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

Input statement: XIV-D and XIV-C

H0: copied handoffs and their domains › The retained germ, characteristic locus, and contacts · lines 473–531

XIV-H@1#input:DC

The full 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} .

On the retained mixed patch,

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

The kernels $K_{6}, K_{8}, K_{9}$ are supported on the actual local source or metric attachment incidence $a = z$ .

The relation

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

is limited to the leading differential numerator of $B_{6}$ . It is not a section of the complete sum XIVD.

In the common space

W = A \times B \times Z \times Y, (a, b, z, y) in this order,

the test locus is

N = N_{att} = {a = z} \cap {y = a + α ℓ_{n}, b = a + β ℓ_{n}, 0 < α < β},

where $ℓ_{n} = (1, n)$ and $n \in S^{2}$ . It has codimension eight in the sixteen-dimensional space.

Writing

q_{R} = (b - a)^{2}, q_{1} = (y - a)^{2}, q_{2} = (b - y)^{2},

the copied positive relation is

- \frac{d q _{R}}{2 β} + \frac{d q _{1}}{2 α} + \frac{d q _{2}}{2 ( β - α )} = 0.

It is diagnostic input data, not an output symbol relation.

Defined collision contacts vanish on the retained collision-free attachment neighborhood XIVC,XIVD.

Displayed formulas in this passage

unlabeled · line 476
$O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D} .$
unlabeled · line 482
$K_{ret} = K_{4} + K_{5} + K_{6} + K_{7} + K_{8} + K_{9} .$
unlabeled · line 489
$p_{α} p_{μ} a_{2} ˙^{α μ} [G; p \otimes k + k \otimes p] = G (p^{♯}, p^{♯}) (p \cdot k)$
unlabeled · line 498
$W = A \times B \times Z \times Y, (a, b, z, y) in this order,$
unlabeled · line 503
$N = N_{att} = {a = z} \cap {y = a + α ℓ_{n}, b = a + β ℓ_{n}, 0 < α < β},$
unlabeled · line 516
$q_{R} = (b - a)^{2}, q_{1} = (y - a)^{2}, q_{2} = (b - y)^{2},$
unlabeled · line 522
$- \frac{d q _{R}}{2 β} + \frac{d q _{1}}{2 α} + \frac{d q _{2}}{2 ( β - α )} = 0.$