From Immensity to Zero? Extending RAYOBETH Theory to Arms Races, Deterrence and the Disarmament Endgame

Global nuclear stockpiles rose from 6 warheads in 1945 to about 70,000 in 1986 and then fell by 83% under arms control. In recent years the decline has slowed almost to a halt, and the main treaty that limited the two largest arsenals expired in February 2026. The formal literature on arms races, built on Richardson’s linear model, explains how races start and when they are stable, but it does not explain why reductions stall short of zero or what it would take to finish them. This article extends RAYOBETH Theory, a conditional theory of generative systems, to that endgame. Stockpiles are modeled as a repertoire pushed up by rebuild pressure, whose elasticity with respect to the stockpile is β, and pulled down by reduction capacity, whose elasticity is φ. A disarmament endgame rule shows that reductions converge on a positive floor whenever φ exceeds β, and that zero is reachable only when part of reduction capacity does not shrink with the arsenal. A turning point theorem shows that when the stockpile has reached its floor, the total inventory keeps falling only while a backlog of retired warheads is dismantled, and then turns. A floor risk theorem shows that any positive floor with a positive annual risk of use implies eventual use with certainty. Applied to warhead estimates for nine states from 1945 to 2026, military spending for 11 rivalries and proliferation counts, the evidence supports the rule. The buildup elasticity was 0.58 (95% interval 0.53 to 0.63) for the Soviet arsenal, while the elasticity of reductions with respect to the stockpile was 1.69 (1.06 to 2.32) for the United States and Russia combined. The endgame elasticity was 1.00 from 1986 to 2010, a path to zero, and 0.85 (0.72 to 0.99) from 2011 to 2026, a path to a floor estimated at 7,880 warheads against 8,100 held. The world military stockpile reached its minimum of 9,272 in 2017 and has since risen to 9,745; the total inventory will stop falling around 2033 at about 10,100. Years with active verification saw reductions faster by 4.1 percentage points a year. None of 11 rivalries is in the explosive regime. The answer to the title’s question is that the world is not on a path to zero, and the theory names what would put it back on one.