The Trinity Lattice — 3 wavons + 9 gauge seats + 27 particle seats = 39

Abstract

Abstract This guide is written so that a reader seeing the lattice figure V4 (2906·2907) for the first time canread the whole of Wavon Mechanics from one figure. It starts from one line: a vibrating wave thatwinds itself closed becomes a wavon, and three wavons entangled at 120° become a particle. Forthree to cancel, 120° is required, and this forces complex numbers.From this come 39 seats built from three letters (a, b, c) on three sites — 3 in the one-letter room, 9in the two-letter room, 27 in the three-letter room. Charge is fixed in every room by one formula Q =q₀ − Σ/3; the three-letter room has only nine charge values, with a ceiling of 4/3. The three-letterseats split into three by shape: three identical letters are photon-like (3), two alike and one differentare quark-like (18), all three different are lepton-like (6). And a seat containing the letter a belongsto the bright world (19); a seat without it, to the dark world (8).The geometry of the wavon gives this classification its meaning. a is a wave standing in place, goingboth ways; b and c are half-twists in opposite directions. So b and c are each other's antiparticles,and antiparticles stand in left–right mirror positions across the center of the lattice figure (V4).When three a gather at 120°, the backward-turning part is erased by 1 + ω + ω² = 0 and a rotationresults — the photon. When antiparticles meet, b faces c at every site and everything unwinds intoa: b + c → 2a, bb + cc → 2aa, bbb + ccc → 2aaa.What the Standard Model and other classification hypotheses (Gell-Mann–Nishijima, the eightfoldway and the quark model, Sakata, Pati–Salam, SU(5), rishons, helons, E8, Kelvin's vortex atoms)classified, and where they stopped, is recorded alongside. No particle, force, or charge is added.Claims, non-claims, and kill conditions are listed in §14.