Conclusion

Displayed formulas in this passage

• unlabeled · line 1286

  $$\boxed{\begin{array}{c}\text{parameter-local/one-retarded output}+\text{ free-shell descent}⟹{\bar{\delta }}_{\xi }=0,\\ \theta =[h\zeta {\partial }_t,(t-t_{\ast })h\zeta {\partial }_t]=h^2{\zeta }^2{\partial }_t,\\ {\mathfrak{B}}_{\theta }(u_{\ast })=-8I<0,(d_{\bar{\delta }}\bar{\mathfrak{B}})(\xi ,\eta )=-{\bar{\mathfrak{B}}}_{\theta }\ne 0,\\ {\mathfrak{K}}_{\mathrm{loc},\mathrm{R}}\text{ on the detecting fixed data: }\text{Proved obstructed},\\ {\mathcal{C}}_{\theta }(u_{\ast })=8I\text{is an admitted cochain value, not an integrated completion.}\end{array}}$$