One number predicts particle masses across five orders of magnitude. Here's the derivation chain.

OPH (Observer Patch Holography) starts from a single geometric quantity, the pixel area P = 1.63094 in Planck units, and through a chain of exact mathematical derivations produces the W boson mass (0.012% error), Z boson mass (0.035% error), electron mass (0.023% error), muon mass (0.022% error), and tau mass (0.020% error). The math involves heat-kernel regularization on SU(N) gauge groups, modular flow on von Neumann algebras, and circulant mass matrices on Z_3 generation space. One result that might interest this sub specifically: the edge-sector partition function Z = sum_R d_R exp(-t C_2(R)) has been validated against five independent gauge systems (SU(2), SU(3), SU(5), SO(10), E_6) to machine precision (~10^-14), including an overconstrained test with more equations than unknowns. The Koide formula Q = 2/3, a 40-year "numerological coincidence" relating lepton masses, falls out as a consequence of Z_3 symmetry and maximum entropy. The full derivation and Python code are open-source.

Full math in the linked file.