Diskoid representation and correspondence conjecture for abstract key polynomials

Let $b[?]$ be a valuation on $K[X]$ and let $Qb[?]K[X]$ be an abstract key polynomial for $b[?]$, with $b[?](Q)b[?]b[?]b[?](K^b[?])$. A diskoid is a subset $b[?](Q)b[?]b[?]$ whose polynomial-value minima represent the truncation along $Q$. Diskoid representation and correspondence conjecture. There exists a diskoid $b[?](Q)$, which is a finite union of balls, such that for every $fb[?]K[X]$ the minimum exists and satisfies

$$b[?]_Q(f)=b[?]_{xb[?]b[?](Q)}b[?](f(x)).$$

Moreover, there is a bijective correspondence between residually transcendental valuations over $K[X]$ that can be given by a key polynomial and the corresponding diskoids. This conjecture proposes a geometric realization of truncations and a classification of the relevant valuations by finite unions of balls.