  Gated first-passage processes, where completion depends on both hitting a
target and satisfying additional constraints, are prevalent across various
fields. Despite their significance, analytical solutions to basic problems
remain unknown, e.g. the detection time of a diffusing particle by a gated
interval, disk, or sphere. In this paper, we elucidate the challenges posed by
continuous gated first-passage processes and present a renewal framework to
overcome them. This framework offers a unified approach for a wide range of
problems, including those with single-point, half-line, and interval targets.
The latter have so far evaded exact solutions. Our analysis reveals that
solutions to gated problems can be obtained directly from the ungated dynamics.
This, in turn, reveals universal properties and asymptotic behaviors, shedding
light on cryptic intermediate-time regimes and refining the notion of
high-crypticity for continuous-space gated processes. Moreover, we extend our
formalism to higher dimensions, showcasing its versatility and applicability.
Overall, this work provides valuable insights into the dynamics of continuous
gated first-passage processes and offers analytical tools for studying them
across diverse domains.
