What was already known
The Courtade–Kumar inequality was previously proved only in restricted noise ranges or for special classes of Boolean functions, according to the manuscript’s prior-work section.
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 Courtade–Kumar conjecture for all Boolean functions and noise levels, with a sharper output-bias refinement.
Limitations
The statement concerns a uniform input cube and independent symmetric noise; the information bound is measured in bits.
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 a binary channel on a uniform discrete cube under independent symmetric noise, a noisy coordinate maximizes retained information at fixed initial information; for Boolean functions this gives I(f(X);Y) ≤ 1 − h₂(ε) at crossover probability 0≤ε≤1/2.
- 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