What was already known
Vinogradov conjectured the p^δ bound. The 2017 theorem of Bhargava, Ivanyos, Mittal and Saxena gives a polylogarithmic bound under a uniform weak-GRH zero strip, while GRH gives a stronger logarithmic-squared bound. No unconditional uniform strip of the required fixed width had been established.
AI involvement
OpenAI is credited as author of the manuscript and states that an internal frontier model produced the release’s mathematics. The specific corollary is an AI-authored deduction combining the manuscript’s claimed new zero-free theorem with an earlier human theorem; task-only autonomy is undocumented.
OpenAI is the author and credits its internal frontier model with the mathematics. This corollary is an AI-authored deduction from the manuscript’s asserted 7/8 zero-free theorem and the earlier Bhargava–Ivanyos–Mittal–Saxena result; individual human inputs are not fully disclosed.
- Supporting source (openai.com) — Mathematics release and model attribution
Importance
If the new zero-free theorem is correct, this corollary establishes Vinogradov’s classical conjecture and a polylogarithmic bound on least quadratic nonresidues.
Limitations
Corollary 1 derives the bound from the same manuscript’s claimed uniform Dirichlet zero-free half-plane Re(s)>7/8 and the earlier Bhargava–Ivanyos–Mittal–Saxena theorem. Its validity therefore depends on that separately curated zero-free theorem. The published Lean scope explicitly excludes the paper’s later applications, including this corollary; no completed check of the corollary itself was found.
Technical verification
The manuscript derives the nonresidue bound from its asserted 7/8 zero-free theorem and Bhargava–Ivanyos–Mittal–Saxena Theorem 6.7. The official Lean scope explicitly excludes later applications, including this corollary; a completed direct check was not identified.
Human understanding
No named human explanation of the new zero-free argument underlying this corollary was identified. The deduction through the published conditional theorem is stated plainly, but that alone does not document human understanding of the central new reasoning.
Correction and publication history
Distinct Corollary 1 claim, inherited zero-free dependence, prior theorem, attribution and exclusion from Lean scope reviewed for non-notifying local inclusion.
Read this published revision