Manuscript XIV-F@1 · XIV-F.tex · input · bae5a40b

Input statement: Pair, local incidence, and branch diagnostic

F0: copied analytic inputs › XIV-D and XIV-C: the retained instance · lines 469–505

XIV-F@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},

and

G_{gr}^{R} = - P E_{0}^{R}, C_{tot} \subseteq C_{part} .

On $A \times B \times Z$ ,

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 species expression has its inherited mixed factor $i$ and scalar–scalar factor $i /2$ . The scalar–scalar channel vanishes only on the 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 472
$O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D},$
unlabeled · line 477
$G_{gr}^{R} = - P E_{0}^{R}, C_{tot} \subseteq C_{part} .$
unlabeled · line 481
$K_{Σ} = K_{4} + K_{5} + K_{6} + K_{7} + K_{8} + K_{9} .$
unlabeled · line 495
$p_{α} p_{μ} a_{2} ˙^{α μ} [G; r] = G (p^{♯}, p^{♯}) (p \cdot k) = Q λ .$

Input statement: Pair, local incidence, and branch diagnostic

Displayed formulas in this passage

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