Source labels openChecked July 26, 2026

Exponentials conjectures and theorems

The four exponential conjecture would imply that for any irrational number $t$ , at least one of the numbers $2^t$ and $3^t$ is transcendental.

Number theory AMS 11

Mathematical statement

The four exponential conjecture would imply that for any irrational number $t$ , at least one of the numbers $2^t$ and $3^t$ is transcendental.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

two_pow_three_pow_transcendental

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem two_pow_three_pow_transcendental (t : ℝ) (h : Irrational t) :    Transcendental ℚ (2 ^ t : ℝ) ∨ Transcendental ℚ (3 ^ t : ℝ) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipediabackground