Source labels openChecked July 26, 2026

Erdős Problem 872: Ii

Erdős Problem 872, part (ii) (strong form): for every $\epsilon > 0$ , the game length is at least $(1-\epsilon) \cdot n / 2$ for all sufficiently large $n$ .

Combinatorics AMS 5 AMS 11 AMS 91

Mathematical statement

Erdős Problem 872, part (ii) (strong form): for every $\epsilon > 0$ , the game length is at least $(1-\epsilon) \cdot n / 2$ for all sufficiently large $n$ .

Status note: the forum thread (April-May 2026) records Shortener strategies giving $L(n) \leq (23/48 + o(1)) \cdot n$ (described in the thread as accepted as correct, with a Lean formalization in progress) and a claimed $L(n) \leq 0.19 \cdot n$ , either of which would answer this question negatively under the Prolonger-first convention. Neither is published, so the statement is recorded here as the original Erdős question.

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

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

erdos_872.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_872.parts.ii : answer(sorry) ↔    ∀ ε > (0 : ℝ), ∀ᶠ n in atTop, (L n : ℝ) ≥ (1 - ε) * n / 2 := 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 erdosproblems.com/872background erdosproblems.com/forum/thread/872background