p22: evanescent components (EV-M2), evanescent counterterms (EV-CT) and the runtime d guard

-CT: the counterterms. The coefficient is $-(\text{UV pole})$ in the $N_{ϵ}{\kappa }^2/ϵ$ normalisation of P14. There are three pieces:

• h.h operators for the eight $\tilde{g}$ structures, summed over D01+D03+D11: $g_4\tilde{g}(p^2{)}^2$: $-7i/120$ (twice); $g_{4,mr}{\tilde{g}}_{ns}(p^2{)}^2$: $-i/160$; $\tilde{g}\tilde{g}(p^2{)}^2$: $i/160$ (twice); $\tilde{g}pp{p}^2$: $7i/120$ (twice), $i/160$. Per-graph values are in certificates/P22_evanescent.json.

• the K${}^{\prime }$.c operator for D13 $E_2$, with coefficient $-1/16$;

• its ghost-equation partner $\bar{c}{\Sigma }_{\mathrm{SE}}c$, with coefficient $+1/8$.

Closure. ${\sigma }_0$ of the counterterms is zero in every sector, so full closure holds with the evanescent counterterms included. In h.c, the per-graph $p\cdot T$ of D01 and D03 cancel in the sum, D11 is transverse, and $E\cdot E_2=0$. In c.b, the ghost equation with $\rho =1/2$ (calibrated on the 4D pair) holds exactly in $d$ for $E_2$ and ${\Sigma }_{\mathrm{SE}}$. c.cbs is unreachable. Identity. The h.h slot values of the counterterm sum are zero in all six external modes, and the K.c slot values are zero, so the projected identity is unchanged. Remnants. The finite evanescent parts are nonzero, but they vanish identically on hatted external legs. With QdS external legs there is no $O(ϵ)\times$pole effect. If external traces are taken with $g_4$ (Q4S), a finite term $7i{p}^2(\hat{a}\cdot \hat{b}{p}^2-\hat{a}\cdot p\hat{b}\cdot p)/60$ arises. It is disclosed as a scheme choice. Mutations. Each of the following is detected: dropping the D01 or D03 counterterm; doubling D03; dropping the SE partner; flipping the sign of the $E_2$ counterterm; and putting a trace operator in place of $s_{0}h$. Status. P.5 calculation status is renormalized (one loop, ${\kappa }^2$, the two-point functions hh / K${}^{\prime }$.c / $\bar{c}$c, MS-bar in DRED with the p22 evanescent counterterms, external legs in QdS). It does not cover higher points, two loops, bulk symmetry or O.1.

{Runtime $d$ guard.} The guard intercepts the following calls whenever the caller is outside sympy/mpmath/dred: subs, xreplace (including on a bare $d$), replace, evalf/n, the Poly value and coefficient accessors, coeff, as_independent, as_coeff_exponent, series, collect, limit, Lambda, and $d==d$. Any of them that would give $d$ a value raises PrematureD4Substitution. Authorised paths (substitute_d, authorised_d) still work. A live probe in the gate runs 30 forms on 4 expressions: every reviewer form from p21, the power-base hole, alias and free_symbols lookups, Symbol.__new__ and Function calls. All of them raise, and ordinary algebra is unchanged. Some bypasses cannot be intercepted at runtime: identity (is) tests, string round-trips and Poly.rep. These are disclosed and covered only by the secondary static allow-list scan.