p23: the O.1 requirement, one-loop power counting and the P.6 entry inventory

.1, exactly. The XVI-O ledger O_quantum_target.json (o70-sync; verbatim copy in provenance/XVI-O, sha pinned, read only) states the O.1 target: the one-loop ${\kappa }^2$ bulk two-point sector on $S_{\mathrm{inv}}$ (graviton, scalar, ghost, including the gh$=0$ BV source seeds; frozen gauge fermion; $m=0$). O.1 closes iff this sector closes under a verified retained quantum identity. Every checklist item must be earned: O.2 (classical ${\kappa }^2$ master, including grav ${\ell }_4$), O.4 (inventory), O.5 (graphs evaluated), O.6 (identity verified) and O.7 (remainder cancellation / counterterm solution). The target must first be enlarged if the identity constrains more legs or orders at ${\kappa }^2$. In XVI-P scope: O.4, O.5, the projected part of O.6/O.7, and the enlarge rule. Out of scope: O.2 and the bulk ST4b identity, which belong to XVI-O/XVI-N and stay untouched. Hence O.1 is not closable inside XVI-P, and it stays NOT_CLOSED.

one-loop power counting. Every interaction vertex of the frozen inventory carries ${\kappa }^{\text{legs}-2}$, with antifield sources counted as legs. This is checked vertex by vertex. A one-loop graph has $I=V$, so it is ${\kappa }^E$ with $E$ external legs. The one-loop identity at ${\kappa }^2$ is $(S^{(0)},{{\Gamma }_1}^{(2)})+(S^{(1)},{{\Gamma }_1}^{(1)})$; the term $(S^{(2)},{{\Gamma }_1}^{(0)})$ vanishes because ${{\Gamma }_1}^{(0)}$ is field independent. Only $E=2$ and $E=1$ enter. A mechanical enumeration of all one-loop 1PI graphs (declared propagators $hh$, $\varphi \varphi$, $c\bar{c}$) gives the following:

• for $E=2$ it reproduces the frozen ${\kappa }^2$ inventory exactly (D01–D06, D11, D12, D13: 9/9);

• for $E=1$ it gives the 3 graphs of the one-point row;

• it detects four mutations (a wrong $\kappa$ power, two dropped vertices, a spurious propagator).

The enlarge rule is not triggered: there is no one-loop three-point sector at ${\kappa }^2$.

.6 entry (honest partial). Three-point functions first appear at ${\kappa }^3$. The one-loop ${\kappa }^3$ three-point inventory has 15 graphs: $hhh$ 5, $h\varphi \varphi$ 4, $c\bar{c}h$ 2, $Kch$ 2, $c^{\ast }cc$ 1, ${\varphi }^{\ast }c\varphi$ 1. This is a topology-level inventory only. The amplitude rules, the counterterm domain over $\mathbb{Q}(i)$ (including evanescent operators), the evaluation, the three-point defect and ${\sigma }_0$ closure are not done in p23, so no defect outcome is claimed.

from the p22 review. (i) Polynomial-domain refusal (p23 contract revision, one block appended to dred.py). From outside sympy, polynomial algebra that can evaluate $d$ raises: rem, prem, div, resultant, compose, Poly.shift, Poly.rem, and similar. Internal renames of $d$ are admitted only to a Dummy, so Matrix.subs(d$\to$y) raises. A live probe runs 9 forms on 4 expressions, and rational-function algebra is unchanged. (ii) The gate now checks the values $\rho =1/2$, $E_2$ coefficient $-1/16$, SE coefficient $+1/8$, and the summed h.h coefficients against both pinned values and the archived p22 certificate. (iii) The README title line carries “two-point functions with QdS external legs”.