The airborne fraction, the share of anthropogenic $CO_2$ emissions that stays in the atmosphere rather than being absorbed by land and ocean, tracks the carbon cycle's response to human activity and informs the carbon budgets behind climate targets. Whether it is rising has been debated for two decades, with studies reaching opposite conclusions from near-identical data. Here we show the disagreement stems from two overlooked statistical problems, and resolve both. A few high-leverage years after the $1991$ Pinatubo eruption dominate the natural-variability correction, masking the trend, while treating land-use emissions as a single series discards the information needed to detect it. Folding this disagreement into uncertainty-derived weights, we find the airborne fraction has risen from $0.32-0.40$ in $1959$ to $0.47-0.50$ by $2024$, robust across estimators and specifications. This rise tightens every climate target: it shrinks the remaining carbon budget by $20-47$ $GtCO_2$, up to a year of global fossil emissions.

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