The integer Hom grading of the literal mesh category

noncomputable def MagnitudeConjecture.MeshCategory.homGrading {k : Type u} [Field k] {Q : Type v} [Quiver Q] [(x : Q) → Fintype ((y : Q) × (x ⟶ y))] (T : RightMeshData Q) : GradedCategory.HomGrading k (RawCategory T)

Mesh path length, extended by zero to negative degrees.