What was already known
Earlier nonuniversality results covered sequences whose consecutive ratios tend to one and patterns with stronger additive structure. The single dyadic sequence has persistent geometric gaps and was not covered by those criteria (companion manuscript introduction, Related results, pp. 1–2).
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
Proves that the dyadic sequence is not measure universal, a geometric-progression case of the Erdős similarity conjecture.
Limitations
The selected theorem treats only ratio 1/2. The first manuscript’s assertion for every fixed ratio q in (0,1), and the full conjecture for arbitrary infinite sets, are outside the Lean scope.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note formalizes compact near-full-measure dyadic avoidance for every translation and nonzero dilation, including both signs.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every eta in (0,1), a compact set E subset [0,1] of measure greater than 1−eta contains no affine copy of {2^(−n):n>=1} for any translation and nonzero real dilation.
- 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 companion manuscript, attribution, prior-work, and exact Lean-scope review for non-notifying local inclusion.
Read this published revision