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Surface rotation and photometric activity for Kepler targets I. M and K main-sequence stars

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Wavelet-plus-autocorrelation analysis of Kepler light curves yields reliable rotation periods for 15,910 M and K dwarfs, 4,431 of them new, and shows faster rotators are more active.

desk verdict Solid catalog paper whose main asset is 15,910 rotation periods and Sph values, with 4,431 new detections; the interpretation of the fast-rotator branch is shakier than the catalog itself. read the letter →

arxiv 1908.05222 v2 pith:WL3S2X7P submitted 2019-08-14 astro-ph.SR

A. R. G. Santos , R. A. García , S. Mathur , L. Bugnet , J. L. van Saders , T. S. Metcalfe , G. V. A. Simonian , M. H. Pinsonneault This is my paper · ORCID
classification astro-ph.SR
keywords stars:low-massrotationactivitystarspotstechniques:photometricmethods:dataanalysiscatalogsgyrochronology
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a rotation-detection pipeline combining wavelet time-frequency analysis, the autocorrelation function, and their product (the composite spectrum) can extract trustworthy surface rotation periods from Kepler light curves of low-mass stars, going beyond what an autocorrelation-only analysis achieves. Applied to 26,521 M and K main-sequence dwarfs, the pipeline reports periods and photometric activity levels for roughly 60 percent of the sample, including 4,431 stars with no previously published period. For the 11,209 targets in common with the earlier McQuillan catalog, the two analyses agree within $2\sigma$ for 99.4 percent. The resulting sample supports three physical claims: hotter dwarfs rotate faster, faster rotators show higher photometric activity (for K dwarfs in particular), and the rotation-period distribution is bimodal. A careful reader would care because rotation periods feed gyrochronology — the use of spin-down to estimate stellar ages — and a larger, cleaner period catalog sharpens that age clock.

What carries the argument

The object that carries the argument is the three-diagnostic rotation pipeline. First, a Morlet-wavelet time-frequency decomposition yields the wavelet power spectrum and, summed over time, the global wavelet power spectrum (GWPS); the rotation estimate is the central period of the highest fitted Gaussian peak, with the half-width as its uncertainty. Second, the autocorrelation function (ACF) of the light curve, smoothed with a Gaussian whose width is one tenth of the dominant Lomb-Scargle period, yields the highest significant peak as an independent period. Third, the composite spectrum (CS) is the product of the normalized GWPS and the normalized ACF resampled onto the same period grid, so that periods present in both methods are enhanced. A period is accepted when GWPS, ACF, and CS agree within $2\sigma$, the estimates agree within 20 percent across the appropriate high-pass filters, and the peak-height thresholds hold ($G_{\rm ACF} \geq 0.2$, $H_{\rm ACF} \geq 0.3$, $H_{\rm CS} \geq 0.15$). The companion object is the activity proxy $S_{\rm ph}$, defined as the standard deviation of light-curve sub-series of length $5 \times P_{\rm rot}$ with photon noise subtracted; it converts a measured period into a magnetic-activity measure and underlies the rotation–activity relation.

What would settle it

Take the fast-rotating K dwarfs with photometric activity above roughly 10,000 ppm — the group the paper itself cautions about — and obtain high-resolution spectra or Gaia astrometric orbits for about 100 of them. If more than a small fraction show binary motion, the fast-rotator branch of the activity–rotation relation, and part of the derived bimodal period distribution, is contaminated by synchronized binaries rather than single-star rotation. A purely photometric version of the same test: require every reported period to be recovered independently from the first and second halves of the light curve; stable spot modulation should persist across both halves, while quarter-dependent pollution would not.

Watch

Extended reading notes

Core claim

The paper's central claim is that its KEPSEISMIC light curves — its own calibration of Kepler pixel data, high-pass filtered at 20, 55, and 80 days — together with a three-diagnostic rotation pipeline yield reliable rotation-period estimates for 15,290 M and K dwarfs, with a further 620 flagged candidates (possible classical pulsators or close-in binaries, and multi-period sources) reported separately. Reliability is defined internally as agreement among the wavelet global power spectrum, the autocorrelation function, and the composite spectrum within $2\sigma$, plus agreement within 20 percent between different filters, plus peak-height thresholds; externally it is validated by 99.4 percent agreement within $2\sigma$ with the McQuillan et al. catalog across 11,209 common targets. The discovery is the catalog itself and the population statements built on it: the newly measured stars are on average cooler and fainter than previously cataloged rotators, rotation periods shorten as effective temperature and mass increase, the photometric activity proxy $S_{\rm ph}$ spans a wider range for hotter stars, $S_{\rm ph}$ grows as rotation speeds up, and the rotation-period distribution is bimodal. The paper also claims to clean the sample by removing 1,221 misclassified red giants, eclipsing binaries, RR Lyrae stars, and photometrically polluted light curves.

Load-bearing premise

The load-bearing premise is that each detected periodic brightness variation is starspot rotation, not pulsation, binarity, eclipses, or light from a nearby star; the paper itself flags 368 classical-pulsator/close-binary candidates, 270 multi-signal light curves, and a set of very fast rotators with unusually large activity as cases where this premise is uncertain.

Editorial extensions

If this is right

  • The 4,431 newly reported periods extend rotation measurements to cooler and fainter M and K dwarfs, giving gyrochronology relations more calibration points at the low-mass end.
  • Confirmation of the bimodal rotation-period distribution by an independent pipeline strengthens the case that the bimodality is a real feature of the low-mass field-star population rather than an artifact of one method.
  • The K-dwarf anti-correlation between $S_{\rm ph}$ and rotation period ties photometric activity to spin rate and anchors comparisons with solar activity, which the paper quotes at 314.5 ppm at maximum and 67.4 ppm at minimum.
  • Removal of 1,221 misclassified red giants and flagging of 368 pulsator/close-binary candidates changes the effective M and K dwarf population counts derived from the Kepler catalog.
  • The catalog tables, with pollution and binarity flags, become a reference data set for stellar spin-down studies, exoplanet-host rotation, and tests of magnetic-braking models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the pipeline resolves factor-of-two period ambiguities as well as the comparison with the prior catalog suggests, applying the same three-diagnostic scheme to older G and F dwarfs could sharpen the debate over weakened magnetic braking, since spurious half-rotation signals are exactly the kind of error that mimics faster-than-expected spin-down.
  • A testable extension: the 3,562 targets with visible but unrecoverable spot modulation form a natural completeness sample, so modeling their detection failure as a function of brightness and period would let catalog users correct selection bias in the reported period distribution.
  • Because the paper flags fast rotators with very large $S_{\rm ph}$ as possibly tidally synchronized binaries, gyrochronology or activity studies that use the fast-rotator branch should test how their conclusions change when high-activity fast rotators are excluded.
  • The wider $S_{\rm ph}$ range at higher temperature, combined with the catalog's detection limits, suggests a re-interpretation test: if intermediate-period stars are under-detected because dark spots and bright faculae cancel, the bimodal gap should widen when the analysis is restricted to low-noise, high-amplitude light curves.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript presents a homogeneous rotation-period and photometric-activity catalog for 26,521 Kepler M and K main-sequence stars selected from KSPC DR25. Rotation periods are derived with a pipeline combining wavelet analysis, autocorrelation function, and composite spectrum applied to KEPSEISMIC light curves, with PDC-MAP light curves used as a cross-check. The authors report reliable periods for 15,910 targets, including 4,431 targets not in McQuillan et al. (2013b, 2014), and find 99.4% agreement within 2σ with that catalog for the 11,209 common targets. They also compute the photometric activity proxy Sph and report a mild decrease of rotation period with increasing temperature, an anti-correlation between Sph and rotation period for K dwarfs, and a bimodal rotation-period distribution. Potential polluters are identified and flagged, including classical pulsator/close-in binary candidates, multiple-signal systems, misclassified red giants, eclipsing binaries, and photometrically polluted light curves.

Significance. If the catalog is sound, this is a valuable community resource: it extends rotation measurements to fainter and cooler M and K dwarfs than the McQuillan et al. catalogs, adds roughly 4,400 new period estimates, and provides a homogeneous activity proxy tied to the rotation period. The methodology follows the pipeline previously benchmarked in Aigrain et al. (2015), and the agreement with an independent catalog on common targets is a strong validation of the period measurements. The Sph proxy has also been externally validated against solar and chromospheric activity data in prior work. The main scientific claims about bimodality and the Sph-Prot relation are consistent with earlier studies but are more fragile because they depend on the purity of the fast-rotator, high-Sph branch, as the authors themselves caution.

major comments (4)
  1. [§5.3 and §5.5] The physical conclusions of the paper, specifically the bimodal rotation-period distribution and the Sph-Prot anti-correlation for K dwarfs, are most sensitive to the fast-rotator, high-Sph branch. The authors state in §5.3 that fast rotators with very large Sph resemble Type 1 CP/CB candidates but have three or fewer harmonics and therefore are not flagged, and in §5.5 that approximately 70% of likely tidally-synchronized binaries have Sph above 10^4 ppm. Yet these targets remain in the main analysis and in Figs. 5-9 only some are excluded by the Berger/Simonian flags. This means an unknown fraction of the extreme fast-rotator branch may be contamination rather than single-star spot modulation. The paper needs a quantitative robustness test: for example, repeating the Prot and Sph distributions and the Sph-Prot correlation with all Berger et al. (2018) binary candidates, Simonian et al. (2019) synchronized binaries, and Type 1 CP/CB candidates excluded, and comparing with the full-sample results. Without such a test, the physical claims extend beyond what the current analysis can support.
  2. [§3.1.2] The catalog relies heavily on visual inspection: 6,324 of the 15,910 period estimates come from the visual check described in §3.1.2. The paper does not report any reproducibility or validation statistics for this subset, such as inter-inspector agreement, a blind test on simulated light curves, or a separate comparison with McQuillan et al. (2014) restricted to visually selected targets. Since the automatic selection thresholds are the only objective component and are applied to only ~60% of the catalog, the reliability of the remaining ~40% is not demonstrated. The authors should either provide such validation or flag the visually selected periods as lower confidence in the catalog tables.
  3. [§2.2 and Table 4] The red-giant removal, which removes 1,221 targets from the sample, depends on a companion paper described only as 'García et al. in prep' and on neural-network and machine-learning methods that are cited but not described in sufficient detail. Since misclassified red giants are a principal source of spurious periods, the reproducibility and correctness of this step are load-bearing for the catalog's purity. The manuscript should either summarize the red-giant identification criteria, provide a public list of the removed targets, or state that the companion paper will be submitted concurrently so that the criteria can be evaluated. As written, a reader cannot independently reproduce the red-giant mask.
  4. [§5.4] The comparison with McQuillan et al. (2013b, 2014) is reported as 99.4% agreement at 2σ for common targets, but the paper does not separate the agreement for automatically selected versus visually selected targets. Because the visual subset is subjective and forms a large fraction of the catalog, reporting the agreement separately for that subset would directly address whether the visual periods are as reliable as the automatic ones. This is a concrete and feasible analysis that would substantially strengthen the central claim.
minor comments (6)
  1. [Figure 5] The y-axis label in the left panels reads 'Franction' instead of 'Fraction'; please correct the typo.
  2. [Appendix A] The sentence 'we do not perform the rotation analysis for ... and and Type 2 and 3 CP/CB candidates' contains a doubled 'and'; please fix the wording.
  3. [§5] The text states that Type 1 CP/CB candidates and multiple-signal targets are 'neglected in Figs. 5-9', but Fig. 5 shows a 'Full sample' distribution in black whose definition is not precisely specified. Please clarify exactly which targets are included in the 'Full sample' curves of Fig. 5.
  4. [§2.2 and §5.5] Several references are to works described as 'in prep', including 'Szabó et al. in prep' and 'García et al. in prep'. These should be identified or, if unpublished, the relevant data should be made available in supplementary material.
  5. [§4] For the 1% of targets where the Jenkins et al. (2010) correction gives a negative Sph, the paper says the correction is instead computed from the flat component of the power density spectrum but does not specify how this alternative is implemented or whether the resulting Sph values are flagged. Please add a brief description.
  6. [§2.1] The high-pass filter choices of 20, 55, and 80 days are described, but the criterion for selecting the 'appropriate filter' in §3.1.1 is described in words; a compact table or equation summarizing the period-dependent filter priority would improve clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: rotation periods are benchmarked externally and the Sph-Prot relations are empirical outputs; self-citations to the pipeline and Sph are non-load-bearing.

full rationale

The central claim is the catalog of measured rotation periods plus the reported Sph-Prot and period-distribution trends. The period pipeline (wavelet + ACF + composite spectrum) is adopted from Ceillier et al. (2016, 2017), and Sph from Mathur et al. (2014), both involving overlapping authorship. But these self-citations are not the load-bearing evidence: the pipeline was ranked best in the simulation comparison of Aigrain et al. (2015), and the actual periods are checked against the independent McQuillan et al. (2013b, 2014) catalog, with ~99.4% agreement within 2 sigma for 11,209 common targets. The 4,431 newly reported periods and the bimodal distribution are empirical outputs, not parameters fitted to those conclusions. Sph is defined as the standard deviation of 5xProt subseries, but the Sph-Prot anti-correlation is not forced by construction: Prot is a periodicity measurement while Sph is a separate amplitude statistic, and using shorter subseries does not by itself produce larger standard deviations. The paper's own cautions about fast rotators with large Sph, Type 1 CP/CB candidates, multiple-signal targets, and tidally-synchronized binaries are contamination and interpretation caveats, not circularity: they weaken the physical interpretation of the fast-rotator branch but do not reduce any prediction to its input. No equation or selection rule in the paper equates a predicted quantity to the quantity used to define or fit it, so no specific circular reduction can be exhibited.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are postulated. The analysis rests on the assumed spot-rotation origin of the detected signals, the adopted Sph activity proxy, the KSPC DR25 stellar parameters, and the unpublished companion catalogs used for polluter removal.

free parameters (3)
  • Automatic selection thresholds = GACF >= 0.2, HACF >= 0.3, HCS >= 0.15
    Adopted from Ceillier et al. (2017), these hand-chosen quality thresholds decide whether a period estimate is accepted or rejected, so they directly affect the composition of the published catalog.
  • High-pass filter cutoffs = 20, 55, and 80 days
    Three filtering timescales are chosen to separate rotation from instrumental trends; the choice of which filtered light curve is authoritative depends on the rotation period, which influences the final period estimate.
  • Rotation period regime boundaries for filter priority = 23 and 60 days
    Hand-chosen boundaries that switch the primary filter between the 20-day, 55-day, and 80-day light curves; not derived from data in this paper.
assumptions (5)
  • domain assumption Brightness modulation with a period matching the pipeline detection is caused by starspots rotating on the stellar surface.
    Section 3 assumes spot-modulated light curves; the paper acknowledges that binaries, pulsators, and pollution can masquerade as rotation, which is why it screens polluters.
  • domain assumption KSPC DR25 effective temperatures, masses, and surface gravities are accurate enough for sample selection and the Teff and mass trends.
    Sample selection (Teff < 3700 K for M, 3700 to 5200 K for K) and Figs. 6 and 7 rely entirely on KSPC DR25; vertical features in Fig. 6 are attributed to artifacts in this catalog.
  • domain assumption Sph, defined as the standard deviation of subseries of length 5 times Prot, is a valid photometric activity proxy.
    The proxy is taken from Mathur et al. (2014) and validated on solar VIRGO and GOLF data and chromospheric Ca II indexes (Salabert et al. 2016, 2017), but it is not re-derived here.
  • domain assumption The red-giant and RR Lyrae removal lists are correct.
    Section 2.2 removes 1,221 red giants partly using 'García et al. in prep' and 3 RR Lyrae using 'Szabó et al. in prep', unpublished references, plus machine learning classifiers.
  • standard math Wavelet power spectrum, ACF, and Lomb-Scargle periodogram are valid tools for period extraction in this context.
    Standard statistical time-series methods; the specific adaptation is from Mathur et al. (2010) and Ceillier et al. (2016, 2017).

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Cite this review

Pith. "Pith review of Surface rotation and photometric activity for Kepler targets I. M and K main-sequence stars." pith.science (2026). https://pith.science/paper/WL3S2X7P

@misc{pith2026190805222,
  author       = {Pith},
  title        = {Pith review of: Surface rotation and photometric activity for Kepler targets I. M and K main-sequence stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WL3S2X7P}},
  note         = {Machine review of arXiv:1908.05222}
}
read the original abstract

Brightness variations due to dark spots on the stellar surface encode information about stellar surface rotation and magnetic activity. In this work, we analyze the Kepler long-cadence data of 26,521 main-sequence stars of spectral types M and K in order to measure their surface rotation and photometric activity level. Rotation-period estimates are obtained by the combination of a wavelet analysis and autocorrelation function of the light curves. Reliable rotation estimates are determined by comparing the results from the different rotation diagnostics and four data sets. We also measure the photometric activity proxy Sph using the amplitude of the flux variations on an appropriate timescale. We report rotation periods and photometric activity proxies for about 60 per cent of the sample, including 4,431 targets for which McQuillan et al. (2013a,2014) did not report a rotation period. For the common targets with rotation estimates in this study and in McQuillan et al. (2013a,2014), our rotation periods agree within 99 per cent. In this work, we also identify potential polluters, such as misclassified red giants and classical pulsator candidates. Within the parameter range we study, there is a mild tendency for hotter stars to have shorter rotation periods. The photometric activity proxy spans a wider range of values with increasing effective temperature. The rotation period and photometric activity proxy are also related, with Sph being larger for fast rotators. Similar to McQuillan et al. (2013a,2014), we find a bimodal distribution of rotation periods.

Figures

Figures reproduced from arXiv: 1908.05222 by the authors.

Figure 1
Figure 1. Surface gravity-effective temperature diagram of the 26,521 M and K dwarfs according to KSPC DR25 (Mathur et al. 2017), color coded by number of stars in each bin. The size of Teff and log g bins is ∼ 16 K and ∼ 7×10−3 dex, respectively. For context, other stars in KSPC DR25 are plotted in gray. Effective temperature (Teff) and surface gravity (log g) values are adopted from KSPC DR25. We expect a number of differen… view at source ↗
Figure 2
Figure 2. Light curve and power density spectrum for an example of the three classical pulsator or close-in binary candidates. Left-hand: KIC 2996903, Type 1 CP/CB candidate, which exhibit high-amplitude flux variations and high-amplitude peaks with a large number of harmonics in the power density spectrum. Middle: KIC 5522761, Type 2 CP/CB candidate, which exhibit high-amplitude flux variations and a large number of high-amp… view at source ↗
Figure 3
Figure 3. shows the ACF for a given target in the sample. Finally, the third method of estimating rotation pe￾riod utilizes the composite spectrum (CS), which com￾bines the GWPS and the ACF as described by Ceil￾lier et al. (2016, 2017). The composite spectrum cor￾responds to the product of the normalized GWPS and the normalized ACF resampled in the same period of the GWPS. Periods present in both methods, GWPS and ACF, are en… view at source ↗
Figures from the paper (17 more)
Figure 5
Figure 5. Figure 5: summarizes the results for the targets with period estimate. M dwarfs have on average longer rota￾tion periods and larger Sph values than K dwarfs, which is consistent with the results in McQuillan et al. (2014). In the following sections, we take a more detailed look …
Figure 4
Figure 4. Figure 4: Comparison between the magnitude distribution for stars with Prot estimate (excluding CP/CB candidates; black solid line) and that for: CP/CB candidates (left; red), stars with possible spot modulation (middle; blue), and stars without spot modulation (right; green). D…
Figure 6
Figure 6. Figure 6: Rotation period as a function of effective temperature (left) and mass (right) color coded by number of stars in a given parameter range. Brighter colors indicate higher density regions than darker colors. Stellar effective temperature and mass are taken from KSPC DR25…
Figure 7
Figure 7. Figure 7: Photometric activity index Sph as a function of effective temperature (left) and mass (right) color coded by number of stars in a given parameter range. Stellar effective temperature and mass are taken from KSPC DR25 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Comparison between the stellar masses from Mc￾Quillan et al. (2014, MassMcQ) and Mathur et al. (2017, MassKSPC DR25). The transition between fully convective stars and stars with a radiative core is expected to take place at 0.35M (e.g. Chabrier & Baraffe 1997). If the…
Figure 10
Figure 10. Figure 10: Comparison between the rotation estimates from this work (Prot, This work) and those from McQuillan et al. (2013b, 2014, Prot, McQ). The dashed lines indicate the two-to-one, one-to-one, and one-to-two lines. We provide rotation-period estimates for 4,431 targets (3,8…
Figure 9
Figure 9. Figure 9: Photometric activity proxy as a function of the rotation period color coded by number of stars in a given parameter range for: all M and K dwarfs (top), M dwarfs (middle), and K dwarfs (bottom). For comparison, the Sph values at solar activity maximum (314.5 ppm) and m…
Figure 11
Figure 11. Figure 11: Distribution of the number of Prot estimates from this work (red) and from the analysis in McQuillan et al. (2014, black) as a function of effective temperature (left) and Kepler magnitude (right). 5.5. Gaia binary candidates In this section, we compare our target sam…
Figure 12
Figure 12. Figure 12: Summary of our results for targets identified as binary candidates by Simonian et al. (2019, left) and Berger et al. (2018, right). The size of the slices only concern the targets that are binary candidates. The annotations indicate the fraction of targets flagged as …
Figure 13
Figure 13. Figure 13: shows the surface gravity-effective temperature diagram for some of the potential non-single M and K stars. Targets in our sample that were flagged as binaries by Berger et al. (2018, 2,841 targets) are shown in blue, while tidally-synchronized binaries identified by …
Figure 14
Figure 14. Figure 14: Same as in [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]
Figure 15
Figure 15. Figure 15: Same as left-hand panels of Figs. 6 and 7 but also including potential non-single non-main-sequence stars [PITH_FULL_IMAGE:figures/full_fig_p022_15.png]
Figure 16
Figure 16. Figure 16: Same as left-hand panels of Figs. 6 and 7 but including binaries identified by Berger et al. (2018, blue circles), tidally-synchronized binaries identified by Simonian et al. (2019, green stars), and Type 1 CP/CB candidates identified in this work (red squares). For r…
Figure 17
Figure 17. Figure 17: Same as left-hand panels of Figs. 6 and 7 but including the targets whose light curves show multiple signals (orange diamonds). For reference the single M and K dwarfs are marked in gray. For illustration purpose the Prot axis is different in this figure. 10 100 1000 …
Figure 18
Figure 18. Figure 18: Same as in [PITH_FULL_IMAGE:figures/full_fig_p023_18.png]
Figure 19
Figure 19. Figure 19: Same as in [PITH_FULL_IMAGE:figures/full_fig_p024_19.png]
Figure 20
Figure 20. Figure 20: Rotation-period distributions for KEPSEISMIC (red) and PDC-MAP (black) light curves. Only the common automatically selected targets (11,131 targets) are represented [PITH_FULL_IMAGE:figures/full_fig_p024_20.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hints of enhanced magnetic activity after the intermediate rotation period gap as traced by the chromospheric Ca ii infrared triplet

    astro-ph.SR 2026-07 accept novelty 6.0 of 10

    Main-sequence Kepler stars exhibit enhanced chromospheric Ca II IRT activity after the intermediate-period gap, paralleling the photospheric Sph signature.

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