Manuscript XIV-H@1 · XIV-H.tex · section · 695c7c3a

The existing tree maps with z retained

H2d: the two internal placements in K 5 › The existing tree maps with z retained · lines 1190–1216

XIV-H@1#eq:L

Define the coordinate-response line

L^{μ, I} (s, a) = σ_{ε} (a) A^{λ μ, I} \partial_{a^{λ}} R (s - a) .

Thus

X^{μ} [h] (s) = \int L^{μ, I} (s, a) h_{I} (a) d^{4} a .

The two terms of $K_{5}$ have the actual internal maps

z ⟶ s ⟶ b, s = a,

and

a ⟶ s ⟶ b, s = z,

respectively. The equalities $s = a$ and $s = z$ come from the displayed local metric factor in that placement. They are not assignments of a singular internal point to a retained configuration.

Displayed formulas in this passage

XIV-H@1#eq:L · line 1193
$L^{μ, I} (s, a) = σ_{ε} (a) A^{λ μ, I} \partial_{a^{λ}} R (s - a) .$
unlabeled · line 1200
$X^{μ} [h] (s) = \int L^{μ, I} (s, a) h_{I} (a) d^{4} a .$
unlabeled · line 1205
$z ⟶ s ⟶ b, s = a,$
unlabeled · line 1209
$a ⟶ s ⟶ b, s = z,$

The existing tree maps with z retained

Displayed formulas in this passage

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