Identity at κ 3 (ledger Constructed)

$(S,{\Gamma }_1)=A_1$ at ${\kappa }^3$ is $(S_0,{{\Gamma }_1}^{[3]})+(S_1,{{\Gamma }_1}^{[2]})+(S_2,{{\Gamma }_1}^{[1]})+(S_3,{{\Gamma }_1}^{[0]})$. The last two terms vanish (${{\Gamma }_1}^{[1]}=0$ by D14; ${{\Gamma }_1}^{[0]}$ is field independent). The ghost-number-1 three-field rows are enumerated mechanically: 14 rows. Four are odd under $\varphi$-parity (zero), six contain auxiliary or nonminimal fields, and four need P.6 inputs ($chh$, $c\varphi \varphi$, $cc\bar{c}$, $ccK$); each needed input is recorded. The ${\kappa }^3$ counterterm domain is given only as structural monomial counts (4D versus evanescent); its BRST/${\sigma }_0$ reduction is Missing.