Angular-ratio fingerprint: σ(π/2)/σ(π) = sin⁴(π/2)/sin⁴(π/4) = 1/(1/4) = 4. Canonical pins: cross-section at θ=π (backscatter, σ=Z_p²Z_t²e_q⁴/(16E²)); at θ=π/2 (σ=Z_p²Z_t²e_q⁴/(4E²)); their ratio = 4 (exact integer).
Angular-ratio fingerprint: σ(π/2)/σ(π) = sin⁴(π/2)/sin⁴(π/4) = 1/(1/4) = 4. Canonical pins: cross-section at θ=π (backscatter, σ=Z_p²Z_t²e_q⁴/(16E²)); at θ=π/2 (σ=Z_p²Z_t²e_q⁴/(4E²)); their ratio = 4 (exact integer).