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

Input statement: Lifts, phase exclusion, and quadratic defect

F0: copied analytic inputs › XIV-E: the exact successor package · lines 415–463

XIV-F@1#input:geometryE, XIV-F@1#eq:copied-quadratic

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

the two characteristic lifts are

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

Their intersection is transverse.

The elementary product phase of XIV-E has rank-six auxiliary equations and a codimension-eight critical set. It is neither nondegenerate nor clean.

On the affine transverse slice

b - a = β ℓ_{n} + (0, v), y - a = α ℓ_{n} + (0, w), v, w \in n^{⊥},

the exact identity is

- \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:copied-quadratic) 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-F@1#eq:copied-quadratic · line 448
$- \frac{q _{R}}{β} + \frac{q _{1}}{α} + \frac{q _{2}}{β - α} = - \frac{∣ α v - β w ∣ ^{2}}{α β ( β - α )} .$
unlabeled · line 418
$W = A \times B \times Z \times Y, P (a, b, z, y) = (b, a, y),$
unlabeled · line 424
$N_{att} = P^{- 1} (N^{\circ}), D_{obs} = {a = z} \cap W, N_{att} = N_{att} \cap D_{obs} .$
unlabeled · line 430
$codim_{W} N_{att} = 4, codim_{W} D_{obs} = 4, codim_{W} N_{att} = 8.$
unlabeled · line 442
$b - a = β ℓ_{n} + (0, v), y - a = α ℓ_{n} + (0, w), v, w \in n^{⊥},$