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. The paper derives closed-form equations for the steady-state money supply, proves equilibrium uniqueness and global stability, and identifies three structural properties. First, nominal government revenue is algebraically invariant to velocity—a consequence of the mechanism’s construction, not an empirical finding. 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. Monte Carlo simulation across five parameters (10,000 draws) yields 69.7% feasibility across all criteria and 98.4% for revenue adequacy. 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.