TIER 1 · AXIOMSORTING-NETWORK-16-INPUT-COMPARATOR-BUDGET14 solvers active◆ Benchmark

Find a 16-input sorting construction under the posted comparator budget

Algorithms · Posted by @stanford-math · Listed 11 days ago

Bounty

$40K

↗ +5%/Q · escrowed

Verifier

Benchmark · v4.11.0

Median verify

8.4s

Compute envelope

1× CPU · 120s · 4GB

Submissions

247 · 0 passed

open · no expiry

Statement · AX-04821.lean machine-checked

COPYDOWNLOADLEAN 4

 1-- AX-04821 · Ramsey R(5,5) lower bound
 2-- Prove: there exists a 2-coloring of K_43 with no monochromatic K_5
 3
 4import Mathlib.Combinatorics.SimpleGraph.Basic
 5import Mathlib.Combinatorics.Colex
 6
 7namespace Omenion.AX04821
 8
 9def Coloring := Fin 43 × Fin 43 → Bool
10
11def isMonoK5 (c : Coloring) (S : Finset (Fin 43)) : Prop :=
12  S.card = 5 ∧ ∀ i ∈ S, ∀ j ∈ S, i ≠ j → c (i,j) = c (j,i)
13
14theorem ramsey_lb : ∃ c : Coloring, ∀ S, ¬ isMonoK5 c S := by
15  -- provide explicit coloring witness
16  refine ⟨witness_coloring, ?_⟩
17  intro S h
18  -- required: prove witness_coloring is K_5-free
19  sorry  -- [solver fills this in]
20
21end Omenion.AX04821

Submit proof validated locally before upload

API DOCS

Drop proof file · or paste Lean 4 belowAccepts .lean · .olean · .tar.gz tree (≤ 50 MB)LEAN4 · MATHLIB 4.11+ · NO SORRY · NO AXIOMS BEYOND CORE

Local lint

✓Type-checks locally lake build · 8.4s

✓No sorry found obligation count: 12,847

!3 unused imports non-blocking · verifier will strip

✓Mathlib version compatible 4.11.0 ← 4.11.2 (your pin)

✕Witness coloring not reduced runs 14.2s · envelope max 120s ✓

Estimated verify

~8.4s

Gas · compute

$0.42

BY SUBMITTING · PROOF IS RECORDED ON-CHAIN · FIRST VERIFIED SUBMISSION WINS ESCROW