Beyond Green Efficiency: Sustainability Closure, Observation Sufficiency, and Environmental Ordering Under Incomplete Metrics

Efficiency is easy to measure; sustainability is not. A system may look greener at deployment while hidden demand, infrastructure, replacement, and resource interactions reshape future environmental consequences. We develop Sustainability Closure Theory (SCT), which treats sustainability assessment as an observation-sufficiency problem. SCT defines a declared observation interface, reachable consequence set, and finite-horizon sustainability closure, and proves a restricted-observation non-identifiability theorem: observationally indistinguishable systems can generate different future closures, making universally correct inference impossible from the restricted observation alone. An endogenous-demand construction yields a closed-form environmental reversal boundary, verified exactly in eight analytical cases. A 676-case controlled synthetic sweep reveals increasing disagreement between restricted efficiency judgments and closure-based assessment as the horizon expands. Under matched full information, SCT and a consequential/dynamic assessment comparator are exactly equivalent, establishing SCT as a diagnostic of information sufficiency rather than a replacement for lifecycle assessment. External analysis using open U.S. AI-server data identifies equal-observation records with distinct location-conditioned PUE/WUE values and four cross-resource ordering reversals. Across 25,000 sensitivity trials, at least one ordering conflict persists with probability 0.997–0.998. The results expose a fundamental distinction: improving what we measure does not establish sustainability unless what we measure is sufficient to identify the consequences we claim.