Which formation channel produces most hot Jupiters?

In plain words

Three routes could make hot Jupiters, and each leaves different marks on orbits and neighbors. The share of each route is not known.

Precise statement

For giant planets with orbital period $P < 10\,\mathrm{d}$ around FGK stars (occurrence about 0.5-1 percent), determine the fractions formed by disk migration, high-eccentricity tidal migration (Kozai-Lidov cycles, planet-planet scattering, secular chaos) and in situ formation, using stellar obliquities, eccentricities, nearby companions, outer companions and system ages. The answer is the fraction per channel with uncertainties.

What would settle it

Population synthesis fitted to homogeneous samples of obliquities, companion statistics and ages from TESS, Gaia and radial-velocity surveys.

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