Known topological quantum matter, including topological insulators and Dirac/Weyl semimetals, often hosts robust boundary states in the gaps between bulk bands in energy-momentum space. Beyond one-gap systems, quantum crystals may also feature more than one inter-band gap. The manifestation of higher-fold topology with multiple nontrivial gaps in quantum materials remains elusive. In this work, we leverage a photoemission spectroscopy probe to discover the multi-gap topology of a chiral fermion material. We identify two sets of chiral surface states. These Fermi arcs exhibit an emergent ladder structure in energy-momentum space, unprecedented in topological materials. Furthermore, we determine the multi-gap chiral charge $textbf{C}=(2,2)$. Our results provide a general framework to explore future complex topological materials.
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