Item AbInitioQHub#3: distribute the Sigma^C inner qy work across ranks (extend the tuple distribution to (s,k,qx,qy)); per-tile partials, final reduce unchanged in result. Item AbInitioQHub#4: distribute Pi^C over (s,k,qx,q_ext) and REPLACE the replicated T0/T1/M0/M1 pair caches (4*ns*nk*nq_ext*nt*Nb2*Np, the AbInitioQHub#1 memory wall) with per-tile recompute (one tile live) -> per-rank pair-cache memory down by factor ns*nk*nq_ext (toy: 350KB -> 39KB). Item AbInitioQHub#5-finish: node-share X_skPa/X_C (Xhat deferred to M3/AbInitioQHub#9). All reduction-order changes (qy/q_ext splitting); per-tile DLR channel / twisted-pair arithmetic byte-identical, only the sums reorder. Validated: NEW Sigma^C + Pi^C rank invariance P=1 vs 4/8/16 <= 5.5e-16 (contract 1e-11); C=empty + sym-noop EXACT (==); conservation identity (both cuts), sigma/pi pins, refinement2, wredist within the tolerance table; pair-cache memory reduction asserted. Clean make -j4. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Uh oh!

Unit tests are too slow #4

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