What was already known
Kraetzer predicted B_b(p)=p²/4 for |p|≤2. Earlier rigorous upper bounds at p=−1 were 0.403 and 0.388, above 1/4.
AI involvement
OpenAI is credited as author and attributes the manuscript and Lean artifact to an internal model; individual human direction is not detailed.
The OpenAI-authored strict-bound manuscript and associated Lean theorem are identified as model-produced results in the release; no individual-session autonomy is established.
Importance
The strict p=−1 bound contradicts the predicted universal formula.
Limitations
It does not determine the full spectrum or the p=1 value. The separate Brennan inverse-square endpoint is a different result.
Technical verification
The cited Lean main theorem states the uniform inverse-first-power estimate, B_b(−1)<1/4 and failure of the universal Kraetzer identity. The repository reports Lean formalizations as verification artifacts. This is source-reported machine checking; the project was not rebuilt here.
Formal checking
Lean theorem OAI.StrictInverseFirstPower.main assembled from formalized endpoint results
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- A uniform inverse-first-power bound implying boundedSpectrum(−1)<1/4 and failure of Kraetzer's identity
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named person's explanation of the critical-point pairing and strictness argument is documented. Few is the evidence default, not a claim that experts cannot understand it.
Correction and publication history
The strict p=−1 bound contradicts the predicted universal formula.
Read this published revision