From F4 to E6: The Worldline Unfolds the Vacuum—Chirality, Lepton Families, and Trinification

In the Selection–Stitch Model, the vacuum is a face-centered-cubic lattice carrying a stabilizer code, and matter is a node trapped in a tetrahedral void; a predecessor construction closes the bond algebra of vacuum and matter into the algebra f4, with color a factor of the fixed subalgebra of a triality twist and electric charge quantized in thirds. This paper is an algebraic result with a physical interpretation, and the two are kept separate throughout. The two tetrahedral void orientations are exact inversion partners in the static crystal, so orientation is not a label there; but on a chronological defect worldline, the pairing relaxes from P to PT, and doubling every matter weight by the now-physical orientation label—with the three glue classes at 120∘ in a new plane—assembles the 72-root system of E6, verified by reflection closure, rank, and Cartan determinant, the charge-based competitor failing. The orientation flip is an automorphism folding e6 back to f4; trinification follows from the root system, and the 27’s color-singlet block is a lepton-family-structured sector whose fold is the predecessor’s octet plus one singlet. The same geometry selects a charge direction: among Cartan charges commuting with color, those odd under the extended inversion and even under the orientation flip, which every hop performs, form one line, unique up to sign, spanned by Q, on which the 27 carries the Standard Model charges, integer unit included; of eighteen operators with that spectrum, only ±Q passes. Reading Q as the physical electric charge rests on identifications of the two operations that are argued, not proved. No gauge dynamics is constructed; a table maps each claim to its type, status, source, and falsifier, and the open frontier is the chiral projection.