C3 repaired: the boundary identity and its orientation

Builder/output: boundary_identity.py, P13_boundary_identity.json.

Defect. The p09/p10 control C3 evaluated the identity on $g=\eta +A(x^0)e_{00}$. This metric is locally flat ($x^0\mapsto \int \sqrt{1+A}d{x}^0$ removes $A$); its only nonzero symbol is ${\Gamma }^0{}_{00}$, and $\sqrt{-g}R=L_{\Gamma \Gamma }=B^{\mu }={\partial }_{\mu }{B}^{\mu }=0$ identically. The check was therefore vacuous and could not detect a sign; the source comment “keeps $\partial B$ nontrivial” was false. p09/p10 also stated the orientation as $\sqrt{-g}R-L_{\Gamma \Gamma }=+{\partial }_{\mu }{B}^{\mu }$. That orientation is wrong.