Manuscript XIV-J@1 · XIV-J.tex · input · 1c0e72ca

Input statement: XIV-D and XIV-C

J0: copied premises and their domains › Earlier analytic handoffs · lines 642–689

XIV-J@1#input:DC

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

the retained mixed germ is the complete six-branch sum $K_{4} + \dots + K_{9}$ . Other branches are zero only on their proved local germ or species channel.

The test locus is

N = N_{att} = {a = z, y = a + α ℓ_{n}, b = a + β ℓ_{n}, ℓ_{n} = (1, n), 0 < α < β},

with $n \in S^{2}$ . It has dimension eight and codimension eight in $W$ .

For

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.

Defined interaction collision contacts vanish on the retained separated attachment neighborhood.

The identity

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

is a branch-limited numerator, not a joint section XIVD,XIVC.

Displayed formulas in this passage

unlabeled · line 645
$W = A \times B \times Z \times Y, (a, b, z, y),$
unlabeled · line 653
$N = N_{att} = {a = z, y = a + α ℓ_{n}, b = a + β ℓ_{n}, ℓ_{n} = (1, n), 0 < α < β},$
unlabeled · line 667
$q_{R} = (b - a)^{2}, q_{1} = (y - a)^{2}, q_{2} = (b - y)^{2},$
unlabeled · line 673
$- \frac{d q _{R}}{2 β} + \frac{d q _{1}}{2 α} + \frac{d q _{2}}{2 ( β - α )} = 0.$
unlabeled · line 682
$p_{α} p_{μ} a_{2} ˙^{α μ} [G; p \otimes k + k \otimes p] = G (p^{♯}, p^{♯}) (p \cdot k) = Q λ$

Input statement: XIV-D and XIV-C

Displayed formulas in this passage

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