Mediation, Différance, and the V&V Asymmetry: A Discrete-Phenomenological Universal Form of the OODA Loop

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 explaining why the cycle takes that shape has been absent. We supply one by reading Derrida's différance as a discrete differential operator D on symbolic content, paired with aggregation, accumulation, and a non-commuting pair (Vver, Vval). The resulting fixed-point iteration is the universal form of which the OODA loop is one special case. Three axioms carry it: C1, the recursive and constitutive structure of signs; C2, the irreversibility of mediated observation; and C3, the finite closure of any decision system. C3 is new in this version and is not a further assumption about the world: a process that does not close in finite tempo is not a decision system. Its consequence is the paper's central claim. C1 and C2 make the abstraction ladder unbounded upward and downward alike, and neither yields a bound; C3 does. Scale separation is therefore not a property of the world but a consequence of acting finitely. Selection of a working window within those bounds remains what the “Decide” operator enacts by an act of valuation, not a theorem awaiting proof. The treatment is deliberately discrete, in the engineering-pragmatist line of Bridgman, Peirce, and Quine. The payoff is a diagnostic protocol for cross-domain decision systems whose failure modes are named in the construct itself. Note on this version. v3 changes the axiom system of v1–v2. An axiom of finite closure (C3) is stated explicitly; v2's §4 used that premise without stating it. The v2 claim that scale separation was eliminated as an axiom is withdrawn and replaced by the weaker and correct claim that it is derived in part from finite closure. v2 also announced the Dual Impossibility as a Conjecture whose proof was deferred to a companion paper; that deferral is withdrawn. Readers citing the Proposition of §4 should cite this version. Files: letter.pdf / letter.tex are the English edition, which is canonical. letter_bilingual.pdf / letter_bilingual.tex are the parallel EN/JA edition.