Remark: How J 3 is specified, and how it is implemented

Equation (eq:L-J3) specifies $J_3$ only implicitly: through $V_1$, $V_2$, which are built from the curvature atoms (eq:L-fc). XII-C prints no table of elementary monomials of $J_3$, and none is typed into XVI-L. The script source_full.py implements $J_3$ through exactly these printed definitions (atoms $\to$$R_n$, $r_n$$\to$$V_1,V_2$$\to$ (eq:L-J3)); the coefficient table $P_{J_3}$ below is an output of that implementation, never an input. The same holds for $C_2$ (via (eq:L-C)) and $M_2$ (via (eq:L-C), (eq:L-fc), (eq:L-M2)).