Settlement-Based Accountability ----A Witness-Verifiable Ordering Framework

Settlement-Based Accountability is a formal framework for defining auditable ordering in systems where responsibility, rather than physical influence or execution order, is the primary concern. The framework distinguishes propagation from settlement:an input only becomes an event when it is explicitly accepted and irreversibly committed by the system. Each settlement must produce a publicly verifiable witness, from which an ordering relation is induced. This ordering represents responsibility-bearing structure, not physical causality. The core formalism is defined independently of implementation details. Irreversibility, conflict exclusion, and observer convergence are introduced explicitly as bridge assumptions, rather than being implicitly embedded in the logic. The framework is intentionally falsifiable, with concrete conditions under which it must fail. The theory is formalised in Coq, admits non-trivial concrete instances (including a transaction commit system), and is applicable to domains such as distributed systems, audit logs, AI decision accountability, and compliance infrastructures. It does not aim to redefine physical causation, but to provide a precise and verifiable notion of accountability ordering in complex systems.