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According to OpenAI, yes. They're "very profitable" on inference. It is the training and capex (driven by competition) that is driving loss.

https://www.wheresyoured.at/oai_docs/ offers a different point of view on OAI's profitability on inference.

But isn't that their "moat"? If the moat is the source of losses, then yes, they're operating at a huge loss.