The Closing Technological Window: AI-Accelerated Search, Recursive Industrial Closure, and the Finite Horizon of Planet-Dependent Civilizations

This paper develops a unified dynamical model for the transition of a planet-dependent biological technological civilization into an autonomously reproducible technological lineage. The critical transition is defined not as crewed spaceflight or settlement, but as recursive industrial, informational, and organizational closure: an off-world system reaches a state Z* for which the reproduction operator satisfies F(Z*) = Z* without mandatory support from the origin planet. The model combines six mechanisms that are usually treated separately: growth of technological capability, growth of recursive complexity, loss of executable technological knowledge, recoverable civilizational shocks, irreversible absorbing risk, and normative constraints on admissible solution paths. Artificial intelligence enters as a structural accelerator of effective search, knowledge accessibility, coordination, and potentially physical automation. A Bayesian non-achievement layer then produces a counterintuitive result: if AI causes effective search to grow rapidly, persistent failure to achieve closure becomes informative rapidly as well. AI can therefore compress the calendar-time opportunity window rather than merely expand it. An illustrative Monte Carlo stress test for an Earth-2026 fast-track regime, using explicit broad priors rather than empirical frequencies, produces five structural outcomes: Fast Closure (22.96%), Delayed Closure (13.56%), Fast Negative Learning (33.81%), Complexity/Recovery Trap (16.64%), and Normative Non-Closure (13.03%). The numerical values are not forecasts. The robust conceptual claim is that under sufficiently strong AI-driven acceleration, outcome discrimination can concentrate on century rather than millennial timescales. The paper proposes measurable observables for progressively replacing the illustrative priors with empirical Earth data.