Let's use the opportunity to ask technical questions / confirm my interpretation...

When I was young, nobody was sure if the https://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%8... was real or complex. IIUC Wikipedia, now it's confirmed to be complex!!! [1]

The CP (charge-parity) symmetry is interesting, because if it is broken it means that the T (time) symmetry is also broken. In Quantum Mechanics if the operator to calculate the energy is real, then the system is invariant if you magically change the variable t to -t, this is call time inversion, that sounds cool but it's just a mathematical trick and not a device to travel back in time.

So a complex Cabibbo–Kobayashi–Maskawa matrix ensure there is a "problem" when you change t to -t and this indirectly may explain why if the initial universe has the same amount of matter than antimatter, now it's not balanced.

If I can continue with some speculations because my handwaving is not strong enough ... In https://www.nature.com/articles/s41586-025-09119-3/figures/1

* in the top diagram a bottom quark transforms into a up quark, and W- particle, and then the W- particle decays into a strange and anti-up quark. This transformations uses 1 or 2 of the coefficients of the matrix.

* in the bottom diagram, there is an intermediate top quark, but after more interactions the result is the same. But the top quark here forces to use the others coefficients of the matrix. So the result has not only a different amplitude, but it's also complex!!! [1]

For the final result you must combine both diagrams and also a standard complex phase caused by the advance of time, something like |A*e^{itm}+B|^2. When you replace t with -t, the sign of the phase changes. If both diagrams had real amplitudes A and B it doesn't matter because |A*e^{-itm}+B|^2.

But if A is real and B=b+ci then |A*e^{itm}+b+ci|^2 is different of |A*e^{-itm}+b+ci|^2 and you get an asymmetry.

Is this correct? Anything to add/remove/rewrite?

[1] Sorry fo the exclamations marks. Nobody told me. 68.8°±4.5° is a lot. It's not slightly complex, it's very complex.