What was already known
Without exact overlaps, an entropy-over-Lyapunov dimension formula was known; Varjú’s survey formulated the extension using random-walk entropy rate when exact overlaps occur.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the entropy-rate dimension conjecture for finite real self-similar measures.
Limitations
The statement concerns lower Hausdorff dimension and does not assert absolute continuity.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every finite real self-similar probability measure with positive weights and nonzero contraction ratios of absolute value below one, dim_H μ=min(1,h_RW/χ), even with exact overlaps and unequal signed ratios.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision