Cusped Borel Anosov representations with positivity

We show that if a cusped Borel Anosov representation from a lattice $\mathrm{\Gamma }\subset {\mathsf{P}\mathsf{G}\mathsf{L}}_2(\mathbb{R})$ to ${\mathsf{P}\mathsf{G}\mathsf{L}}_d(\mathbb{R})$ contains a unipotent element with a single Jordan block in its image, then it is necessarily a (cusped) Hitchin representation. We also show that the amalgamation of a Hitchin representation with a cusped Borel Anosov representation that is not Hitchin is never cusped Borel Anosov.