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P vs NP: Proof by Combat is a top-down roguelite shooter set on a living mathematical plane. Move, dodge, and fight through escalating lemmas while your weapon fires projectile paths shaped by equations.

Collect theorem mods that alter damage, fire rate, range, projectile streams, pass-through, and trajectory shape. A simple shot can become a sine wave, Lissajous curve, spiral field, or dense multistream proof depending on the parts you install.

Each run pushes the arena into stranger pressure patterns: lattice fields, implicit boundaries, theorem gates, enemy swarms, chain reactions, and reactive neon effects that turn combat into mathematical noise and light.

Survive long enough to unlock permanent tools, refine your build, and chase deeper proofs.