As a quantum gravity cut-off, the species scale Λ s $\Lambda _s$ gets naturally compared to energy of scalar potential V in an EFT. In this note, scale, its rate | ∇ / $|\nabla \Lambda _s|/\Lambda and their field dependence, those is compared. To that end, string compactification leading with same properties as namely, being positive, starting at maximum bulk space going asymptotically zero fir...

1 Three Axioms for a Determinant Function Let d be a scalar-valued function on the space Mn×n of all n×n matrices. Let A1, A2, . . . , An be the n rows of an n×n matrix A. We will denote the value d(A) of A under the function d as d(A) = d(A1, A2, . . . , An), indicating that d is a scalar-valued function of n n-dimensional row vectors A1, A2, . . . , An. The scalar-valued function d is called ...