The bounded negativity conjecture for plane curves with rational components

Let $K$ be a fixed algebraically closed ground field. A multiplicity sequence is a positive integer sequence $(d,m_1,\ldots,m_r)$ arising from a reduced plane curve of degree $d$, with the $m_i$ recording the multiplicities of all its singular points, including infinitely near points. A curve has multiplicity bound $m$ if every recorded multiplicity satisfies $m_i\leq m$. Bounded negativity conjecture for rational components. There are only finitely many multiplicity sequences arising for reduced plane curves over $K$ with multiplicity bound $m=3$, having no points of multiplicity $2$ and whose components are all rational.

This is proposed as a characteristic-free replacement for bounded negativity in a setting involving plane curves with controlled singularities. The source presents it as consistent with current knowledge; its status is not otherwise established there.