DeepSeek hasn't proven anything except what they say. You're inherently trusting a company's statements over others. When an independent third party corroborates the numbers then we know for sure. Until then, every company is just selling a story for investors and users.

Does DeepSeek offer a heavily subsidized subscription that provides 20x+ more usage than the equivalent value in API tokens?

API usage being profitable is completely plausible, but almost nobody pays API prices for Claude and GPT, nor would they be able to afford them if the subscription suddenly stopped existing.

Not DeepSeek themselves, but their open models are run by third-party companies in a profitable way. The unsustainable interference theory has been debunked.

The conditions for DeepSeek's profitability are very very narrow. A key piece being that they have cheap energy, a second key is that they have west/east clients and thus extremely high uptime.