bernoulli_pair_decoupling_spectral_tail_bound_offdiag

Faithful (corrected) order-2 de la Peña–Montgomery-Smith pair decoupling tail bound for the spectral norm over the Bernoulli powerset sampling model, carrying the EXACT tetrahedral / off-diagonal hypothesis the theorem requires. There exist universal constants $K,L>0$ (the order-2 decoupling constant $C_2$) such that for every matrix-valued bilinear sampling kernel $G$ that admits an off-diagonal bilinear representation $G(\Omega_1,\Omega_2)=\sum_{w_1\neq w_2}(\xi_{w_1}(\Omega_1)\,\xi_{w_2}(\Omega_2))\,a_{w_1 w_2}$ (centered indicators $\xi$, the $w_1\neq w_2$ guard being de la Peña–Montgomery-Smith's tetrahedral constraint $i_1\neq i_2$), the tail of the diagonal (coupled) statistic $G(\Omega,\Omega)$ under the single-sample measure is controlled by the tail of the decoupled statistic $G(\Omega_1,\Omega_2)$ under the independent-pair measure: if $\Pr[\,\|G(\Omega_1,\Omega_2)\|\le C_{dec}\,t\,]\ge 1-c_{dec}f$ then $\Pr[\,\|G(\Omega,\Omega)\|\le K\,C_{dec}\,t\,]\ge 1-L\,c_{dec}f$. This is the order-2 case of de la Peña–Montgomery-Smith, Decoupling Inequalities for the Tail Probabilities of Multivariate U-Statistics, Ann. Probab. 23 (1995), no. 2, 806–816 (arXiv:math/9309211), Theorem 1: $P(\|S\|\ge t)\le C_k P(C_k\|S'\|\ge t)$, summed over the tetrahedral index set $i_1\neq i_2$. NOTE: this replaces the earlier under-specified node bernoulli_pair_decoupling_spectral_tail_bound (3b904726), which dropped the tetrahedral hypothesis and quantified over an arbitrary $G$; decoupling is FALSE for kernels with a diagonal part, so the off-diagonal representation hypothesis is essential.