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

One ambient space

F2: ambient space and the intrinsic conormal matching › One ambient space · lines 878–917

All new matching calculations take place in

W = A \times B \times Z \times Y, dim W = 16,

with coordinate order $(a, b, z, y)$ .

The three loci remain distinct:

N^{\circ} \subset B \times A \times Y, codim = 4,

N_{att} = P^{- 1} (N^{\circ}) \subset W, codim = 4,

N_{att} = N_{att} \cap D_{obs} \subset W, codim = 8.

No three-vertex degree or codimension is substituted for a common-kernel degree or codimension.

We work on the already retained chronological neighborhood

y^{0} - a^{0} > 0, b^{0} - y^{0} > 0.

Write

d = a - z .

Define the six-constraint stage and the full incidence set by

S_{6} = {q_{1} = q_{2} = 0, d = 0} \subset W, N = {q_{R} = q_{1} = q_{2} = 0, d = 0} .

By the copied zero-locus result,

N = N_{att} .

Displayed formulas in this passage

unlabeled · line 881
$W = A \times B \times Z \times Y, dim W = 16,$
unlabeled · line 887
$N^{\circ} \subset B \times A \times Y, codim = 4,$
unlabeled · line 890
$N_{att} = P^{- 1} (N^{\circ}) \subset W, codim = 4,$
unlabeled · line 893
$N_{att} = N_{att} \cap D_{obs} \subset W, codim = 8.$
unlabeled · line 900
$y^{0} - a^{0} > 0, b^{0} - y^{0} > 0.$
unlabeled · line 904
$d = a - z .$
unlabeled · line 908
$S_{6} = {q_{1} = q_{2} = 0, d = 0} \subset W, N = {q_{R} = q_{1} = q_{2} = 0, d = 0} .$
unlabeled · line 914
$N = N_{att} .$