This paper argues that at a certain point in research toward AGI, the problem may become well-enough theorized that a clear roadmap exists for achieving it, such that a Manhattan Project-like effort could greatly shorten the time to completion. If state actors perceive that this threshold has been crossed, their incentives around openness and international cooperation may shift rather suddenly, with serious implications for AI risks and the stability of international AI governance regimes. The paper characterizes how such a 'runway' period would be qualitatively different from preceding stages of AI research, and accordingly proposes a research program aimed at assessing how close the field of AI is to such a threshold - that is, it calls for the formulation of a 'roadmap to the roadmap.'