OpenFrontiers
Join
← Back to the index
OP-12126Status unassessedAnalysis

de Bruin-Sharma Problem (AlphaEvolve problem 24)

de Bruin-Sharma Problem (AlphaEvolve problem 24). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 30C10 · Polynomials and rational functions of one complex variable

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

For n≥4n \geq 4, let Ω(n)\Omega(n) be the set of pairs (α,β)∈R+2(\alpha,\beta) \in \mathbb{R}_+^2 such that, whenever PP is a degree nn polynomial whose roots z1,…,znz_1,\dots,z_n sum to zero, and ξ1,…,ξn−1\xi_1,\dots,\xi_{n-1} are the critical points (roots of P′P'), that

∣ξ1∣4+⋯+∣ξn−1∣4≤α(∣z1∣4+⋯+∣zn∣4)+β(∣z1∣2+⋯+∣zn∣2)2.|\xi_1|^4 + \dots + |\xi_{n-1}|^4 \leq \alpha (|z_1|^4 + \dots + |z_n|^4) + \beta (|z_1|^2 + \dots + |z_n|^2)^2.

What is Ω(n)\Omega(n)?

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Background

The repository status chart does not categorize this problem. See Section 6.9, in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

The repository page records no bounds for this problem.

References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — de Bruin-Sharma Problem (AlphaEvolve problem 24) linkApache-2.0 (repository license); problem pages reproduced with attribution.

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.