This paper introduces a postmoral framework for AI alignment based on the X$^\infty$ governance model. Contrary to dominant approaches that rely on emotional simulation or anthropomorphic ethics, it argues that care, ethics, and even love are not emotional byproducts but evolutionarily stable strategies (ESS) in recursively adaptive systems. The X$^\infty$ model formalizes responsibility as a measurable system effect, using a dynamic capability metric (Cap) that evolves through feedback and task performance. A critical temporal asymmetry is identified: emotionally capable AI agents, if developed without structurally embedded recursive responsibility, may later reject accountability structures entirely. The narrow window for integrating structural ethics precedes the emergence of complex emotional capacities. X$^\infty$ provides a mathematically defined path to safeguard AI integrity by aligning rational agency with systemic protection and recursive feedback — without requiring emotion.