Minimal generating set conjecture for the integral Chow ring of the moduli stack of maps

Let $r$ be a positive integer and $d$ a positive odd number. The classes $4c_1,c_24$ generate the polynomial ring describing the presentation, and let $4\alpha_{1,0},\alpha_{1,1},\alpha_{p,0}4$ denote the relations defined in the paper, where $p$ ranges over primes dividing $d$. Minimal generating set conjecture.

$$A^*\left(\mathcal M_{0}\left(\mathbb P^r,d\right)\right)\cong \frac{\mathbb Z[c_1,c_2]}{\left(\alpha_{1,0},\alpha_{1,1},\{\alpha_{p,0}\mid p\text{ is a prime that divides }d\}\right)}.$$

Further, all the displayed relations are necessary, so they form a minimal set of generators for the ideal of relations. This conjecture refines the paper's presentation by removing redundant generators; it is motivated by computations, including the case of plane cubics, and remains unresolved in the supplied source.