Antithetic SNIS identity: Y_{2m} − (Y₁+Y₂)/2 = (B₁−B₂)(Y₁−Y₂)/(2(B₁+B₂)), where B_h are the half-sample mean weights and Y_h the half-sample SNIS outputs

The exact identity behind the external reviewer's antithetic multilevel route (2026-10-05): the level difference is a product of two first-order fluctuations, so under a bounded weight envelope its second moment is O(m⁻²) and randomised dyadic levels with probabilities ∝ 2^{−γℓ}, 1 < γ < 2, give exactly unbiased SNIS without a dense terminal level at O_{K,F}(ε⁻²) expected draws. The identity is proved here; the moment bounds and the level randomisation are the reviewer's paper argument, with constants depending on the envelope K rather than on the cost factor alone.