Proposition 7.8 . [0566] 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 7.8 .
On the intersection 𝐈𝐈 − ∩ 𝐈 ∩ X ^ t {\bf{II}_{-}}\cap{\bf{I}}\cap\widehat{X}_{t} k ≥ 0 k\geq 0
(7.131) | ∇ k ( ϕ t , 𝐈𝐈 − − ϕ t , 𝐈 − − d 1 log t ) | = ϵ ¯ T 2 , |\nabla^{k}(\phi_{t,\bf{II}_{-}}-\phi_{t,\bf{I}_{-}}-d_{1}\log t)|=\underline{\epsilon}_{T^{2}},
where the derivative and norm are taken with respect to ω ( t ) \omega(t)