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Inside, the Flux Loft was a sensory dream. The lighting was set to "twilight drift": deep indigos and soft ambers that shifted as slowly as clouds. There were no DJs on a high stage. Instead, musicians were scattered among the crowd—a cellist in a hammock overhead, a handpan player sitting cross-legged on a pouf, a spoken-word artist whispering into a microphone wrapped in vines. There were no DJs on a high stage

This paper presents a detailed analysis of the Hybrid Symplectic-optimized, second-order, and symplectic-momentum (HSODA) method for numerical integration of Hamiltonian systems. We examine the theoretical properties of HSODA, including its stability, accuracy, and efficiency. The method is then applied to several benchmark problems in molecular dynamics and astronomy.