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

Input statement: XIV-F's geometric release

G0: copied inputs and the unchanged stop › XIV-F: immediate successor package · lines 357–417

XIV-G@1#input:Fgeometry, XIV-G@1#eq:Fquadratic, XIV-G@1#eq:Fdefect, XIV-G@1#eq:Fform

In the common space $W$ , the regular manifold is

S_{6} = {q_{1} = q_{2} = 0, a = z}, dim S_{6} = 10.

Its parameterization is

z = a, y = a + α (1, n_{1}), b = y + δ (1, n_{2}), α, δ > 0.

The exact formula is

q_{R} ∣_{S_{6}} = α δ ∣ n_{1} - n_{2} ∣^{2}, β = α + δ .

The selected conormal matching has

dim F_{match} = 15, dim (linearized matching) = 17.

It is smooth and not clean. Its tangent-defect quotient has rank two and is identified by

d_{w} (u) = α (δ b - δ a)_{⊥} - β (δ y - δ a)_{⊥} .

The copied quadratic form is

q_{w} (d_{⊥}) = - \frac{∣ d _{⊥} ∣ ^{2}}{α β ( β - α )} .

The covector-sum projection satisfies

rank d J = 14, dim (local fiber of J) = 1.

Its image is isotropic of dimension fourteen, not Lagrangian in $T^{*} W$ .

“The two components of $α v - β w$ measure a failure of clean tangency. They are not, merely by that calculation, an excess-two integration fiber.”

The two-dimensional tangent discrepancy persists under the specified smooth frequency reparameterizations and local vertical product reductions.

The ending is “Unresolved at F2, within the inherited E1/D2/J2 stop” XIVF.

Displayed formulas in this passage

XIV-G@1#eq:Fquadratic · line 371
$q_{R} ∣_{S_{6}} = α δ ∣ n_{1} - n_{2} ∣^{2}, β = α + δ .$
XIV-G@1#eq:Fdefect · line 385
$d_{w} (u) = α (δ b - δ a)_{⊥} - β (δ y - δ a)_{⊥} .$
XIV-G@1#eq:Fform · line 392
$q_{w} (d_{⊥}) = - \frac{∣ d _{⊥} ∣ ^{2}}{α β ( β - α )} .$
unlabeled · line 360
$S_{6} = {q_{1} = q_{2} = 0, a = z}, dim S_{6} = 10.$
unlabeled · line 364
$z = a, y = a + α (1, n_{1}), b = y + δ (1, n_{2}), α, δ > 0.$
unlabeled · line 379
$dim F_{match} = 15, dim (linearized matching) = 17.$
unlabeled · line 400
$rank d J = 14, dim (local fiber of J) = 1.$