证明
Corollary 25 ([Contraction of antisymmetric products]). There are ν'>0 , s_0<∞…Lemma 27 ([Normalized insertion tail]). There are constants ξ>0 , m_0<∞ , and…观点
Take concentric cuts about the origin, starting at radius 10m and ending at a radius comparable with a small fixed fraction of R , with consecutive radii in ratio L . Round the final radius down to the last such scale. Its ratio to R is bounded below by a positive constant depending only on the already fixed L . All cut collars lie strictly inside both rectangles and outside both inserted points. If necessary, enlarge the fixed lower bound on R/m ; the remaining bounded ratios follow by increasing C , since all four scalar quantities in the determinant are bounded. First restrict every test to success of every cut screen, with the screens evaluated on the common base process. The probability discarded is bounded by C∑_ j≥0 (-cm^2L^ 2j ) ≤Ce^ -c'm^2 . At the first cut let a be the signed connection-state message obtained by changing the central color. Let b_y be the difference of this message with and without the extra fair point at y . Both have zero mass conditional on each seam, and their total variation norms are bounded by 2 and 4 , respectively. They depend on neither R nor R' : on screen success their construction uses only the common interior Poisson variables and the first seam. In particular this description does not require disjoint neighborhoods of 0 and y . Let T be the composed transfer through the intervening cuts. The exterior crossing tests in RQ_0 and R'Q_0 define bounded linear functionals ℓ_R and ℓ_ R' at the final cut. The four restricted expectations are ℓ_R(Ta), ℓ_ R' (Ta), ℓ_R(Tb_y), ℓ_ R' (Tb_y). Their determinant is the evaluation of T^ ⊗2 on b_y⊗a-a⊗b_y by ℓ_R⊗ℓ_ R' . Corollary 25 ([Contraction of antisymmetric products]) therefore bounds it by C(m/R)^ 2λ+ν' . Restoring the discarded events changes the determinant by at most Ce^ -cm^2 , because each scalar factor is bounded. This proves.