The selected coordinate of the arrow-cokernel radical section

theorem MagnitudeConjecture.BoundQuiver.StringPresentation.arrowCokernelRadicalSection_selectedCoordinate {k A Q : Type u} [Field k] [Ring A] [Algebra k A] [Fintype Q] [Quiver Q] [(x y : Q) → Fintype (x ⟶ y)] (P : StringPresentation k A Q) {x y : Q} (a : x ⟶ y) (z : ↥(Module.jacobson P.quotientCategoryAlgebraᵐᵒᵖ ↑(P.arrowCokernelFGObj a))) : (P.incomingArrowRangeFamilyRadicalLinearEquiv y).symm ((P.arrowCokernelRadicalSection a) z) ⟨x, a⟩ = 0

The canonical radical section has zero selected-arrow coordinate.