Although 3D Gaussian Splatting (3DGS) supports real-time rendering, training relies on offline geometry, long-horizon densification, and memory-intensive differentiation. We cast post-capture static-scene training as resource-constrained finite-horizon optimization, where terminal quality depends jointly on the initial representation and reference-consistent gradient execution. To the best of our knowledge, PocketGS is the first publicly documented pipeline to complete geometry construction, Gaussian initialization, and 3DGS optimization on a commodity smartphone. Its I, G warm start combines refined poses, a filtered dense prior, and surface-aligned anisotropic Gaussians. Its T operator replays compositing interactions and scatters gradients to canonical parameters, matching a numerical reference at the reported precision. Controlled 500-step experiments on LLFF, Mip-NeRF 360, and MobileScan show high-quality reconstruction at the device horizon. Across MobileScan, every scene remains below 3 GB peak memory and post-capture processing averages 255.2 s, enabling an on-device capture-to-render workflow. Separate 30k experiments characterize native-schedule behavior.

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