The ±4/3 Seats and Charge Closure — A Falsification Condition for the Three-Letter Lattice

Abstract. On the 39 seats formed by words of length ≤ 3 in three letters a·b·c (windingnumbers 0, +1, −1), the charge Q = q₀ − Σ/3 takes exactly nine values, S = {0, ±1/3, ±2/3, ±1,±4/3}. This note wagers that set in two sentences and adds one conditional sentence on thenumber of generations. (A) The seat bcc with Q = +4/3 and the seat cbb with Q = −4/3correspond to one particle and its antiparticle. Version 2.0 fixes all eight a-free seats as dark(author decision — a reading the definition does not force, now fixed). The pair is therefore adark pair that does not interact with light, and its Q is a lattice quantity, not an electric charge.(B) No new elementary particle that would occupy a single seat can carry a charge outside S:±5/3, ±2, any |Q| ≥ 5/3, and any charge that is not an integer multiple of e/3 are forbidden.Since (A) fixes no mass, lifetime, spin, colour or mode of detection, and being dark is invisibleto electromagnetic searches, a non-discovery does not falsify the lattice. (B) is different: asingle 5σ confirmation of an elementary particle with Q ∉ S falsifies this lattice and allseventeen papers built on it. (C, conditional) If the generation Z₃ is the same as the lattice Z₃,there is no fourth state of the same charge and kind at any mass — vector-like T and B, a fourthcharged lepton and a fourth neutrino included. The circle has three places, 0°, 120°, 240°, andthe next is not 360° but 0°. That identification has not been computed, so (C) is a falsificationcondition for the identification, not for the lattice. The author renounces in advance everyrescue — adding a fourth letter layer, re-reading the particle as a composite, changing thenormalisation constant, or re-reading a fourth state as "the first come round again". This notefollows one rule: it wagers only what the definition forces; a reading fixed by the author islabelled [author decision] and is not made a falsification condition. To the question "why 3"one conditional theorem is attached: if charge is the real part of the rotating phasor sum(Paper 02), then cos(2π/N) is rational only for N = 3, 4, 6 (Niven), and 4 and 6 are degenerate orduplicate forms of 3, so N = 3 remains. Present status [measured]: no X₅/₃ below 1.33 TeV, noH±± below 1.08 TeV, no long-lived |q| = 2e–7e particle below 1.06–1.60 TeV, no millicharge, N_ν= 2.984 ± 0.008, a sequential fourth generation excluded by the Higgs signal strength — allconsistent with (B) and (C), but also with the Standard Model, so none of it is yet a point for thelattice. The lattice parts from the Standard Model at two places, and at three if theidentification holds: a dark 4/3 seat pair is in, 5/3 is out, and (under the identification) there isno fourth generation.