From Immensity to Infinite Irreversibility: Extending RAYOBETH Theory to Explain Climate Change and the Shrinking Space of Viable Futures

Climate research is divided among fields that study emissions budgets, technological learning, ecological tipping points and adaptation, yet all of them study the same object: a set of futures that remain possible and that shrinks as warming proceeds. This article extends RAYOBETH Theory, a conditional theory of generative systems, to give that object a formal definition, a measurable rate of decline and a condition under which its loss is infinite. Climate change is modeled as a race between two generative repertoires, a clean technology and adaptation repertoire that grows by recombination and learning, and a depleting feasible set whose attrition rises with temperature. Six results follow. A race theorem shows that each year of delay raises the decline rate required to meet a carbon budget hyperbolically, so the feasible set of policies closes in finite time. A peak fossil threshold states that fossil electricity falls exactly when clean additions exceed growth in demand. A weakest sector law shows that cumulative emissions and the date of net zero are governed by the slowest sector. An irreversibility theorem proves that hysteresis, the failure of cooling to restore a lost system, occurs if and only if regeneration has increasing returns (β > 1), and derives the tipping temperature in closed form. An infinite irreversibility theorem shows that the value foregone by an irreversible loss is unbounded exactly when the generative growth it forecloses is at least as fast as the discount rate, so that no finite compensation exists. An adaptation insurance result shows that diversified adaptation loops reduce collapse risk geometrically except against common shocks. Applied to public data, the theory finds that the 1.5°C budget requires cuts of 25% to 33% a year from 2026, about five times the largest annual fall ever recorded; that solar costs fall 30% with each doubling of cumulative output while deployment grows with an elasticity of 0.87, below the explosive threshold; that global fossil electricity reached the peak threshold in 2025; that five of ten emission sectors still grow; and that the probability of national clean energy takeoff rises from 3% to 79% with the existing share, a critical mass that only 30% of African countries have passed.