Interval-certified bounds on the area of the Mandelbrot set
Year: 2026
Type: preprint
Abstract: Interval-certified bounds on the area of the Mandelbrot set: $1.5064820 \le \mu(M) \le 1.5643498$. The lower bound sums certified lower bounds on the areas of 3,352,592 hyperbolic components (Krawczyk-isolated centres, exact periods, the first three terms of the area formula for the inverse multiplier map). The upper bound is a depth-17 dyadic quadtree minus cells certified exterior by escape or a Koebe-type distance estimate with explicit truncation bounds. All arithmetic is Arb ball arithmetic, and both certificates were audited in full by independently written checkers. The lower bound exceeds every published lower bound we know of; the upper bound improves on Fisher and Hill (1993) and on every certified upper bound we found, but not on Förstemann's uncertified 1.53121. Version 1: an independent review of the mathematics is pending.
Author: Lindheim, Björn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225731689
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