Global Frobenius minimality for the ED degree of Segre–Veronese cones

For every Segre–Veronese cone and every positive definite real inner product
on its ambient partially symmetric tensor space, its Euclidean distance degree
is at least the degree for the Frobenius inner product. The argument uses a
basis of Chern–Schwartz–MacPherson classes indexed by product-linear sections.
Every corresponding signed Euler characteristic is at least one: a positive
multihomogeneous form has a coercive dehomogenization, while a logarithmic
differential on a resolution counts its critical points without boundary
zeros. The ED degree is a linear combination of these integers with nonnegative
coefficients. For the Frobenius form all the integers equal one. This proves
the inequality conjectured by Kozhasov, Muniz, Qi and Sodomaco (their
Conjecture 3.9).