Weak asymptotic magnitude conjecture for compact Euclidean subsets

Let $\bar{\mathcal{C}}$ be a set of compact subsets of Euclidean spaces $\mathbb R^m$ that includes polyconvex sets, circles, and Cantor sets. For $A\in\bar{\mathcal{C}}$, let $|tA|$ denote its magnitude when defined, and let $\mu_i(A)$ be the $i$th intrinsic volume; write $\omega_i$ for the volume of the unit $i$-ball.

Weak magnitude conjecture. There is a unique function $P\colon\bar{\mathcal{C}}\to\mathbb R$ such that:

1. $|tA|$ is well-defined for $t\gg0$ and

$$|tA|-P(tA)\to0\qquad\text{as }t\to\infty;$$

2. $P$ satisfies the inclusion-exclusion principle; and
3. if $A$ is polyconvex, then

$$P(A)=\sum_{i\geq0}\frac{1}{i!\,\omega_i}\mu_i(A).$$

This conjecture proposes a common asymptotic description of magnitude for polyconvex sets and fractal examples such as circles and Cantor sets, extending the intrinsic-volume formula beyond the polyconvex setting. The source does not state a resolution, so its status remains open.