Proposition 7.7 . [0564] 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 7.7 .
In the Region 𝐈𝐈 − ∩ U β , t 1 {\bf{II}_{-}}\cap U_{\beta,t}^{1} k ≥ 0 k\geq 0
(7.107) | ∇ k ( ϕ t , 𝐈𝐈 − ∘ ( π β 𝒩 ) − 1 − ϕ − ) | = ϵ ¯ T 2 , |\nabla^{k}(\phi_{t,\bf{II}_{-}}\circ(\pi_{\beta}^{\mathcal{N}})^{-1}-\phi_{-})|=\underline{\epsilon}_{T^{2}},
where derivative and norm are taken with respect to the metric ω T \omega_{T}