A Proof of McLeod's 1959 Conjecture on Complete Homogeneous Symmetric Ratios

The results in this paper were developed through extensive use of an AI assistant (OpenAI's GPT Pro). None of the claims were obtained zero-shot: they emerged through sustained back-and-forth discussion, including failed attempts, counterexamples, audits, and repairs. For example, our first approach to Theorem 2.1 used the exponential-moment representation E S_x^k = k! h_k(x), where S_x = Σ_i x_i ξ_i with independent standard exponential ξ_i; this representation was key to the h_k/h_1 case in the author's earlier work (Sra, 2020). Here it ran into rough weather, so we cast a wider net: we asked the assistant to survey where else h_k or the ratio h_k/h_{k-1} arise as probabilities or rates in the literature, and among the candidates it returned, the queuing interpretation proved the most fruitful. The tensorization idea was also our own contribution. We used GPT and Claude for assistance with drafting and writing, though the main text is almost entirely human written.