Chiral Orientation of the Directed Heisenberg Frontier

The angular generation split of the projected Dirac residue E_Π is carried, on the directed Heisenberg frontier, by a chirally dressed cocycle signal Θ_χ = σL\,(2π/q)\,Δ Ac∂⁺. The raw cocycle average and the maximal-locking bound θₘₐₓ are computable from the arithmetic backend, but the signal itself depends on the chiral weight σL, whose origin lies in the Lorentzian spin-lift and not in the arithmetic frontier. We prove that σL cannot be any function of the real cascade generator $T(e)$: edge inversion and the residual reflection φ both act as T↦ -T, so every $f(T)$ has identical arrow-parity and φ-parity, whereas σL must be arrow-even and φ-odd. The resolution is that σL is the Weyl representation type, 2 versus 2̄: group inversion preserves the representation (arrow-even) while complex conjugation exchanges it (φ-odd). In the inherited Heisenberg central-phase lift the chiral phase is the linear cyclotomic character ω_χ(e)=ζq^Δ Ac(e), with no Gauss, Maslov, or √5 component; on the nonzero-cocycle support the natural branch satisfies σL(e)=sign \,ζq^Δ Ac(e) = signΔ Ac(e), giving ρ_χ = 1 and NA = θₘₐₓ ≠ 0. This establishes [H-orient] in the inherited Heisenberg central-phase lift, not unconditionally: the only remaining obstruction is an additional spin-Galois phase outside the central character, in particular a √5 or ADE-spin factor orthogonal to ζq. The result is a conditional derivation of the frontier amplitude datum; it does not derive u≠ 0, which still requires the Schur transport of the polarisation onto the J_Π-odd generation sector.