Manuscript XIV-G@1 · XIV-G.tex · input · 791c6644

Input statement: Pair, species, and branch limitation

G0: copied inputs and the unchanged stop › XIV-D and XIV-C: the retained germ and conormal relation · lines 546–578

XIV-G@1#input:D

The frozen pair has

O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D} .

On the retained common-variable patch,

K_{Σ} = K_{4} + K_{5} + K_{6} + K_{7} + K_{8} + K_{9} .

The kernels $K_{6}, K_{8}, K_{9}$ are supported on $a = z$ .

“The complete mixed germ is therefore a six-branch sum. In particular, neither the coordinate gravitational leg $B_{8}$ nor the scalar gravitational leg $B_{9}$ may be omitted.”

The inherited mixed species factor is $i$ . The scalar–scalar factor is $i /2$ , and that channel vanishes only on the specified retained output-location patch.

For $p^{2} = 0$ and $r = p \otimes k + k \otimes p$ ,

p_{α} p_{μ} a_{2} ˙^{α μ} [G; r] = G (p^{♯}, p^{♯}) (p \cdot k) = Q λ .

“The proposition computes only one branch's leading differential numerator. It supplies no sum identity or sum nonvanishing theorem for that complete expression.”

The first unresolved step is D2, within J2 XIVD.

Displayed formulas in this passage

unlabeled · line 549
$O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D} .$
unlabeled · line 554
$K_{Σ} = K_{4} + K_{5} + K_{6} + K_{7} + K_{8} + K_{9} .$
unlabeled · line 568
$p_{α} p_{μ} a_{2} ˙^{α μ} [G; r] = G (p^{♯}, p^{♯}) (p \cdot k) = Q λ .$

Input statement: Pair, species, and branch limitation

Displayed formulas in this passage

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