Tube-like: What tube amp can be the benchmark?

Atma-sphere (no affiliation). Natural, not fatiguing, and the perception that you're listening to music- not a "system" or a stereo or even speakers for that matter (as Sounds Real Audio mentioned).
Objective characteristics would include flat frequency response across the audio spectrum (often extending to 100khz- to ensure flat response), Low distortion, transient response (high slew-rate) for dynamic range among others.

Sure. But we never make things that simple here, do we? :)

Look at all the threads looking for a best tube amp or a solid state amp sounds more like tubes. Seems to me before one can even begin to answer those kinds of questions, one needs to define the characteristics of tube sound. And by that I mean what might be the ideal "tube-like" sound?

Here, we might get into some very subjective characteristics like an amp that let's you step inside the music. But what, then, are the objective characteristics of that sound? And what amp or amps might be the reference?

Just curious...

Some might

The benchmark might be that you really enjoy listening and forget completely about your system.