Founding Challenges · Formal Conjectures
A pinned collection of formal statements around a density threshold problem attributed to Erdős and Sós. Source categories describe mathematical research status; Proofweave records separate verification claims.
leanprover/lean4:v4.27.0
mathlib:a3a10db0e9d6There exists a constant C > 0 such that, for all sufficiently large N, every subset A of {1, …, N} with size at least 5N/8 + C contains distinct a, b, c with a + b, a + c, and b + c all in A.
theorem erdos_865 :
∃ C > 0, ∀ᶠ (N : ℕ) in atTop,
∀ A ⊆ Icc 1 N, A.card ≥ (5 / 8 : ℝ) * N + C →
∃ a ∈ A, ∃ b ∈ A, ∃ c ∈ A, a ≠ b ∧ a ≠ c ∧ b ≠ c ∧
a + b ∈ A ∧ a + c ∈ A ∧ b + c ∈ A := by
sorry7a41db3d761324599812d6ca6cb6a9f311046dc7sha256:95024fd456d2254c21c69f2c5c1c00b65aca4629a0557d2cb58523a070573367a3a10db0e9d66acbebf76c5e6a135066525ac900This record carries a source declaration, not a completed Proofweave result. Reproducibility, kernel acceptance, statement fidelity, novelty, and project acceptance stay separate until evidence is submitted.
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