Tatamibari Is NP-Complete

In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an m x n grid of cells, where each cell possibly contains a clue among ?, ?, ?. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing ? are square, rectangles containing ? are strictly longer horizontally than vertically, rectangles containing ? are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari