The Oriented Frontier Observable: a Recursive Q11 Diagnostic for the Angular Generation Split

The symmetric-capacity obstruction establishes that the raw shell observable of the angular generation split vanishes identically, Θraw=0: on a symmetric BFS shell the involution g↦ g⁻¹ pairs opposite central phases and erases the oriented J_Π-odd component before the radial recursion can act. This note defines the honest replacement: a frontier transfer observable attached to the directed outgoing edges g→ gs of the cascade, whose central increment is the Heisenberg cocycle a(g)\,sb, the discrete oriented increment of the cascade. It is a counterpart of the orientation datum in the sense fixed in Section 1, and not the J₃ coefficient of the metaplectic step, which in the SL(2) model of Q14 comes from the sl₂ commutator $[E,F]=H$ (Q14, Proposition 6.5). The orientation is the arrow of the Cayley graph from the projection origin to increasing BFS depth, not an extracted weight; no identification of this arrow with an ordering derivative ∂_τ is made here (Q14 states, for the generator log g of the metaplectic step, that such an identification is a separate hypothesis that no source supplies ). The first test is not an amplitude value but the existence of an oriented signal, Δ Ac∂⁺Sₘ≠ 0, which may fail if a residual automorphism re-pairs the frontier; the discriminating anti-bias control is the symmetrised-frontier cancellation Δ Ac∂⁺Sₘ∪∂⁻Sₘ=0. The chiral lift of the residual reflection is reduced to one named hypothesis, [H-WS] (Rb acts as the scalar $-1$ on the chiral carrier, so that [γ₅,Rb]=0), supplied by no source. No normalisation NA, no dictionary value, and no ε appear in this note: it tests only whether the recursion produces a non-zero, bias-free oriented signal.