A Classification of the Sectors: How the Type of Conserved Invariant Determines Physical Character

The G2 framework breaks into six sectors, conventionally described as four forces and two properties. We show this description is not a list but a theorem: the physical character of each sector is determined by the type of conserved invariant it carries. A sector carrying a continuous invariant form becomes a Lie-group gauge force, by the gauge-emergence mechanism in which the gauge group is the stabiliser of the form; a sector whose invariant is the metric becomes gravity, geometric rather than gauge; and a sector carrying a global invariant — continuous or discrete — becomes a property sector producing a non-thermal condensate rather than a thermal force. The three division-algebra forms (octonionic, quaternionic, complex) give the three gauge forces; the single metric gives the single gravitational sector; and the two global invariants, one continuous (the holographic entropy bound) and one discrete (CPT), give the two property sectors, which we identify with dark matter and the axion. The partition 6 = 3 + 1 + 2 thus acquires a structural reading. The classification yields corollaries absent from the original description: that gravity is not a gauge force but a geometric sector; that exactly two non-thermal relics exist; that gauge sectors thermalise while property sectors condense; and that no fourth class of fundamental sector is possible. We present the theorem, its derivation from the invariant type, and these consequences.