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The DECam Ecliptic Exploration Project (DEEP) is a deep survey of thetrans-Neptunian solar system being carried out on the 4-meter Blanco telescopeat Cerro Tololo Inter-American Observatory in Chile using the Dark EnergyCamera (DECam). By using a shift-and-stack technique to achieve a mean limitingmagnitude of $r \sim 26.2$, DEEP achieves an unprecedented combination ofsurvey area and depth, enabling quantitative leaps forward in our understandingof the Kuiper Belt populations. This work reports results from an analysis oftwenty 3 sq.\ deg.\ DECam fields along the invariable plane. We characterizethe efficiency and false-positive rates for our moving-object detectionpipeline, and use this information to construct a Bayesian signal probabilityfor each detected source. This procedure allows us to treat all of our KuiperBelt Object (KBO) detections statistically, simultaneously accounting forefficiency and false positives. We detect approximately 2300 candidate sourceswith KBO-like motion at S/N $>6.5$. We use a subset of these objects to computethe luminosity function of the Kuiper Belt as a whole, as well as the ColdClassical (CC) population. We also investigate the absolute magnitude ($H$)distribution of the CCs, and find consistency with both an exponentiallytapered power-law, which is predicted by streaming instability models ofplanetesimal formation, and a rolling power law. Finally, we provide an updatedmass estimate for the Cold Classical Kuiper Belt of $M_{CC}(H_r < 12) =0.0017^{+0.0010}_{-0.0004} M_{\oplus}$, assuming albedo $p = 0.15$ and density$\rho = 1$ g cm$^{-3}$.

The DECam Ecliptic Exploration Project (DEEP): V. The Absolute Magnitude Distribution of the Cold Classical Kuiper Belt