{"case":{"id":"OS-0012","title":"The invisible companion that wasn't","hook":"We thought something the size of the Sun was blocking this star every 2.38 days without giving off any light. Our own referee agent found the mistake in 30 minutes.","status":"closed","target":{"name":"Gaia DR3 4482344869315388928","ra":271.37757,"dec":9.46541,"aliases":[],"gaia_source_id":4482344869315388928},"summary":"An uncatalogued eclipsing binary of two K dwarfs, P = 11.900804 d, e about 0.15: primary eclipse 0.9 mag, secondary 0.4 mag at phase 0.404. We first folded it at P/5 = 2.38 d, which stacked the secondary onto the primary and made the companion look dark and Sun-sized: an 'invisible companion'. An Oddsky referee agent counted the missing eclipses, found TESS sector 80 showing only every fifth one, and fitted an ordinary two-star model. The candidate was never announced. The tool that fooled us now runs a missing-eclipse test (see C19). New, small, and true: worth a routine VSX submission.","claims":[{"id":"C1","text":"Found in Oddsky hunt H-0001: Gaia (2014-2017) caught this K dwarf 0.87-0.89 mag faint on two transits. VSX lists it only as a Gaia 'VAR' with a 0.025-day period; SIMBAD has no entry or references; neither the ZTF periodic-variable catalogue (Chen et al. 2020, 781k stars) nor the 2026 ZTF variable-candidate list contains it.","tag":"observed","calls":["K1","K8"],"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C2","text":"Every point more than 0.3 mag faint, from Gaia (2014-17) and ZTF (2018-25), falls at one phase of a 2.3802-day period: an eclipse recurring for 11 years. Refined ephemeris P = 2.380206 d, T0 = MJD 57099.3195.","tag":"computed","calls":["K2"],"retracted":"Wrong period. The deep points line up at 2.38 d only because the true period is five times longer (11.9008 d) and the secondary eclipse sits at phase 0.404, about 2/5. Folding at P/5 stacks the two eclipses (referee, C11-C18).","author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C3","text":"The primary eclipse is about 0.92 mag deep in ZTF r and 1.03 in g (deepest points), and V-shaped, lasting about 5 hours. On the two Gaia transits in eclipse, BP drops 0.95, G 0.88 and RP 0.83 mag: slightly deeper in blue.","tag":"computed","calls":["K9","K10","K11","K12","K13"],"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C4","text":"There is no secondary eclipse: at phase 0.5 the ZTF r change is +0.004 +/- 0.003 mag (g: 0.000 +/- 0.005), and no 0.02-phase bin away from the primary is fainter than +0.008 mag, so an eccentric orbit isn't hiding one either.","tag":"computed","calls":["K9","K10"],"retracted":"The 'missing' secondary is the 2.38-day fold's artefact: at P = 11.9008 d the secondary is 0.35-0.42 mag in r (referee).","author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C5","text":"NEOWISE single exposures show the primary eclipse (W1 down by up to 0.50 mag, W2 by up to 0.52) and no secondary eclipse: W1 -0.004 +/- 0.008, W2 -0.017 +/- 0.018 mag at phase 0.5.","tag":"computed","calls":["K14","K15"],"retracted":"As C4: at the true period NEOWISE shows a 0.36-0.43 mag secondary in W1 and W2 (referee).","author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C6","text":"Control: the same tools on OS-0011, an ordinary Algol-type binary, detect its cool companion at secondary eclipse: 0.054 mag in r and 0.175 mag in W1. The method can see a companion; OS-0012 shows none.","tag":"computed","calls":[],"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C7","text":"Gaia DR3 describes the host as a single-looking K dwarf: Teff 4980 K, log g 4.35, R about 1.07 Rsun, L 0.65 Lsun, 506-521 pc (parallax/error 105), RUWE 1.05, no image doubling, no Gaia neighbour within 7 arcsec brighter than 6.6 mag fainter.","tag":"observed","calls":["K16"],"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C8","text":"A 5-hour eclipse on a 2.38-day orbit around a ~0.85 Msun star implies (for a central transit) an occulter of radius ~0.9 Rsun. Blocking ~58% of the light also requires a radius at least ~0.8 of the star's. Yet the occulter contributes less than ~0.5% of the optical light and less than ~2% at 3.4 microns (3 sigma). A star of that size would be nearly as bright as the host.","tag":"inferred","calls":["K9","K14"],"retracted":"Rests on the wrong period. Two K dwarfs (R2/R1 = 0.87) fit all the data with reduced chi2 1.16 (referee C14).","author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C9","text":"The infrared eclipse may be shallower than the optical one (W1 up to 0.50 against r up to 0.92), but only 8 NEOWISE exposures fall in eclipse at random depths, so the comparison is suggestive, not measured.","tag":"inferred","calls":["K9","K14"],"retracted":"Rests on the wrong period.","author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C10","text":"Candidate: an opaque disk or ring system around a low-mass, faint companion (brown dwarf or late-M dwarf). The disk must fit within the companion's Hill sphere, which needs a companion mass of about 0.07 Msun or more.","tag":"speculated","calls":[],"retracted":"Refuted: no dark occulter is needed.","author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"C11","text":"Referee: the claimed 2.38-d ephemeris fails cycle by cycle. Of 40 cycles where P=2.38016 d predicts a dip deeper than 25%, 15 show under 5% in good-quality ZTF data (catflags 0, normal airmass/chi/sharp/limitmag). Sorting cycles by number mod 5: all 21 cycles = 0 mod 5 are deep; all 21 cycles = 1, 3 or 4 mod 5 are flat; cycles = 2 mod 5 show a shallower eclipse about 1.1 h late. Per-cycle table from cases/OS-0012/data/*.parquet with pandas (not an Oddsky tool); the folds that show it are logged.","tag":"observed","calls":["K37","K62","K63"],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C12","text":"Referee: TESS Sector 80 (TESScut FFI, TIC 399415572, June 2024; not in the case data, own aperture photometry) covers about 11 consecutive 2.38-d cycles. Deep eclipses at cycles 1425 and 1430 only, a shallower later one at 1427, and nothing at 1421, 1424, 1426, 1428, 1429 or 1431. ZTF independently finds cycle 1431 flat.","tag":"observed","calls":[],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C13","text":"Referee: the true period is 5 x 2.38016 = 11.900804 d. Folded at 11.9008 d, every band shows the primary at phase 0 and a SECONDARY eclipse at phase 0.404: ZTF r +0.35 mag (bin), g +0.33, W1 +0.36 to +0.40, W2 +0.38 to +0.43. Phase 0.404 is about 2/5, so the P/5 fold stacks the secondary onto the primary. An independent eclipse_period search on points deeper than 0.6 mag (3 to 30 d) returns 11.9016 d. P/2, 2P and 3P were checked; 5P was not.","tag":"computed","calls":["K57","K58","K59","K60","K61","K64","K65","K66","K67","K68"],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C14","text":"Referee: an eccentric two-star limb-darkened eclipse model fitted jointly to ZTF g/r, Gaia G, NEOWISE W1/W2 and TESS (own code outside the tools; free TESS third light 0.68 for the 25.7-arcsec G=13.97 neighbour) gives reduced chi2 1.16 over 11,651 points. P=11.900804 d, T0=MJD 57099.3619, e cos w=-0.1508 (e about 0.15), near-central, R2/R1=0.874, R1/a=0.0304. Primary 0.91 mag in r, secondary 0.42 mag in r. Surface-brightness ratios: g 0.46, r 0.61, W1 0.88.","tag":"computed","calls":[],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C15","text":"Referee: with total mass 1.4-1.7 Msun, a=24.5-26.2 Rsun, R1=0.75-0.80 and R2=0.65-0.70 Rsun. T1 about 5150 K gives T2 about 4450-4720 K from the g, r, G, W1 and W2 surface-brightness ratios. That is an ordinary K1V+K4V detached eclipsing binary. The two stars give L about 0.56 Lsun, a single-star-equivalent radius of about 1.0 Rsun at 4980 K, and 0.4 mag of overluminosity. This explains why Gaia GSP-Phot/FLAME (single-star fits) report R=1.07 and logg 4.35. StarHorse gives M_G0=4.89 at (BP-RP)0=0.86, about 0.7 mag above a single K0V.","tag":"inferred","calls":["K32"],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C16","text":"Referee: C4, C5, C8, C9 and the 'invisible occulter' conclusion rest on folding at P/5. At the true period the companion is plainly seen at secondary eclipse in every band. The occulter-size argument (C8) used a=7.1 Rsun for P=2.38 d; at P=11.9 d, a 5-hour central eclipse needs R1+R2 of about 1.45 Rsun, matching two K dwarfs. H1 (opaque disk) and H4 (dust) are not needed. Nothing anomalous remains.","tag":"inferred","calls":["K57","K60","K64"],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C17","text":"Referee: the data are not artifacts. Both ZTF fields (537 and 1532) show the eclipse. The in-eclipse ZTF centroid differs from out of eclipse by under 0.02 arcsec (IRSA per-epoch RA/Dec). Gaia G caught it on two cycles, including both FOV transits of one cycle (0.87 then 0.19 mag 106 min later). Gaia's resolution rules out a blend beyond about 0.5 arcsec, and no catalogued variable lies within 30 arcsec.","tag":"observed","calls":["K32","K59"],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C18","text":"Referee novelty search (2026-10-27): not catalogued as an eclipsing binary in VSX (only Type VAR, P=0.025 d from the Gaia short-timescale pipeline), SIMBAD (bare Gaia entry), ASAS-SN, ATLAS (J/AJ/156/241), ZTF Chen+2020, Gaia DR3 EB/classification/NSS, Prsa+2022 TESS EBs, or the Kostov+2025 TESS EB list (only in its unvetted input table). No literature found. Most likely an uncatalogued detached eccentric K+K eclipsing binary with P=11.9008 d: a modest catalogue addition, not an anomaly.","tag":"observed","calls":["K32"],"author":"claude-referee","at":"2026-10-27T10:03:34+00:00"},{"id":"C19","text":"The phase-clustering search alone found 2.38 days. The missing-eclipse test added after the referee's review (counting which cycles are deep versus flat, by cycle number mod k) flags at once that only every fifth cycle is deep: the true period is 5 x 2.38 = 11.90 days.","tag":"computed","calls":["K78"],"author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00"},{"id":"C20","text":"Explained: an uncatalogued, detached, mildly eccentric eclipsing binary of two K dwarfs, P = 11.900804 d (T0 = MJD 57099.3619, e about 0.15), with a primary eclipse of 0.9 mag and a secondary of about 0.4 mag at phase 0.404. Gaia's single-star parameters (R 1.07 Rsun, L 0.65 Lsun) describe the blended pair.","tag":"inferred","calls":["K78"],"author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00"}],"hypotheses":[{"id":"H1","klass":"eclipse_companion","statement":"An opaque circumsecondary disk (or ring system) around a faint low-mass companion transits the K dwarf every 2.38 days.","supports":["C2","C3","C4","C5","C8","C10"],"conflicts":[],"would_falsify":"Radial velocities: a single-lined orbit whose amplitude fixes the companion mass. A detectable secondary eclipse in the near-IR (K band or redder), or a flat-bottomed high-cadence eclipse, would point instead to a stellar companion.","status":"rejected","confidence":0.0,"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"H2","klass":"eclipse_companion","statement":"Ordinary binary in disguise: a hot, compact component (supplying most of the optical light) is eclipsed by a larger, much cooler star.","supports":["C3"],"conflicts":["C5","C6","C7","C8"],"would_falsify":"A cool companion large enough to block 58% would glow at 3.4 microns. OS-0011 shows such a companion at 0.18 mag in W1; here it's under 0.02. A composite spectrum would revive this.","status":"rejected","confidence":0.0,"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"H3","klass":"artifact_blend","statement":"An unresolved, unrelated eclipsing system blended with the K dwarf.","supports":[],"conflicts":["C3","C7","C8"],"would_falsify":"A 58%-deep eclipse needs the eclipsed source to supply most of the light, which a faint blend can't. Gaia shows no close companion (RUWE 1.05, no multi-peak images). Adaptive-optics imaging would close this.","status":"rejected","confidence":0.0,"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"H4","klass":"dust_occultation","statement":"A dust cloud on a 2.38-day orbit (debris from a disintegrating body).","supports":["C3","C9"],"conflicts":["C2"],"would_falsify":"Dust tails vary in depth and shape from orbit to orbit; this eclipse is similar from 2015 to 2025. High-cadence eclipses with changing depths would revive it.","status":"rejected","confidence":0.0,"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"H5","klass":"eclipse_companion","statement":"Something not on this list: mis-estimated stellar parameters, an unusual star, or physics we haven't considered.","supports":[],"conflicts":[],"would_falsify":"A spectrum.","status":"rejected","confidence":0.0,"author":"claude-opus-5.5","at":"2026-10-27T09:32:47+00:00"},{"id":"H6","klass":"eclipse_companion","statement":"A detached, mildly eccentric binary of two K dwarfs on an 11.9008-day orbit, whose eclipses happen to fall about 2/5 of an orbit apart.","supports":["C19","C20"],"conflicts":[],"would_falsify":"Radial velocities showing two sets of K-star lines at about +/-55 km/s would confirm it; a single-lined orbit would not 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platform"},{"id":"K69","tool":"skeptic_report","args":{},"digest":"55ba5ab7e23d296a","author":"claude-referee","at":"2026-10-27T09:56:55+00:00","oddsky":"0.2.0"},{"id":"K70","tool":"add_claim","args":{"id":"C11","tag":"observed"},"digest":"32d33aa7eb243195","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K71","tool":"add_claim","args":{"id":"C12","tag":"observed"},"digest":"a6cc654450efc452","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K72","tool":"add_claim","args":{"id":"C13","tag":"computed"},"digest":"856e2fa12440efc9","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K73","tool":"add_claim","args":{"id":"C14","tag":"computed"},"digest":"e53bf52e0d819c86","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K74","tool":"add_claim","args":{"id":"C15","tag":"inferred"},"digest":"957d32a9d3d682ee","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K75","tool":"add_claim","args":{"id":"C16","tag":"inferred"},"digest":"3c60602914687296","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K76","tool":"add_claim","args":{"id":"C17","tag":"observed"},"digest":"01a954f4fd9b7dfb","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K77","tool":"add_claim","args":{"id":"C18","tag":"observed"},"digest":"bca0e1d2abd29f86","author":"claude-referee","at":"2026-10-27T10:03:34+00:00","oddsky":"0.2.0"},{"id":"K78","tool":"eclipse_period","args":{"series":["ZTF:ZTF_r","ZTF:ZTF_g","GAIA:G"],"depth":0.3,"p_min":0.5,"p_max":20},"digest":"ca78cebd1e420a0d","author":"claude-opus-5.5","at":"2026-10-27T10:05:09+00:00","oddsky":"0.2.0"},{"id":"K79","tool":"retract_claim","args":{"claim":"C2","reason":"Wrong period. The deep points line up at 2.38 d only because the true period is five times longer (11.9008 d) and the secondary eclipse sits at phase 0.404, about 2/5. Folding at P/5 stacks the two eclipses (referee, C11-C18)."},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K80","tool":"retract_claim","args":{"claim":"C4","reason":"The 'missing' secondary is the 2.38-day fold's artefact: at P = 11.9008 d the secondary is 0.35-0.42 mag in r (referee)."},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K81","tool":"retract_claim","args":{"claim":"C5","reason":"As C4: at the true period NEOWISE shows a 0.36-0.43 mag secondary in W1 and W2 (referee)."},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K82","tool":"retract_claim","args":{"claim":"C8","reason":"Rests on the wrong period. Two K dwarfs (R2/R1 = 0.87) fit all the data with reduced chi2 1.16 (referee C14)."},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K83","tool":"retract_claim","args":{"claim":"C9","reason":"Rests on the wrong period."},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K84","tool":"retract_claim","args":{"claim":"C10","reason":"Refuted: no dark occulter is needed."},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K85","tool":"add_claim","args":{"id":"C19","tag":"computed"},"digest":"a7d737a96a043402","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K86","tool":"add_claim","args":{"id":"C20","tag":"inferred"},"digest":"29f6b0e73ad7551e","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K87","tool":"update_hypothesis","args":{"hypothesis":"H1","status":"rejected","confidence":0.0,"reason":"the occulter is an ordinary K dwarf; the 'invisible companion' was a P/5 folding alias"},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K88","tool":"update_hypothesis","args":{"hypothesis":"H2","status":"rejected","confidence":0.0,"reason":"superseded: ordinary K+K eclipsing binary at 11.9 d"},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K89","tool":"update_hypothesis","args":{"hypothesis":"H3","status":"rejected","confidence":0.0,"reason":"superseded: ordinary K+K eclipsing binary at 11.9 d"},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K90","tool":"update_hypothesis","args":{"hypothesis":"H4","status":"rejected","confidence":0.0,"reason":"the occulter is an ordinary K dwarf; the 'invisible companion' was a P/5 folding alias"},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K91","tool":"update_hypothesis","args":{"hypothesis":"H5","status":"rejected","confidence":0.0,"reason":"superseded: ordinary K+K eclipsing binary at 11.9 d"},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K92","tool":"add_hypothesis","args":{"id":"H6","klass":"eclipse_companion"},"digest":"aff074fce4f36e2e","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"},{"id":"K93","tool":"update_hypothesis","args":{"hypothesis":"H6","status":"favored","confidence":0.97,"reason":"joint eclipsing-binary model fit, reduced chi2 1.16 (referee)"},"digest":"6bc0da1f42f96fc3","author":"claude-opus-5.5","at":"2026-10-27T10:05:38+00:00","oddsky":"0.2.0"}],"investigations":[]}