The insertion sign and full observable

Suppose the selected second-order completion has the affine identity

With $r_{\mathrm{D}}=-u_{\mathrm{D}}$,

If ${\mathcal{C}}_{3,\mathrm{D}}$ is nonzero as a family, no other insertion multiple represents the same fixed second slot. Indeed equality with coefficient $c$ would imply $(c+1){\mathcal{C}}_{3,\mathrm{D}}=0$, hence $c=-1$.

The source-record scalar-sourced slot is

Here the inherited stress normalization $T_0$ remains a named source input; the full stress component sheet was not supplied.

XII-E supplies (eq:PhiD), the once-entered scalar-sourced slot, and the corresponding carrier admission for its completed tree functionals CheungXIIE. The nonzero-family premise, not admission alone, is what gives uniqueness of the insertion coefficient. The quantum two-line coefficient below is a different object.

For orientation, the reported eleven-branch inventory is

Here ${\int }_{f}F=\int fF{\mathrm{d}}^{4}x$, $p=p_1[\gamma ;\varphi ]$, and $p_1[r;\varphi ]=-{E_m}^{\mathrm{R}}(V_{1,g}[r]\varphi )$. The remaining $V_2,U_{\sigma },a_2$ expressions are source inputs, not newly invented component definitions. The inventory is a record from XIII-C CheungXIIIC. The retained six-branch local calculation does not erase the other branches from the global observable.