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, $\Theta_{\mathrm{raw}}=0$: on a symmetric BFS shell the involution $g\mapsto g^{-1}$ pairs opposite central phases and erases the oriented $J_\Pi$-odd component before the radial recursion can act. This note defines the honest replacement: a frontier transfer observable attached to the directed outgoing edges $g\to gs$ of the cascade, whose central increment is the Heisenberg cocycle $a(g)\,s_b$, 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 $J_3$ coefficient of the metaplectic step, which in the $\mathrm{SL}(2)$ model of Q14 comes from the $\mathfrak{sl}_2$ 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 $\partial_\tau$ 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, $\langle\Delta A_c\rangle_{\partial^+S_m}\neq 0$, which may fail if a residual automorphism re-pairs the frontier; the discriminating anti-bias control is the symmetrised-frontier cancellation $\langle\Delta A_c\rangle_{\partial^+S_m\cup\partial^-S_m}=0$. The chiral lift of the residual reflection is reduced to one named hypothesis, [H-WS] ($R_b$ acts as the scalar $-1$ on the chiral carrier, so that $[\gamma_5,R_b]=0$), supplied by no source. No normalisation $\mathcal{N}_A$, no dictionary value, and no $\varepsilon$ appear in this note: it tests only whether the recursion produces a non-zero, bias-free oriented signal.