Mattress startup Casper Sleep Inc. typifies the kind of startup that Silicon Valley investors fawned over through the 2010s, defined by big vision and rapid growth at the expense of profits.

Now, it is seeking to go public at the very time that such a model appears to have fallen out of favor, in a test of what is to come for dozens of similar loss-heavy startups that need to raise money as private fundraising becomes more difficult.

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