DDI or not

[Sukruti]

Hello,

Given a particular identity for expressions in terms of the Riemann/Ricci tensors and the Ricci scalar, is it possible to find out whether the identity is a dimensionally dependent identity (DDI)?

I find there are some identities in four spacetimes dimensions that are generated via both ConstructDDIs as well as RiemannSimplify (under TInvar). As has been mentioned by Barry earlier (https://groups.google.com/g/xact/c/QhPXZ42gANE/m/jSMKexNuAAAJ), TInvar does not implement DDIs via RiemannSimplify acting on tensor expressions. This makes me suspect that even though the tensor expression identities under question can be generated by (RiemannSimplifying) ConstructDDIs, they may not actually be DDIs.

Additionally, I have also derived identities for two six-derivative scalar expressions for which RiemannSimplify can implement DDIs. But again, it's not clear whether the RiemannSimplified identities are DDIs or not.

One way to check this could have been to act RiemannSimplify on these identities in a dimension other than four. Unfortunately, RiemannSimplify does not work in dimensions other than four. The identities I'm talking about are in the attached notebooks.

Any idea how to check whether these identities are DDIs or not?

Best,

Sukruti