Proposition 7.10 . [056A] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Proposition 7.10 .
In the intersection 𝐈𝐈𝐈 − ∩ U β , t 1 {\bf{III}_{-}}\cap{U_{\beta,t}^{1}} k ≥ 0 k\geq 0
(7.140) | ∇ k ( ϕ t , 𝐈𝐈𝐈 − ∘ ( π β 1 ) − 1 − ϕ 1 ) | = ϵ ¯ T 2 , |\nabla^{k}(\phi_{t,\bf{III}_{-}}\circ(\pi_{\beta}^{1})^{-1}-\phi_{1})|=\underline{\epsilon}_{T^{2}},
where derivative is taken with respect to the metric ω T Y , 1 \omega_{TY,1}