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Modern industrial civilization operates above a critical thermodynamic threshold: an Energy Return on Investment (EROI) of approximately 12:1, below which the complex service economies that sustain advanced research and development become unviable. Climate change imposes a compounding ``survival basket tax'' on global output, diverting an increasing share of productive capacity toward food, water, cooling, and infrastructure maintenance. We argue that these two dynamics interact to create a \emph{closing window} for the development and deployment of commercial-scale fusion energy---which both decarbonizes the economy and restores the energy surplus needed to sustain advanced innovation. Using a stochastic simulation over the period 2026--2100, we show that the timing of fusion commercialization is the single strongest determinant of long-run economic outcomes---more influential than climate sensitivity, institutional resilience, baseline growth rates, or pre-fusion clean energy (solar, wind, fission) even under quite optimistic assumptions. Under one plausible calibration, each year of delay costs on the order of 100 trillion dollars in expected terminal GDP; the annual marginal cost of delay is already steep in 2026, and remains so through the late 2030s. The vast majority of paths pass through a period where things get worse before they get better; fusion timing determines the depth and duration of the trough. Approximately 25% of paths fail to recover to 2026 baseline levels by 2100, while $\sim$50% reach a state of abundance ($>$500T GDP). These specific figures are sensitive to parameter choices and should be interpreted as order-of-magnitude estimates rather than precise forecasts, but the \emph{structural} finding is robust: across a wide range of calibrations, fusion timing dominates all other variables, the window is narrow, and no adjustment to non-fusion parameters compensates for late fusion. This strongly suggests that fusion energy policy should be understood not as one priority among many, but as the critical-path variable governing whether civilization achieves escape velocity from thermodynamic decline. The policy implication is a fundamental reorientation of priorities: massive, sustained and strategically targeted investment in fusion commercialization, alongside institutional resilience measures that keep the window open long enough for deployment to succeed.