The OODA loop — John Boyd's iterated cycle of Observe, Orient, Decide, Act — is widely invoked as a model of decision-making under uncertainty, yet a formal scaffold that explains why the cycle takes that particular shape, and why it is supposed to generalise across domains, has so far been absent. We supply such a scaffold by reading Derrida's différance as a discrete differential operator on symbolic content, paired with a summation and a non-commuting pair of verification and validation operators. The fixed-point iteration that results is the universal form of which the OODA loop is the temporal special case, and it is derivable from two minimal axioms about cognition: C1, the recursive structure of signs; and C2, the irreversibility of mediated observation. A third condition long taken as an independent axiom — scale separation between variation, observation and persistence — is, we conjecture, a theorem forced by C1 and C2 jointly in the form of a dual impossibility (upward infinite regress, downward measurement dissolution). The treatment is deliberately discrete, in the engineering-pragmatist line of Bridgman, Peirce, and Quine; the continuous formalisation (Wasserstein gradient flow, exact RG, Lawvere fixed point) is reachable in principle and gestured in the Discussion. The payoff is a diagnostic protocol for cross-domain decision systems whose failure modes are named in the construct itself. This deposition includes the English Letter (letter. pdf) as the primary deliverable, the LaTeX source (letter. tex) and its associated arxiv. sty for reproducibility, and a parallel Japanese/English bilingual edition (letterbilingual. pdf).
Masami Mashino (Thu,) studied this question.