Reading’s sign-coherence separation conjecture

Reading’s conjecture concerns sign-coherence and separation phenomena in cluster theory, linking several categorifications. The available report describes a claimed resolution rather than a verified theorem.

Known results

An earlier preprint establishes ordinary $F$-invariant theory: for cluster monomials $u,u'$, $(u\mid\mid u')_{F}=0$ if and only if $uu'$ is a cluster monomial, and relates the $F$-, $\mathfrak d$-, and $E$-invariants.

September 8, 2026 claimed resolution

A preprint titled Partial F-invariants and cluster categorifications claims that mutation theory for partial $F$-invariants yields Reading’s separation conjecture and connects several cluster categorifications. The claim is presented as an unrefereed preprint and remains unverified.

Current status (as of September 2026): A preprint claims the conjecture is proved via partial $F$-invariants, but the result has not been independently verified; no counterexample is reported.