass-forming liquids cannot yet. Non-certification, however, does not establish proxyhood. Certification warrants bounded, domain-relative projection, while leaving its stronger realist interpretation open.