Detection of nuclear-decay $gamma$ rays provides a sensitive thermometer of nova nucleosynthesis. The most intense $gamma$-ray flux is thought to be annihilation radiation from the $beta^+$ decay of $^{18}$F, which is destroyed prior to decay by the $^{18}$F($p$,$alpha$)$^{15}$O reaction. Estimates of $^{18}$F production had been uncertain, however, because key near-threshold levels in the compound nucleus, $^{19}$Ne, had yet to be identified. This Letter reports the first measurement of the $^{19}$F($^{3}$He,$tgamma$)$^{19}$Ne reaction, in which the placement of two long-sought 3/2$^+$ levels is suggested via triton-$gamma$-$gamma$ coincidences. The precise determination of their resonance energies reduces the upper limit of the rate by a factor of $1.5-17$ at nova temperatures and reduces the average uncertainty on the nova detection probability by a factor of 2.1.
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