This paper presents a monetary architecture that unifies money creation, supply regulation, government funding, and universal basic income (UBI) into a single mechanism defined by six rules and five parameters. Money is created through universal individual claims, destroyed through a uniform transaction burn, and expires if inactive. Government revenue arises from two protocol-level mechanisms—a burn share and a topper—without requiring external taxation. Cross-denomination transfers settle through swap matching, and the creation event is protocol-protected: no entity can redirect or prevent it. The paper derives closed-form equations for the steady-state money supply, proves equilibrium uniqueness and global stability, and identifies three structural properties. First, steady-state nominal government revenue is algebraically invariant to velocity—a consequence of the mechanism's construction, not an empirical finding (during transitions between steady states, revenue varies). Second, the system is counter-cyclical by construction: reduced economic activity expands the money supply as destruction falls while creation continues unchanged. Third, the burn rate functions as a monetary policy instrument with negligible fiscal side effects, decoupling monetary and fiscal functions. At an illustrative US calibration, the steady state yields money supply $29.5 trillion, annual government revenue $10.1 trillion and a lending pool comparable to the current US benchmark. The contribution is the existence proof: no prior work has demonstrated that a self-funding UBI admits a stable mathematical equilibrium. All results are computationally verified and independently reproducible.