What was already known
The plane’s conjectured positive-order range was known. In three dimensions, Gao, Wu, and Xi reached the strict range for max(p,p-conjugate) >= 22/7, leaving the central L3 case. The manuscript also notes Zipeng Wang’s proposed all-dimensional proof (Bochner–Riesz manuscript introduction, 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
Establishes the remaining central exponent and hence the full strict-order Bochner–Riesz multiplier range in three dimensions.
Limitations
The statement is strict in the order parameter and does not assert the order-zero ball multiplier bound. The separate OpenAI local-smoothing manuscript derives the same nonmaximal range by an independent route; this record counts the Bochner–Riesz theorem once and does not treat the two AI arguments as mutual proof checks.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
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 and independent route reviewed at the same claim scope for non-notifying local inclusion.
Read this published revision