Weak representability of relation algebra 1311₁₃₁₆

Determine whether relation algebra 1311₁₃₁₆ is weakly representable, despite its non-representability.

Background

The paper proves that relation algebra 1311₁₃₁₆ is not representable by showing, using Ramsey-theoretic arguments and a SAT solver, that it has no representation on any finite number of points permitted by the relevant Ramsey bound. The author observes that these Ramsey-theoretic obstructions do not apply directly to weak representations, which may be viewed as partial edge-colorings or edge-colorings allowing an edge to receive multiple colors.

The unresolved question is therefore whether 1311₁₃₁₆ admits a weak representation even though it has no ordinary representation.