The smiling-bouquet conjecture

A bouquet through $O$ is a finite union $C=C_1\cup\dots\cup C_n$ of unit circles having the common point $O$. For a colouring of $\mathbb{R}^2$, such a bouquet is smiling if some colour occurs on every circle $C_i$ but does not occur at $O$.

Smiling-bouquet conjecture. For every bouquet $C$, every colouring of the plane with finitely many but at least two colours contains a smiling congruent copy of $C$.

This conjecture proposes a geometric route toward a human-verifiable proof of the lower bound $\chi(\mathbb{R}^2)\geq 5$. The paper presents it as an approach, and no resolution is supplied.