Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 148-01. The entropy-rate dimension formula for self-similar measures on the line
Manuscript map · lines 5245–5254
OpenAI@2026-10-07#rem:oai-p-148-01
Authors: OpenAI. Family 148.
Title: The entropy-rate dimension formula for self-similar measures on the line.
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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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