Topological Protection of the Proton: Baryon Number Conservation as a Frozen Fano orbit

The Standard Model treats baryon number conservation as an accidental symmetry. We show that the colour-singlet condition for a baryon is a closed orbit on the Fano plane PG(2,2) and that baryon number equals the winding number of this Fano orbit. Below the QCD snap threshold beta*_QCD (T ~ 155 MeV), the Fano geometry is frozen and the proton is topologically stable. Above beta*_GUT quark-lepton transitions become allowed and proton decay proceeds as a threshold, not smoothly. We test the framework against the lattice QCD proton excited spectrum, the electroweak sphaleron rate, and net-baryon fluctuation data from RHIC.