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I think we are dramatic agreement?

HTTPS = breaking caching.

User Authentication = returning different results for per-resource queries, which is RESTful.

I'm afraid we're not in a dramatic agreement. You point to an exception which REST allows to claim the exception is RESTful.

The exception is there for practical reasons and it doesn't satisfy REST's constraints nor benefits from REST's properties.

Either way, my point's been exhausted, so, I'll shut up now ;)