A proven lower bound on the area of the Mandelbrot set

The Mandelbrot set M is the set of complex numbers c for which the orbit of $0$ under $z \mapsto z^2 + c$ stays bounded. Its area is unknown. Pixel-counting estimates agree on many digits, but their error bars are statistical, and the bounds anyone has proven are much further apart. This work proves that the area of M is greater than . The proof is a computation in ball arithmetic. It certifies a hyperbolic component of M of a stated period at each of approximate centers, and bounds each one's area from below with the area theorem applied to the inverse of its multiplier map. With mirror images, distinct components enter the sum. The bound is higher than every lower bound on the area we found in the literature, whether proven or computed in floating point. Anyone can check the proof by running code/run.