# Self-similar measure dimension workbench

Family 148: The entropy-rate dimension formula for self-similar measures. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Fractal-model researchers can compare entropy-rate dimension with overlap-aware composed-map laws.

## Applicability and commercial boundary

Random-map entropy rate may be hard to compute; exact overlaps and unequal ratios require careful representation. A formula does not supply a fast dimension estimator for arbitrary data.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Identify a finite computable overlap example and estimate entropy-rate calculation cost.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The entropy-rate dimension formula for self-similar measures on the line](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/main.pdf).