A C*-diagonal in the Jiang-Su algebra via entangled matrix cones

We construct the Jiang-Su algebra Z as an inductive limit of dimension drop algebras, describing the latter as entangled matrix cones to explicitly define the connecting -homomorphisms. This construction gives rise to a C-diagonal in Z with one-dimensional spectrum which is not locally connected. Along the way, we give a new characterisation of normalisers in Cartan pairs in terms of state excision.