The GG-6 Lock Cluster: A Non-Spatial Kaluza–Klein Resonance near 3.85 TeV as the Standing LHC Falsifier of GG-Theory

Abstract

Every particle discovered since the mid-1970s — the W and Z, the top, the Higgs — was on the Standard Model's list before it was found. This paper is about the first particle that is not on that list. GG-Theory derives, rather than fits, a new mass scale: the lock cluster at M_lock= 12 M_Ple^-35≃3.849 TeV, fixed by the integer K=35 of the OGN-5 ledger with no adjustable parameter anywhere in the chain. The same number over-constrains the electroweak scale, v=M_lock(2/5)³≈246 GeV: two known scales, one integer, nowhere to hide. At that mass the theory places a three-member cluster — a spin-2 graviton, a color-octet vector g^*, and a leptophobic Z'_B: the discrete modes of a non-spatial (renormalization-group) extra dimension — with derived couplings that are top-rich, dijet-friendly, and lepton-poor, so existing clean-channel limits do not touch it. The un-suppressible member is the octet: σ×BR(t t)=8.7 fb at 13 TeV, Γ/m=15%, with a theorem-fixed interference sign. It sits exactly at the current ATLAS/CMS t t exclusion frontier: the prediction is being tested now. A full simulation anchored to the ATLAS Run-2 analysis (Part VIII) turns this into a calendar. A dedicated reanalysis of data already on tape carries an expected 2.7–3.7σ per experiment, and 4.6–5.2σ for a combined ATLAS+CMS analysis with improved systematics — five-sigma discovery from existing data is a live possibility; failing that, single-experiment 5σ luminosity is on tape during 2032. Because mass, width, rate, sign, and angular shape are all pre-registered, the search pays no look-elsewhere penalty — and a null result at 2 ab⁻¹ retires the implementation outright. The mass is the bet; the LHC is the table. Part of the GG-Theory program, a series of preprints developing a six-dimensional geometric framework and its consequences for particle physics, cosmology, and open-system dynamics. The complete series is available at https://preprints.arisaka-gg.org/