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

Input statement: Lifts and excluded elementary phase

G0: copied inputs and the unchanged stop › XIV-E: regrouping, root, and tested kernels · lines 502–542

XIV-G@1#input:Elifts, XIV-G@1#eq:Equadratic

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

define

N_{att} = P^{- 1} (N^{\circ}), D_{obs} = {a = z}, N_{att} = N_{att} \cap D_{obs} .

The copied codimensions are

codim_{W} N_{att} = 4, codim_{W} D_{obs} = 4, codim_{W} N_{att} = 8.

The elementary phase of XIV-E is neither nondegenerate nor clean. Its auxiliary equations have rank six and its critical set has codimension eight.

On the copied affine transverse slice,

- \frac{q _{R}}{β} + \frac{q _{1}}{α} + \frac{q _{2}}{β - α} = - \frac{∣ α v - β w ∣ ^{2}}{α β ( β - α )} .

“Equation (eq:Equadratic) is a geometric identity, not a scaling degree of a distribution.”

The ending is “Unresolved at E1, within D2/J2” XIVE.

Displayed formulas in this passage

XIV-G@1#eq:Equadratic · line 527
$- \frac{q _{R}}{β} + \frac{q _{1}}{α} + \frac{q _{2}}{β - α} = - \frac{∣ α v - β w ∣ ^{2}}{α β ( β - α )} .$
unlabeled · line 505
$W = A \times B \times Z \times Y, P (a, b, z, y) = (b, a, y),$
unlabeled · line 510
$N_{att} = P^{- 1} (N^{\circ}), D_{obs} = {a = z}, N_{att} = N_{att} \cap D_{obs} .$
unlabeled · line 516
$codim_{W} N_{att} = 4, codim_{W} D_{obs} = 4, codim_{W} N_{att} = 8.$