Source labels openChecked July 26, 2026

Steiner Systems

Construct an $S(t, k, n)$ -Steiner system with $n > k > t > 5$ , $t < 10$ , and $n < 200$ .

Mathematical statement

Construct an $S(t, k, n)$ -Steiner system with $n > k > t > 5$ , $t < 10$ , and $n < 200$ .

No example of a Steiner system with $t > 5$ is known, despite a 2014 existence theorem by Keevash showing that such systems must exist for sufficiently large $n$ . Reference:* Large Steiner Systems

Statement source: Wikipedia 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

large_steiner_systems

Canonical source

Complete statement target, proof intentionally absentLean 4

def large_steiner_systems : LargeSteinerSystemWitness := 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 Large Steiner Systemsbackground Wikipediabackground