Gauge Symmetry as the Stabiliser of a Conserved Form and Why the Framework Must Be Multi-Sector

We address how gauge symmetry arises in a framework where the forces are emergent broken sectors of an exceptional algebra rather than subgroups of a single grand-unified group. We propose a criterion: a sector produces a gauge symmetry when it carries a conserved invariant form, and the gauge group is the stabiliser of that form. We establish the criterion for the strong sector explicitly. G2 geodesic transfer conserves the octonionic associative three-form φ exactly (numerically, the deviation is zero under the fourteen G2 generators and of order ten under the complementary directions), and the stabiliser of φ within G2 — the subgroup fixing a vector in the seven — is SU(3), reproducing colour, with the generation embedding 16 = 2(3) + 2(3̄) + 4(1). We then test whether the full Standard Model gauge group assembles from the two maximal subgroups of G2 (SU(3), stabilising the octonion structure, and SU(2) × SU(2), stabilising a quaternion subalgebra) by intersection. The rigorous computation gives SU(3) ∩ SU(2) × SU(2) = SU(2), of dimension three — not SU(2) × U(1)_Y. Hypercharge is not in the intersection. A rank argument explains why and is the central result: G2 has rank two, exhausted by colour SU(3), so no independent U(1)_Y can be gauged inside the same G2. Hypercharge cannot share the colour algebra; it must belong to a separate sector. The framework is therefore necessarily multi-sector — not by stipulation but because the rank of G2 forbids the Standard Model gauge group from fitting in one copy. We report the bounded assembly honestly: the conserved-form criterion holds and colour is derived, while the single-algebra assembly of the full gauge group fails for a precise structural reason.