Two-Layer Transactions as a Commitment Technology Long-Term Layer Settlement and a Definability Gate for Event Studies

In capitalized economies, transactions affect not only contemporaneous exchange (payment and delivery) but also the allocation of long-run residual claims through capitalization. Yet most institutional “crediting” for long-run value—points, cashback, CLV metrics, or governance narratives—remains mutable and non-auditable, and therefore fails to constitute settlement. This paper formalizes Two-Layer Transactions (TLT) and Long-Term Layer Settlement (LTL), treating settlement as a committed information channel. LTL is an acceptance-grade predicate requiring: (i) existence of a claim object, (ii) third-party replayability, (iii) verifiable finality via publicly visible forward-linked corrections (no silent retroactive rewrites), (iv) hard-budget auditability under a version-bound issuance identity, and (v) visible version binding with activation-time discipline. We derive two feasibility results under hard budgets. If the long-term verifiable object is strictly more Blackwell-informative than price-layer observables, LTL strictly expands the hard-budget feasible set; under state-dependent participation constraints, no policy measurable only in price-layer observables can generally substitute for LTL. Methodologically, we identify a prior gate for event-study/DiD designs: admissible semantics-based treatments must be adapted, i.e., Dt = d(θt) must be Ft-measurable. Without visible versioning and verifiable finality, treatment timing can be non-adapted and hence not well-defined; with committed semantics, it is well-defined. A characterization theorem links externally auditable long-term settlement with definability to LTL with activation discipline. The analysis is value-neutral and scoped to user-facing, verifiable-event environments.