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This reproduces the tangent class and its key properties studied by the first author in arXiv:2606.22650. The main body of this paper was produced autonomously, without human mathematical guidance, by Danus, an AI mathematical reasoning agent. Danus solved the problem before arXiv:2606.22650 was publicly available, demonstrating the potential of AI agents in mathematical research. We reproduce its output faithfully, adding only editorial comments; the expe","title":"Tangent classes of matroids and wonderful compactifications","url":"https://arxiv.org/abs/2607.05835","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.05835v2 Announce Type: replace-cross \nAbstract: For every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\\mathcal{G}$ containing the top flat, we construct an integral tangent class $T_{M,\\mathcal{G}}^{\\mathbb{Z}}\\in K_{\\mathbb{Z}}(M,\\mathcal{G})$; in the realizable case it specializes to the class of the tangent bundle of the corresponding wonderful compactification, it recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it 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. The main body of this paper was produced autonomously, without human mathematical guidance, by Danus, an AI mathematical reasoning agent. Danus solved the problem before arXiv:2606.22650 was publicly available, demonstrating the potential of AI agents in mathematical research. 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