Manuscript XIV-E@1 · XIV-E.tex · section · e89fd2a5

The grouped characteristic target

E0: the six-branch contract › The grouped characteristic target · lines 492–516

XIV-E@1#eq:target

The complete formal two-line expression remains

B_{form} = \frac{i}{2} ⟨ V_{g}^{''} \otimes O^{''}, H_{T}^{\otimes 2} - H^{\otimes 2} ⟩ .

On the retained mixed germ it is

i Contr^{γ ϕ} (V_{g}^{''}_{γ ϕ}, K_{ret}; H_{T}_{γ γ} (y, a) \otimes H_{T}_{ϕϕ} (y, b) - H_{γ γ} (y, a) \otimes H_{ϕϕ} (y, b)), K_{ret} = j = 4 \sum^{9} K_{j} .

The factor $i$ includes the two mixed slot orderings of XIV-D.

This difference stays grouped. Formula (eq:target) specifies the composition to be constructed; it does not assert its existence on the characteristic set.

Displayed formulas in this passage

XIV-E@1#eq:target · line 501
$i Contr^{γ ϕ} (V_{g}^{''}_{γ ϕ}, K_{ret}; H_{T}_{γ γ} (y, a) \otimes H_{T}_{ϕϕ} (y, b) - H_{γ γ} (y, a) \otimes H_{ϕϕ} (y, b)), K_{ret} = j = 4 \sum^{9} K_{j} .$
unlabeled · line 495
$B_{form} = \frac{i}{2} ⟨ V_{g}^{''} \otimes O^{''}, H_{T}^{\otimes 2} - H^{\otimes 2} ⟩ .$