Preprint in the OpenAI Math release
The entropy-rate dimension formula for self-similar measures on the line
OpenAI
Abstract
We prove that the Hausdorff dimension of every finite real self-similar measure equals the minimum of one and its random-walk entropy rate divided by its Lyapunov exponent. Exact overlaps are allowed, and the contraction ratios may be unequal and negative. This resolves the entropy-rate dimension conjecture.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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