An Electroweak-Shaped Structure on the FCC Vacuum: Static Centrosymmetry Forbids Chirality, but a Defect Worldline Relaxes the Obstruction to PT and Violates Parity
Year: 2026
Type: preprint
Abstract: In the Selection-Stitch Model the FCC vacuum has already been shown to carry color: the tetrahedral cage of a trapped defect yields a qutrit and selects SU(3) on the triangular faces of the nearest-neighbor cuboctahedron. We ask whether the same shell carries an electroweak-shaped group-theoretic structure, and report a layered result. The six square faces of the cuboctahedron carry an su(2): three antipodal axis-pairs along the ⟨100⟩ directions that close as so(3) = su(2). We are explicit that this is a group-theoretic correspondence, not yet a demonstration that these spatial rotation axes act as internal gauge generators. With the diagonal bond-phase U(1) the rank equals that of SU(2)×U(1)—a necessary structural condition, not a strong identification. Read as interlayer objects—the square faces are the inter-sheet faces created by the out-of-plane Lift in the crystallization picture—the structure supplies a two-dimensional up/down doublet and an order-two grading that we treat as a candidate chirality (a model grading, not yet the Lorentz/spinor chirality of the Standard Model), so a chiral SU(2)_L is geometrically available as a target. Whether it is realized is then governed by symmetry, and we trace the obstruction through three stages. Statically, the chirality is forbidden: FCC is centrosymmetric (space group Fm-3m), and we prove that at any bulk node the up-Lift and down-Lift environments are exact inversion partners, so their handedness cancels under parity (P). On a chronological defect worldline threading the stack, however, the up-connection lies in the future and the down-connection in the past; spatial inversion no longer pairs them, and the cancellation relaxes from a P relation to a PT relation. A chiral coupling cannot survive a P cancellation but is compatible with a PT (and hence CPT) relation—the weak interaction itself violates P while respecting CPT—so this relaxation removes the prohibition rather than merely weakening it. Beyond removing the prohibition, the oriented Lift supplies a temporal generator that is odd under P and even under PT (the σ_y direction of the doublet): the worldline genuinely violates parity, which the static geometry forbade. What remains unforced is the final step—the left-handed projection P_L that turns parity violation into a chiral gauge coupling; the oriented generator alone produces a vector su(2), acting equally on both chiralities. The result is therefore a three-tier boundary: static chirality is forbidden by centrosymmetry, a defect worldline relaxes the obstruction to PT and the oriented Lift violates parity, and only the chiral projection remains unforced. Hypercharge and anomaly cancellation are untouched. The boundary locates precisely where the geometric derivation of the electroweak sector stands: the gauge structure and genuine parity violation are reached on defect worldlines; the chiral projection that completes SU(2)_L is not yet compelled.
Author: Kulkarni, Raghu
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165369051