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

Input statement: Characteristic configuration and rigidity

G0: copied inputs and the unchanged stop › XIV-D and XIV-C: the retained germ and conormal relation · lines 580–623

XIV-G@1#input:C, XIV-G@1#eq:positive

The fixed retained points are

u_{0} = (t_{*}, 0, 0, 0), y_{0} = (t_{*} + L, L, 0, 0), x_{0} = (t_{*} + 2 L, 2 L, 0, 0),

where

ε < t_{*} < t_{*} + 2 L < T, f (x_{0}) \neq = 0,

and the fixed switch is one near these points.

In the order $(b, a, y) = (x, u, y)$ ,

N^{\circ} = {y = a + α ℓ_{n}, b = a + β ℓ_{n}, ℓ_{n} = (1, n), n \in S^{2}, 0 < α < β} .

It is smooth of codimension four. With

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

the cone differentials have rank two and satisfy

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

The oriented line conormals have the copied positive relation.

“Every defined contact change in $C_{part}$ for this graph restricts to zero on $V$ .”

The first unresolved gate is J2 XIVC.

Displayed formulas in this passage

XIV-G@1#eq:positive · line 611
$- \frac{d q _{R}}{2 β} + \frac{d q _{1}}{2 α} + \frac{d q _{2}}{2 ( β - α )} = 0.$
unlabeled · line 583
$u_{0} = (t_{*}, 0, 0, 0), y_{0} = (t_{*} + L, L, 0, 0), x_{0} = (t_{*} + 2 L, 2 L, 0, 0),$
unlabeled · line 589
$ε < t_{*} < t_{*} + 2 L < T, f (x_{0}) \neq = 0,$
unlabeled · line 595
$N^{\circ} = {y = a + α ℓ_{n}, b = a + β ℓ_{n}, ℓ_{n} = (1, n), n \in S^{2}, 0 < α < β} .$
unlabeled · line 605
$q_{R} = (b - a)^{2}, q_{1} = (y - a)^{2}, q_{2} = (b - y)^{2},$