Source labels openChecked July 26, 2026

Open Quantum Problem 35: existence of absolutely maximally entangled pure states

Open Quantum Problem 35: classify all pairs $(n,d)$ with $n \ge 2$ and $d \ge 2$ for which an $\mathrm{AME}(n,d)$ state exists.

Combinatorics AMS 5 AMS 15 AMS 81 AMS 94

Mathematical statement

Open Quantum Problem 35: classify all pairs $(n,d)$ with $n \ge 2$ and $d \ge 2$ for which an $\mathrm{AME}(n,d)$ state exists.

Statement source: Open Quantum 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

oqp_35

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem oqp_35 :    {nd : ℕ × ℕ | 2 ≤ nd.1 ∧ 2 ≤ nd.2 ∧ ExistsAME nd.1 nd.2} = answer(sorry) := 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