Agency, consciousness and maths

It's all a bit complicated to follow, but I gather that it is a mathematical argument that emergent consciousness is much more than the sum of its parts.  But as that seems sort of obvious to most of us as lived experience, it's hard to understand the significance of a mathematical proof.  And the reductions dispute it shows anything new at all.

Anyway, have a read:   A Theory of Reality as More Than the Sum of Its Parts