Mean value problem

formal-conjectures · wikipedia · ams-12

Given a complex polynomial $p$ of degree $d ≥ 2$ and a complex number $z$
there is a critical point $c$ of $p$, such that $|p(z)-p(c)|/|z-c| ≤ |p'(z)|$.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Mean_value_problem
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.ams.org/journals/bull/1981-04-01/S0273-0979-1981-14858-8/
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://doi.org/10.1016/0885-064X
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/MeanValueProblem.lean
Local target: Corpus.WikipediaMeanValueProblem.mean_value_problem
Source SHA-256: 71d7a5c0dfb616e4d4e42228478f97eafe9b047fea9df54dc24d3644f3a6b544
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record