Web Search in API underperforming compared to ChatGPT's

In ChatGPT, I’m often able to get it to accurately look up the purpose and functionality of various Ethereum addresses (e.g. 0xA5961898870943c68037F6848d2D866Ed2016bcB) by searching the web.

I’m trying to replicate this using the Web Search in the Responses API with models GPT-4.1 and GPT-4o, but it often results in no hits or incorrect information.

I know that ChatGPT has a lot more orchestration and search strategies under the hood that makes it better, but does anyone know what I can do to enhance the performance for my use case?

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Is this documented anywhere?