Combinatorics
WithdrawnWithdrawn 6 Oct 2026
SOLVED_EXTERNALLY (the release coordinator confirmed that arXiv:2609.19123v1 and arXiv:2609.28404v2, Theorem 1, settle the finite hereditary-family case, which is the pinned target over finite ground types, with a public Lean formalization. This retirement did not independently rebuild that proof. See EXTERNAL-SOLUTIONS-2026-10-06.md.)
nobody has started
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«701»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos701.erdos_701" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ {X : Type} [Nonempty X] [Fintype X] (F : Set (Set X)),
IsLowerSet F → ∃ x, ∀ F' ⊆ F, F'.Intersecting → Cardinal.mk ↑F' ≤ Cardinal.mk ↑{A | A ∈ F ∧ x ∈ A}Original conjecture source: FormalConjectures/ErdosProblems/701.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.
Individual lemmas, special cases and supporting work, shown in their original scope.
Nothing has been published against this problem yet.