Particle Decay as the Rearrangement of Simplex Patterns

In IDWT a particle is a pattern of identical portions, bound in d spatial directions and arranged on n levels. The portions occupythe lattice points of a d-dimensional simplex of side n − 1, and their number is the count C = S(n, d) = C(n + d − 1, d). The sameshapes have already given the quark mixing matrix. This paper shows that particle decay is a rearrangement of these shapes,and that two geometric operations account for the observed weak decays. In the first, the parent splits along one of its edgesinto two corner patterns that cover that edge exactly; this is why the parent’s index is the sum of the two daughters’ indices inthe muon decay, both main tau channels, the non-leptonic strange decay and the charmless semileptonic bottom decay. In thesecond, a pattern gains or loses the fourth direction and passes between a four-dimensional pattern and a three-dimensionalpiece of it, a layer or the interior of a side; these are the dominant quark decays: beta decay, charm to strange, bottom to charmand top to bottom. The Cabibbo-suppressed decays are the ones that need an extra step through a corner. Of the observeddecays, only the tau’s muon channel is not accounted for.