  We consider arithmetic analogs of the relative Langlands program and
applications of new non-reductive geometry. Firstly, we introduce mirabolic
special cycles, which produce special cycles on many Hodge type Rapoport-Zink
spaces via pullbacks e.g. Kudla--Rapoport cycles. Secondly, we formulate
arithmetic intersection problems for these cycles and formulate a method of
arithmetic induction. As a main example, we formulate arithmetic twisted
Gan--Gross--Prasad conjectures on unitary Shimura varieties and prove a key
twisted arithmetic fundamental lemma using mirabolic special cycles, arithmetic
inductions, and Weil type relative trace formulas.
