How did warm Jupiters on 10 to 200 day orbits form?
In plain words
Giant planets with orbits of weeks to months are too far out for tides to have circularized them yet too close to have formed where giants usually do. Unlike hot Jupiters, about half of them have small planets nearby, which hints at a gentler origin.
Precise statement
For giant planets with $P \sim 10\text{-}200\,\mathrm{d}$, determine the fraction formed in situ or by disk migration versus high-eccentricity migration caught mid-way, using their eccentricity distribution, stellar obliquities and nearby companions. Huang, Wu and Triaud 2016 (ApJ 825, 98, arXiv:1601.05095) found that about half of warm Jupiters have close small companions while hot Jupiters almost never do. The answer is the fraction per channel versus period and eccentricity.
What would settle it
Obliquity, eccentricity and companion statistics for a large TESS-selected warm Jupiter sample compared with population synthesis of each channel.