Web platforms such as digital libraries, online stores and university sites must classify new pages before anyone labels them. Large language models (LLMs) can label each page from its text, but these labels are noisy, and links could correct them only where linked pages share classes. Existing zero-shot methods ignore the links, or pull a page toward its neighbours as label propagation and graph neural networks (GNNs) do, which hurts where linked pages differ in class. Others weight propagation by an LLM-estimated homophily that costs extra calls and drifts across LLMs. We find that the sign with which links should enter a prediction, which we call structural polarity, is readable without true labels. It is the excess agreement of LLM labels and text-prototype predictions along links. We thus propose ZeroPolar, which gates one signed propagation step by this statistic. Training-free ZeroPolar mixes prototype scores with any number of LLM labels, and ZeroPolar-T denoises the labels with a text classifier once half of the pages carry one. With one GPT-4o label per page, ZeroPolar-T reaches the highest mean accuracy on eleven graphs (73.99%), 6.01 points above LLM-BP and significantly above all eighteen baselines we compare. With LLM labels on only 5% of the pages, training-free ZeroPolar leads a GNN trained on these labels by 10.80 points.

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