The Residual $288$ in an $E_8\timesωE_8$ Program: Representation Accounting and Physical Matter Interfaces
Year: 2026
Type: preprint
Abstract: We examine the accounting identity $496=208+288$ in an octonionic $E_8\timesωE_8$ unification program. The dimensions count selected representation labels, not a closed particle spectrum. In a consistent trinification convention, the quark-doublet labels descend from the $E_6$ adjoint, whereas the lepton-doublet labels descend from the mixed $E_8$ sectors. Their occurrence supplies useful nonabelian multiplicities but does not establish three complete chiral generations. We prove that the stated doublet assignments cannot acquire their Standard-Model hypercharges from a single $E_6$ generator commuting with the full family, colour and weak groups. Separately, a chosen charge-first Clifford benchmark carries three complete families on a $48$-dimensional internal Weyl coefficient space and admits an anomaly-free common family action. We construct explicit subgroup-equivariant lifts of physical scalar currents into $\overline{27}\otimes27=1\oplus78\oplus650$, and show that their nonuniqueness prevents a coupling prediction from normalization alone. The full comparison square contains fundamental family channels; a narrower exclusion applies only to undressed matter bilinears trivial under an independent geometric group. We identify the localization maps, interaction matrix elements, vacuum correlations and kinetic matrices needed to connect the exceptional geometry to physical matter. The geometric interpretation is retained, while generation selection, scalar binding and mass matching remain dynamical problems.
Source: arXiv (Cornell University)
Author: Singh, Tejinder P.
Institution: Tata Institute of Fundamental Research
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164571009