Manuscript X-C@3 · X-C-v3.tex · scope · 2260f5f8

Release: Constructed, through κ 2 at fixed

Release, reassigned target, and the three endings · lines 254–286

{Release: Constructed, through $κ^{2}$ at fixed $ε$ }{ On the X-B-v3 sheet, the maps

R_{1} (V_{2, g}; F_{c}) = ϕ (- L_{2, g} E_{m}^{A} c), \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{c}) = ϕ (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} c)

exist on the frozen off-shell linear tests, have smooth compact retarded output, and carry no positive power of $ℏ$ . Their sum on $F_{f}$ is the copied response $\int f ρ_{2, g}$ , where

ρ_{2, g} [u] = E_{m}^{R} L_{1, g} E_{m}^{R} L_{1, g} u - E_{m}^{R} L_{2, g} u .

The completed coefficient

A_{2} = O^{(2)} + R_{1} (V_{1, g}; F_{c_{1}}) + R_{1} (V_{2, g}; F_{f}) + \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{f})

is invariant in $A_{0}$ on $g_{U}$ , with the free field held fixed. Together with the copied $A_{1}$ , this gives background invariance through $κ^{2}$ . The pure-gauge remainder is cancelled with $O^{(2)}$ retained.

Not claimed: the sharp limit, quantum metric, graviton tree, triangle, $T_{2}$ , $T_{3}$ , nonlinear-insertion $R_{2}$ , or two-point responses.}

Displayed formulas in this passage

unlabeled · line 256
$R_{1} (V_{2, g}; F_{c}) = ϕ (- L_{2, g} E_{m}^{A} c), \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{c}) = ϕ (L_{1, g} E_{m}^{A} L_{1, g} E_{m}^{A} c)$
unlabeled · line 266
$ρ_{2, g} [u] = E_{m}^{R} L_{1, g} E_{m}^{R} L_{1, g} u - E_{m}^{R} L_{2, g} u .$
unlabeled · line 270
$A_{2} = O^{(2)} + R_{1} (V_{1, g}; F_{c_{1}}) + R_{1} (V_{2, g}; F_{f}) + \frac{1}{2} R_{2} (V_{1, g}, V_{1, g}; F_{f})$

Nearby in this section

section: Release, reassigned target, and the three endings