Manuscript X-G-ST@1 · X-G-ST.tex · section · 3c97567f

Bare versus completed counting

Stage 4: graph inventory and the remaining quantum gate › Bare versus completed counting · lines 1764–1786

X-G-ST@1#eq:combinatorics

For a separately specified variational theory, let

V = κ V_{1} + κ^{2} V_{2} + \dots, O = F_{f} + κ O_{1} + κ^{2} O_{2} + \dots .

Its formal retarded expansion would have second coefficient

O_{2} + R_{1} (V_{1}; O_{1}) + R_{1} (V_{2}; F_{f}) + \frac{1}{2} R_{2} (V_{1}, V_{1}; F_{f}) .

This is a counting identity, not existence of the maps on the nonlocal insertion FR,XG.

The bare $O_{1}$ contains $c_{1}$ , not $d_{1}$ followed by a second generation of its scalar completion. Starting from completed (eq:tests) and applying the same full scalar retarded correction again would duplicate terms.

Displayed formulas in this passage

X-G-ST@1#eq:combinatorics · line 1773
$O_{2} + R_{1} (V_{1}; O_{1}) + R_{1} (V_{2}; F_{f}) + \frac{1}{2} R_{2} (V_{1}, V_{1}; F_{f}) .$
unlabeled · line 1767
$V = κ V_{1} + κ^{2} V_{2} + \dots, O = F_{f} + κ O_{1} + κ^{2} O_{2} + \dots .$