tl;dr: A Factorio player models the game's Quality upcycling loops using matrix math, representing item throughput as vectors and crafting/recycling/filtering steps as transition matrices, then solves the resulting equilibrium equations (Ax=b) via Gaussian elimination for exact rational results rather than iterative approximations. The approach handles "washing," crafting+recycling upcycles, and 15-dimensional asteroid reprocessing. The author implemented it as an interactive web calculator (factoqual.grebedoc.dev) using TypeScript, VanJS, and a rational-number library after initially prototyping in Rust.