What was already known
Earlier square-function and finite-scale triangular-form bounds had dependence on the number or range of scales, including hard-truncation bounds growing with log(R/epsilon) at the symmetric tuple. They did not give one pointwise majorant over both endpoints (companion manuscript introduction, Previous work, pp. 2–3).
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
Gives a scale-uniform pointwise maximal estimate at the symmetric triangular Hilbert exponent.
Limitations
The selected Lean scope covers the maximal L3×L3 to L^(3/2) bound and measurability on a common full-measure set. The first manuscript’s stronger annular r-variation estimate and principal-value consequences are outside this assessment.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the symmetric maximal estimate for all complex L3 inputs and a common full-measure set on which the truncated integrals are defined.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- The L^(3/2) norm of the supremum over all finite hard-truncation intervals of the triangular Hilbert transform is bounded by C times the L3 norms of arbitrary complex inputs.
- 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