Cusped Borel Anosov representations with positivity

We show that if a cusped Borel Anosov representation from a lattice \(\Gamma \subset \textsf{PGL}_2({{\,\mathrm{\mathbb {R}}\,}})\) $\mathrm{\Gamma }\subset {\mathsf{PGL}}_2(\mathbb{R})$ to \(\textsf{PGL}_d({{\,\mathrm{\mathbb {R}}\,}})\) ${\mathsf{PGL}}_d(\mathbb{R})$ 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.