Proposition 7.12 . [056C] 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 7.12 .
On 𝐈𝐈𝐈 − ∩ 𝐈𝐈 − \bf{III}_{-}\cap\bf{II}_{-} k ≥ 0 k\geq 0
(7.145) | ∇ k ( ϕ t , 𝐈𝐈𝐈 − − η 1 ) | = O ( e − δ Z 1 T ) , |\nabla^{k}(\phi_{t,\bf{III}_{-}}-\eta_{1})|=O(e^{-\delta_{Z_{1}}T}),
where the derivative and norm are taken with respect to ω ( t ) \omega(t) δ Z 1 \delta_{Z_{1}} 7.4 Z 1 Z_{1}