Manuscript XIV-J@1 · XIV-J.tex · input · 1c0e72ca

Input statement: Both K 5 placements

J0: copied premises and their domains › XIV-H's exact maps · lines 475–517

XIV-J@1#input:H5, XIV-J@1#eq:K5

Put

L^{μ, I} (s, a) = σ_{ε} (a) A^{λ μ, I} \partial_{a^{λ}} R (s - a) .

Then

K_{5}^{I, J} (a, b, z) = \partial_{b^{μ}} [+ f (b) σ_{ε} (a) \partial_{a^{α}} R (b - a) A^{α β, I} \partial_{a^{β}} L^{μ, J} (a, z) f (b) σ_{ε} (z) \partial_{z^{α}} R (b - z) A^{α β, J} \partial_{z^{β}} L^{μ, I} (z, a)] .

Its two seed products are

R (b - a) R (a - z), R (b - z) R (z - a) .

Their actual coordinate maps are tensor-product diffeomorphisms, so the kernels are defined at $a = z$ .

On regular separated-cone charts the upper conormal order is one. On the stated comparable-frequency, noncharacteristic diagonal charts it is $1/2$ .

The internal diagonal and limiting flow-out pieces intersect cleanly in dimension fifteen and have tangent sum seventeen. They do not form one ordinary smooth Lagrangian. This is not XIV-F's non-clean matching XIVH.

Displayed formulas in this passage

XIV-J@1#eq:K5 · line 484
$K_{5}^{I, J} (a, b, z) = \partial_{b^{μ}} [+ f (b) σ_{ε} (a) \partial_{a^{α}} R (b - a) A^{α β, I} \partial_{a^{β}} L^{μ, J} (a, z) f (b) σ_{ε} (z) \partial_{z^{α}} R (b - z) A^{α β, J} \partial_{z^{β}} L^{μ, I} (z, a)] .$
unlabeled · line 478
$L^{μ, I} (s, a) = σ_{ε} (a) A^{λ μ, I} \partial_{a^{λ}} R (s - a) .$
unlabeled · line 500
$R (b - a) R (a - z), R (b - z) R (z - a) .$

Input statement: Both K 5 placements

Displayed formulas in this passage

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