The observed baryon asymmetry of the universe requires combined Charge Parity ($\mathcal{CP}$) violation, likely more than the Standard Model contains. Simultaneously, the scarcity of antimatter makes direct tests of $\mathcal{CP}$-violation difficult to perform in a laboratory, and many tests search for time-reversal violation ($\mathcal{T}$) and use combined $\mathcal{CPT}$-symmetry to equate this with $\mathcal{CP}$-violation. Direct searches involving matter and antimatter are robust and insensitive to false signals like final state interactions. Positronium is a bound state of an electron and a positron, and can be copiously produced in a laboratory. This motivates the design and construction of a dedicated detector array to search for $\mathcal{CP}$-violation in the 3-$\gamma$ decay of ortho-positronium, with a target sensitivity of $10^{-5}$ for the measured asymmetry, a factor of 10 improvement on current limits.The experiment will require tensor polarized positronium, which can be achieved by utilizing a magnetic field. The sensitivity target will require high statistics and large detector acceptances. To these ends the array will feature three rings of $\gamma$-detectors with 16 crystals in each ring. The detector array and all readout electronics will be constructed to fit within the warm bore of the FRIB Positron Polarimeter magnet. The detector geometry and placement were studied in Monte-Carlo simulations in order to optimize the array for this specific experiment. This allowed optimization of detector size, shape, array geometry, and energy and multiplicity cuts.Extensive tests of the crystal shape and geometry were performed, these characterized and removed a geometric light collection distortion. A test stand for optimization of positronium formation was constructed. Tests of multiple powders showed that using chunks of silica-aerogel could achieve a lifetime of 135 ns, and up to 40\% formation fraction. This was then placed in a three crystal demonstrator to prototype the online DAQ. The three crystal and start detector combination was able to remove backgrounds and extract the continuous 2-D energy distribution of ortho-positronium decay. The direct comparison of measured count asymmetries with theory motivated quantities (Lagrangian parameters, mixing coefficients, etc.) is non-trivial, and cannot be done in a model-independent way. A detailed discussion of removal of detector acceptances and efficiencies is presented in the context of a specific model. This further required extension of the theory analysis to incorporate the effects of a static magnetic field, which induces non-trivial time dynamics of the different angular distributions. This clarifies some inconsistencies in the literature on the time dependence of the asymmetry in a magnetic field. The detector array is under construction and will be able to reach the target sensitivity with 35 days of continuous runtime.
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