Exponentials conjectures and theorems

formal-conjectures · wikipedia · ams-33

**Four exponentials conjecture**
Let $x_0, x_1$ and $y_0, y_1$ be $\mathbb Q$-linearly independent pairs of complex numbers,
then some $e^{x_i y_j}$ is transcendental.

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/Four_exponentials_conjecture
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/Exponentials.lean
Local target: Corpus.WikipediaExponentials.four_exponentials_conjecture
Source SHA-256: 50416d678571435ba43b6456f6e3f0c7eda427a823d8861879e9f11eb0705857
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