A T-Fold Black Hole in Doubled Type IIB

We construct an asymptotically flat T-fold representative of a four-dimensional dyonic black-hole charge orbit in doubled type-IIB theory. Starting from the F1-P-NS5-KKM toroidal seed, an integral parabolic T-duality monodromy is imposed on an active doubled three-torus. The non-geometric data enter only through this global patching: the Reissner-Nordström-type term is sourced by conserved four-dimensional electric and magnetic field strengths in the doubled Kaluza-Klein/winding local system, not by an internal algebraic $Q$-flux alone. Exact duality preserves the local equations, the BPS index, and the $O(6,6)$-invariant of the NS-NS/$N=4$ charge sublattice governing the entropy. The minimal Einstein-Maxwell-dilaton slice contains a running-scalar branch and an equal-charge Reissner-Nordström limit; the extremal near-horizon region is locally ${\mathrm{A}\mathrm{d}\mathrm{S}}_2\times S^2$, with the compact factor globally T-duality patched.