Symmetry Descent of the Terminal Retained Carrier SO(3)-type Upstairs, SO(2) Downstairs

The terminal ordered residue X = Ωₜerm|Λ₄ on the minimal complete support Λ₄ = (F₇, F₆, F₂) (T19) admits a canonical symmetry descent forced entirely by the theorem-proved carrier structure. The irreducible triadic support induces a rank-3 carrier CX. Permutation symmetry of the full-carrier quadratic invariants forces SO (3) -type connected symmetry. The canonical binary projector ΠA (T20) reduces the active carrier to a 2-dimensional phase-bearing plane. Order-collapse forces the collapsed plane to carry an isotropic quadratic form, yielding SO (2). The scalar phase defect Δφ (τ) is the terminal scalar shadow of this descent, not a primitive quantity. Under Metric Descent Compatibility (Principle 21. 6), the cross-coupling vanishes (m = 0), the full-carrier symmetry strengthens to exact SO (3), and the carrier admits a canonical su (2) -type Lie algebra structure induced by the Euclidean metric and the orientation sign σ_Γ = −1. The full descent chain is: X SO (3) -type → RA 2D phase-bearing → CA SO (2) → Δφ (τ) scalar No group is assumed. All symmetry groups emerge from the forced carrier architecture of T19 and T20. Status: Solid (unconditional results) ; Conditional on Metric Descent Compatibility for exact SO (3) and su (2) structure. Dependencies: T18, T19, T20 (direct) ; T14–T17 (inherited) Relation to series: Completes the T18–T21 symmetry identification block. T22 will address the SO (3) vs SU (2) double cover question.