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

Input statement: XIV-D: pair and retained germ

Release criteria and copied premises · lines 330–373

XIV-E@1#input:XIVD

The frozen observable is

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} .

The inverse and ambiguity conventions are

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

Let $A, B, Y$ be the pairwise separated neighborhoods of $u_{0}, x_{0}, y_{0}$ , and let $Z \subset A$ be the residual metric neighborhood. In the common variables

a \in A, b \in B, z \in Z, y \in Y,

the mixed observable kernel satisfies

K_{Σ} ∣_{A \times B \times Z} = (K_{4} + K_{5} + K_{6} + K_{7} + K_{8} + K_{9}) ∣_{A \times B \times Z} .

The other branches remain in the global pair and vanish only on the proved germ or species channel. In particular, $K_{8}$ and $K_{9}$ retain both gravitational-response legs.

The kernels $K_{6}, K_{8}, K_{9}$ are supported on the observable metric diagonal $a = z$ . The retained mixed germ has 24 potentially surviving labelled matchings.

The leading fiber identity

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

is a branch diagnostic. It does not decide the complete sum.

No joint symbol or characteristic prescription was constructed. The first missing step was D2 XIVD.

Displayed formulas in this passage

unlabeled · line 333
$O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D} .$
unlabeled · line 339
$G_{gr}^{R} = - P E_{0}^{R}, C_{tot} \subseteq C_{part} .$
unlabeled · line 346
$a \in A, b \in B, z \in Z, y \in Y,$
unlabeled · line 350
$K_{Σ} ∣_{A \times B \times Z} = (K_{4} + K_{5} + K_{6} + K_{7} + K_{8} + K_{9}) ∣_{A \times B \times Z} .$
unlabeled · line 363
$p_{α} p_{μ} a_{2} ˙^{α μ} [G; r] = Q λ, r = p \otimes k + k \otimes p, Q = G (p^{♯}, p^{♯}), λ = p \cdot k,$

Input statement: XIV-D: pair and retained germ

Displayed formulas in this passage

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