This paper argues that AI infrastructure now fails at its boundary as often as inside its fence line: a slipped interconnection agreement, a water moratorium, a denied permit, a community that organizes against the hum. None of these are captured by capacity or efficiency, the two metrics every facility already tracks, because both are measured entirely inside the fence line. The paper defines Infrastructure Health as a boundary property: the degree to which a facility and its host systems (grid, watershed, airshed, land, and community) sustain one another over the asset's operating life. It is bidirectional, since a denied permit is the host rejecting the facility while a three-year queue is the host unable to feed it, and it is temporal, assessed across the operating life through annual re-scoring rather than on the day the doors open. The paper develops the definition into six measurable dimensions (metabolism, hydration, thermal regulation, immunity, symbiosis, and regeneration), each reported as an evidence-graded indicator rather than averaged into a single score, alongside a taxonomy of six failure patterns, a design philosophy, an economic case, and five falsifiable propositions offered for independent testing. It also states plainly where it is weakest. The community dimension needs social-science rigor the author does not claim. The normalization classes need reference data, and their adjustments are proposed defaults rather than settled law. The reference architecture's thermodynamics are published with their bounds rather than their best case. The instrument measures one facility against its hosts and cannot yet capture cumulative load, so a host can be healthy against each project and exhausted by their sum. Its refusal to collapse six dimensions into one composite number is a choice that deserves to be argued with.