Answer: —
Theorem 5.10 — class: other
Given integers \(t,w\) with \(\lceil(t+1)/2\rceil\leq w\leq t\), optimize over societies \(\mu\in\Delta(\{0,1\}^t)\). Let \(M_j(\mu)=\max\{\mu(v_j=0),\mu(v_j=1)\}\), and let \(A_\mu(p)\) be the topics on which proposal \(p\) agrees with the topic-wise majority. Subject to every \(p\) with \(|A_\mu(p)|\geq w\) having \(\mu(\{v:d_H(v,p)\leq\lfloor t/2\rfloor\})<1/2\), determine the supremum of \(\frac{1}{t}\sum_{j=1}^t M_j(\mu)\) and provide an \(\varepsilon\)-optimal society for any \(\varepsilon>0\).
Tier: machine-proved, adversarially reviewed by an independent model. No human has checked this proof. Generated from pipeline artifacts by tools/atlas_build.py.