The Category Mistake of Cislunar Time: Why NASA Cannot Synchronize What Doesn't Exist

In April 2024, the White House directed NASA to establish Coordinated Lunar Time (LTC) by December 2026. The programme assumes that a unified time standard can be constructed by deploying atomic clocks on the lunar surface, computing relativistic corrections, and distributing synchronized time via LunaNet. This paper argues that the entire enterprise rests on a category mistake in the sense introduced by Ryle and developed by Spekkens in quantum foundations: it treats "synchronized time" as an ontic entity - something that exists independently and can be transmitted from authoritative sources to dependent receivers - when it is in fact an epistemic construct: a model-dependent representation of observer-relative clock relationships. We analyze the cislunar time programme through the lens of Forward-In-Time-Only (FITO) assumptions, Spekkens' Leibnizian operationalism, the Wood-Spekkens fine-tuning argument, and the distinction between ontic and epistemic interpretations that has dissolved long-standing puzzles in quantum mechanics. We show that the same conceptual move that dissolves quantum "mysteries" - recognizing what is epistemic versus what is ontic - dissolves the apparent coherence of the cislunar time programme and reveals it as an engineering project built on a philosophical confusion. We sketch a transactional alternative grounded in bilateral atomic interactions rather than unidirectional time distribution.