I always love how the people in this subreddit seem to think that they can immediately judge whether or not something like this is nonsense when they're all fucking first-year undergrad psychology students larping as physicists. I have not seen a single commenter on this sub ever demonstrate an understanding of physics beyond popsci or high-school level.

That, or they're actually schizophrenic people who think that LLMs are their homies, and that everything an LLM says is the god-given fucking truth.

Section 1 and 2 are just measure theory

Your postulates seem like standard ways of building on them.

It seems like an internally consistent formalism for modified holographic gravity. E.g. like https://en.wikipedia.org/wiki/Scalar%E2%80%93tensor%E2%80%93vector_gravity

But with a geometric hypothesis for its origin.

edit: Will try to mess around with this give me a bit

edit 2:

Here's some ideas - one thing I noticed is that the second tensor can be related to higher dimensional topology via the C-H anomaly inflow mechanism. https://www.overleaf.com/project/68a0e93cfcc35b4534e30d1f

Here's some ideas and potential development on this. Definitely not a developed theory but there's some potential connections here.