In this paper, we construct an integral tangent class $T_{M,\mathcal{G}}^{\mathbb{Z}} \in K_{\mathbb{Z}}(M,\mathcal{G})$ for every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\mathcal{G}$ containing the top flat. In the realizable case, this tangent class specializes to the tangent bundle of the corresponding wonderful compactification, recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and satisfies the expected Chern-alpha lower bounds.
This reproduces the tangent class and its key properties studied by the first author in arXiv:2606.22650. Notably, the main body of this paper was autonomously produced by Danus, an AI mathematical reasoning agent, which solved the problem before arXiv:2606.22650 was publicly available, demonstrating the potential of AI agents in mathematical research.
We faithfully reproduce its output, adding only editorial comments; the experiment is documented in Appendix B.
Blogger's Review: This research highlights the potential applications of artificial intelligence in mathematics, particularly in its ability to autonomously solve complex problems. The involvement of AI not only accelerates the research process but also provides new perspectives and tools for traditional mathematical methods, warranting further exploration of its applications across broader fields.