1) I have so far failed to note the completely orthodox relationship between mW, mZ, and the Higgs VEV v, that exists in the standard model, as set out e.g. in equations 1.4 and 1.14 in this thesis. It is:
mW = 1/2 g v
mZ = 1/2 sqrt(g'2+g2) v
where g is the SU(2)L coupling, and g' is the U(1)Y coupling.
2) A paper today informs us of a more arcane t,H,W,Z sum rule, due to Veltman and motivated by naturalness:
mH2 + 2mW2 + mZ2 - 4mt2 = 0
"which is satisfied for a value of the Higgs mass mH ~ 314 GeV in flagrant conflict with experimental data."
The authors go on to speculate that perhaps Veltman's condition might be satisfied at high scales instead. I will just note two things: one has to wonder whether some of the t,H,W,Z formulae I have chronicled here - especially those which actually work but are otherwise mysterious - might be produced by a Veltman-like argument; and Veltman's wrong prediction is rather close to the real Higgs boson mass, times 2.5.