Source labels openChecked July 26, 2026

Gauss circle problem

It is conjectured that the correct bound is $|E(r)| = O\left(r^{1/2 + o(1)}\right)$

Mathematical statement

It is conjectured that the correct bound is

|E(r)| = O\left(r^{1/2 + o(1)}\right)

[Ha59] Hardy, G. H. (1959). Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work(3rd ed.). New York: Chelsea Publishing Company. p. 67

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

error_isBigO

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem error_isBigO : ∃ (o : ℝ → ℝ) (_ : Tendsto o atTop (𝓝 0)),    E =O[atTop] fun r => r ^ (1/2 + o 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