d4-conf-aaai-2012-0194 (d4-conf-aaai-2012-0194)

Answer: —

The anchor (named result in the paper)

Theorem 1 — class: other

PDF text-layer excerpt — equations and symbol order may be approximateSuppose that, as n →∞, nA −nB is ω(1) and O(√n). If µ1 σ1 > µ2 σ2 , then there exists N ∈N such that for all n ≥N, Pr[D1 > 0] > Pr[D2 > 0].

statement extracted from the paper’s text layer; consult the paper for the exact wording

The continuous mirror question, as graded

Given two finite-support rational identity-count distributions \(\pi_1,\pi_2\), each with positive mean and variance, and a sequence of two-type societies with masses \(\mu_N=(p_N,1-p_N)\), where \(Np_N,N(1-p_N)\in\mathbb{N}\), \(p_N>1/2\), and \(d_N=N(2p_N-1)=\omega(1)\) and \(d_N=O(\sqrt{N})\), determine which policy eventually gives the higher probability that \(A\) wins. When the ratios \(\mu_i/\sigma_i\) differ, Theorem 1 ranks the policies by that ratio.

Packaged proof task (what the prover saw — nothing else)

(empty)

Prover output (gpt-6.1-sol / high, Bolzano prover prompt)

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Adversarial review (gpt-6.1-sol / medium, Bolzano verifier prompt)

(empty)

Tier: machine-proved, adversarially reviewed by an independent model. No human has checked this proof. Generated from pipeline artifacts by tools/atlas_build.py.