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

Input statement: Characteristic geometry and contact rigidity

F0: copied analytic inputs › XIV-D and XIV-C: the retained instance · lines 507–550

XIV-F@1#input:C, XIV-F@1#eq:conormal-relation

The 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} .

This is a smooth codimension-four stratum. For

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

the 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 corresponding oriented conormals have a 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-F@1#eq:conormal-relation · line 538
$- \frac{d q _{R}}{2 β} + \frac{d q _{1}}{2 α} + \frac{d q _{2}}{2 ( β - α )} = 0.$
unlabeled · line 510
$u_{0} = (t_{*}, 0, 0, 0), y_{0} = (t_{*} + L, L, 0, 0), x_{0} = (t_{*} + 2 L, 2 L, 0, 0),$
unlabeled · line 516
$ε < t_{*} < t_{*} + 2 L < T, f (x_{0}) \neq = 0,$
unlabeled · line 522
$N^{\circ} = {y = a + α ℓ_{n}, b = a + β ℓ_{n}, ℓ_{n} = (1, n), n \in S^{2}, 0 < α < β} .$
unlabeled · line 532
$q_{R} = (b - a)^{2}, q_{1} = (y - a)^{2}, q_{2} = (b - y)^{2},$