Manuscript XI-C@1 · XI-C.tex · section · acec1422

The named XI-A witness

Normalization to the de Donder violation › The named XI-A witness · lines 836–858

XI-C@1#eq:emptywitness

For

ϕ_{m} (t) = {sin (m t) / m, t, m > 0, m = 0,

XI-A gives $T_{0}^{00} = 1/2$ and $T_{0}^{0 i} = 0$ . Hence

X_{1}^{0} [r_{g} [ϕ_{m}]] = - \frac{1}{4} E_{0}^{R} E_{0}^{R} (\partial_{t} g) \neq \equiv 0.

A nonzero compact interior switch cannot be time independent. Injectivity in Theorem thm:normalization proves the nonzero claim.

Both $r_{g}$ and its divergence exist. The failure is the conservation condition needed for the ungauge-fixed Einstein equation. Therefore $J_{g} (ϕ_{m}) = \emptyset$ remains the XI-A result XIA. The tree does not provide a missing Einstein jet.

Displayed formulas in this passage

XI-C@1#eq:emptywitness · line 844
$X_{1}^{0} [r_{g} [ϕ_{m}]] = - \frac{1}{4} E_{0}^{R} E_{0}^{R} (\partial_{t} g) \neq \equiv 0.$
unlabeled · line 839
$ϕ_{m} (t) = {sin (m t) / m, t, m > 0, m = 0,$