Conjectured initial values of the ML-degree polynomial

Let $\phi(n,d)$ denote the polynomial that gives the dimension of the space of quadrics in $n$ variables passing through $d$ general points and tangent to $\binom{n+1}{2}-d-1$ general hyperplanes. Initial-value conjecture.

$$\phi(0,d)=(-1)^{d-1},\qquad \phi(-1,d)=(-2)^{d-1}.$$

These formulas extend the enumerative-geometric polynomial $\phi(n,d)$ to the initial nonpositive values $n=0$ and $n=-1$, following the program of combinatorial reciprocity. The source notes that these formulas were previously conjectured; their resolution is not established in the supplied context.