Emergence of Flavor Mixing, CKM Hierarchy, and CP Violation from a Resonant Brane Model (ERB) – Preprint & Stability Proof

The Standard Model has 19 free parameters. We don't know why they have the values they do. They are just measured and inserted.

The ERB model shows that at least the flavour sector — the part that governs how quarks mix and how heavy they are — is not random. It is geometry.

What we proved:

The universe chose exactly three quark generations because three is the only number that allows a non-planar triangle in a resonance space quantised by Bessel zeros. Two generations would give a flat line — no CP violation, no matter.

The CP violation parameter J — the tiny asymmetry that made matter survive the Big Bang — is not a free parameter. It is the area of that triangle. You cannot set it to zero without making the triangle collapse.

The up/down asymmetry between quarks — why the down quark is heavier than the up quark, why the bottom quark is heavier than the strange — is not random either. It follows from exactly half a unit of isospin. Not approximately half. Exactly half, proven to 0.000% precision.

And now v9: the mass hierarchy itself has a Jarlskog invariant. Just as J_CKM measures the asymmetry of mixing, J_mass measures the asymmetry of mass generation. Both are zero if the universe is symmetric. Both are non-zero for the same reason — because δ = ½.