A Fully Discrete Heegner-Fractal Knot Model for Standard-Model Mass Hierarchies

I propose a fully discrete mass model in which the physically realized spectrum is the minimal set of stable “knot-words” on a bilayer 2 D substrate. The substrate’s alphabet is the nine Heegner class-number-one values used here as privileged “nodes” because they correspond to unique factorization domains and therefore eliminate arithmetic ambiguity at the foundational level.Dynamics are defined by discrete graph traversal and a discrete rewrite-grammar that selects (i) which words correspond to stable particles, and (ii) each particle’s mass as a product of a single universal stiffness S , a topology-class factor, and a rational traversal functional computed purely by finite arithmetic on Heegner nodes. Using one master equation for all fermions and one resonance rule for the electroweak bosons, the model reproduces the full set of nine charged-fermion running masses at ~ 1 0^ − 4 relative accuracy against their currently accepted standard reference masses, while predicting the W , Z , and Higgs masses within 1SD of PDG values. The model also provides a discrete explanation for the first-generation inversion via parity lock and embeds the weak interaction as the neccesary parity odd "vertical operator. This is not a fully theory, but perhaps a self-consistent ontology of the building blocks, my greatest hope as an outsider trying to make a contribution to a field for which I have deep passion is that these building blocks, and their discrete derivations and descriptions, gives true theorists new tools for interpreting QCD in the 3D bulk we observe and new avenues for making GR consistent with those rules by supposing it operates as a phonon projected from this 2d bilayer substrate. The model makes testable predictions around particle count and neutrino mass.