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This paper claims that the median vertical motion of stars with similar temperature, surface gravity, and chemistry can be turned into stellar ages with ~30% accuracy, producing a self-consistent age catalog for 1.5 million stars in the Mil

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A new catalog of ~1.5 million stellar ages built from the median vertical action of chemically similar stars, calibrated on subgiant ages and cross-validated against clusters, asteroseismology, and gyrochronology.

T0 review reviewed 2026-08-01 challenge →

load-bearing objection A useful, well-calibrated statistical age catalog for 1.5M LAMOST stars, with a real circularity problem in the headline validation and a clear need for per-star uncertainties, but more than worth refereeing. the 4 major comments →

arxiv 2607.22309 v1 pith:NYMVVGEV submitted 2026-07-24 astro-ph.SR astro-ph.GA

Ensemble Kinematic Ages for 1.5 Million LAMOST Stars

Yuxi Lu , Marc H. Pinsonneault This is my paper
classification astro-ph.SR astro-ph.GA
keywords stellar ageskinematic agesvertical actionMilky Way diskage-velocity relationgalactic archaeologyensemble age inferencestellar populations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 stellar kinematics—averaged over carefully chosen groups of similar stars—are a usable stellar age indicator across nearly the whole Hertzsprung-Russell diagram. Each star is assigned the median vertical action of 20–50 stars with matching temperature, surface gravity, metallicity, and detailed element abundances, and that median action is converted to an age using a metallicity-dependent relation calibrated on precise subgiant ages. If correct, ages become available for millions of stars, including giants and dwarfs where traditional methods fail, and different dating techniques can be cross-checked against one another on a common scale. The paper validates the method against subgiant, asteroseismic, cluster, gyrochronology, and wide-binary ages, finding a typical scatter of about 2 Gyr (roughly 30%).

Core claim

The central claim is that a single, continuous metallicity-dependent relation between vertical action and age holds across both the high- and low-alpha disk populations, and that this relation can be calibrated using isochrone ages of subgiants. Using this relation, ages computed as the median action of parameter-matched ensembles reproduce the calibration ages with a median absolute deviation of 2.6 Gyr (about 30%), comparable to carbon-to-nitrogen-based ages, and agree with independent methods across different evolutionary stages. Applied to roughly 1.5 million stars, the method yields an internally consistent age catalog spanning dwarfs and giants, with the caveats that ages above roughly

What carries the argument

The central object is the vertical action J_z, the phase-space area enclosed by a star's vertical oscillation about the Milky Way's midplane. Because J_z is an adiabatic invariant, it accumulates the vertical heating history of the disk and can be computed per star. The method groups stars that are observationally indistinguishable in stellar-parameter space (effective temperature, absolute magnitude or surface gravity, [Fe/H], [alpha/Fe], plus several elemental abundances), takes the median ln J_z of each group of 20–50 stars, and converts that median to an age through a fifth-order polynomial in ln J_z that is scaled linearly by [Fe/H]. The ensemble construction is what converts noisy indi

Load-bearing premise

The load-bearing premise is that a single age–vertical-action relation, calibrated on subgiants that mostly belong to the intermediate-age disk, applies equally well to every other stellar population and evolutionary stage—especially old metal-poor high-alpha stars and lower main-sequence stars; if the relation is not universal, the derived ages for those groups shift systematically.

What would settle it

Compare the inferred ensemble kinematic ages against precise asteroseismic ages for a sample of old, metal-poor red giants with [Fe/H] below about –0.5. If the ages disagree by more than the claimed ~2 Gyr scatter in a way that grows with age or with metallicity, the calibrated relation is not universal. The paper itself flags ages above ~12.5 Gyr and the metal-poor low-alpha region around 7.5 Gyr as regions where the relation already breaks down.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the method works as claimed, ages become available for roughly 1.5 million stars, including many giants and dwarfs lacking asteroseismic or rotation data.
  • Because the same relation assigns ages across evolutionary stages, it provides a common age scale for comparing dwarf and giant populations, with no strong dependence on surface gravity.
  • The approach can serve as a cross-calibration tool: offsets between ensemble kinematic ages and asteroseismic or [C/N]-based ages reveal systematic differences between age scales.
  • Empirical isochrones built from these ages can be compared directly with theoretical tracks, offering a data-driven check of stellar evolution models.
  • The catalog reveals bimodal age distributions in the [Mg/Fe]–[Fe/H] plane, including an old population at low [Mg/Fe] that, if real, bears on how the two disks formed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the subgiant-calibrated relation holds in the metal-poor regime, this method could map age structure in the oldest disk and inner halo, where current indicators are weakest.
  • The requirement that parameter-space bins be approximately coeval implies that combining ensemble kinematics with rotation periods could tighten gyrochronology beyond about 4 Gyr, a range where rotation-age relations are poorly calibrated.
  • Because the method averages over bins, real age spreads within a bin are smeared; the width of the action distribution inside each bin could itself be used as a diagnostic of the remaining age spread.
  • With the next astrometric data release roughly doubling the number of stars with full 6-D motions, the same calibration should yield larger samples and finer bins, improving the precision floor.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper proposes 'ensemble kinematic ages': for each target star, the authors isolate a local ensemble of ~20–50 stars with similar atmospheric and chemical parameters, compute the median vertical action ln J_z of that ensemble, and convert it to an age using Eq. (1), a fifth-order polynomial in ln J_z with a linear [Fe/H] scaling. The relation is calibrated on the subgiant ages of Xiang & Rix (2022). The method is validated against that same subgiant sample (MED = 0.9 Gyr, MAD = 2.6 Gyr, ~30%), then applied to ~1.5 million LAMOST DR5 stars, with comparisons to APOKASC-3, [C/N] ages, open clusters, wide binaries, gyrochronology, and isochrone ages. The paper also constructs empirical isochrones and discusses old low-α and young high-α populations.

Significance. If the central claim holds, the resulting catalog would be a valuable population-level age indicator that can be applied across much of the HR diagram and used as a cross-calibration tool between different age-dating techniques. The paper's strengths include the public release of the catalog (Table 1), the explicit enumeration of assumptions in Sec. 2.2, and the candid discussion of failure regions in Secs. 3.1 and 5. The key weaknesses are that the headline accuracy is measured on the calibration sample itself, and that the universal ln J_z–age–[Fe/H] relation is applied to populations for which the paper's own figures show systematic breakdowns. The independent checks provide partial support but are not broad enough to establish a uniform ~2 Gyr accuracy across the full HR diagram.

major comments (4)
  1. [Sec. 2.4, Sec. 3, Fig. 5] The headline '~30% accuracy' is not an independent validation. Equation (1) is fitted to the running median of ln J_z against subgiant age using the same Xiang & Rix (2022) sample that is then compared in Fig. 5. The quoted MED = 0.9 Gyr and MAD = 2.6 Gyr therefore largely measure the quality of the calibration fit, not predictive accuracy. The paper itself acknowledges this in Sec. 4.1 ('our ensemble kinematic ages show the smallest bias relative to the subgiant ages, since the lnJz–age relation is calibrated on this sample'). Please add a held-out test (e.g., fit on half of the subgiants and validate on the other half) or calibrate on an independent age scale; otherwise the abstract's 'accuracy of ~30%' should be reframed as scatter relative to the calibration scale.
  2. [Sec. 2.4, Sec. 4, Figs. 2 and 6] The universality of Eq. (1) is load-bearing but not established. Fig. 2 shows different slopes and offsets for the high-α and low-α disks; Fig. 6 identifies ages >12.5 Gyr and the ~7.5 Gyr, [Fe/H] ~ -0.75 low-α region as places where the relation fails; Sec. 3.1 states that lower main-sequence stars cannot be robustly aged. Nevertheless, Eq. (1) is applied to all 1.5 million LAMOST stars, including those in these breakdown regions, and the abstract claims ages 'across the full HR diagram.' The catalog should either restrict the applicable parameter ranges, provide per-population validity flags, or calibrate and validate separate relations for high-α, metal-poor, and lower-main-sequence populations. The old high-α and metal-poor stars are precisely the populations of greatest interest to Galactic archaeology, so this is not a minor edge case.
  3. [Sec. 4.1, Figs. 8 and 12] The independent validations are too partial to support a uniform '~2 Gyr' uncertainty. The APOKASC-3 comparison shows a systematic ~2 Gyr overprediction, which the paper attributes to age-scale offsets but does not resolve. Open clusters are concentrated near solar metallicity, as the paper itself notes in Sec. 5, so they cannot test the metal-poor regime. Wide binaries are predominantly main-sequence stars, where stellar parameters provide weak age discrimination. The lack of a strong log g trend in Fig. 12 is suggestive but does not demonstrate that dwarf and giant ages sit on the same absolute scale across metallicity and age. Please report residuals separately for each evolutionary state and metallicity regime, and quantify how age-scale offsets and selection effects affect the claimed accuracy.
  4. [Sec. 4 and Table 1] Applying the method to stars without full 6-D kinematics assumes that the subset of LAMOST stars with Gaia DR3 radial velocities is representative of each parameter bin. The paper states only qualitatively that selection effects matter. If stars with and without radial velocities differ in distance, brightness, or Galactic location, the median ln J_z of the kinematic subset can be biased relative to the full target population. Please quantify the fraction of LAMOST stars lacking radial velocities, test for kinematic differences within bins, or provide selection weights. This directly affects the catalog ages for all stars without measured radial velocities.
minor comments (5)
  1. [Eq. (1)] Please state the units of J_z (kpc km s^-1) and the valid range of ln J_z, age, and [Fe/H] over which the polynomial was calibrated. The text later excludes stars with median ln J_z < 0.5, but the calibration range is not specified.
  2. [Sec. 3, Fig. 5] The definition of MAD as 'Median(|ensemble kinematic ages − Median(subgiant ages)|)' is not a paired residual statistic. The usual MAD for a comparison would use paired differences (ensemble age − subgiant age). As written, it measures scatter of ensemble ages around the median subgiant age rather than the accuracy of individual age recovery. Please correct the definition or state clearly what statistic is shown.
  3. [Fig. 4 caption] The caption reads 'Similar to Figure 4 but over-plotting the best-fit model,' which appears to be a self-reference; it should refer to Figure 1 or Figure 3.
  4. [Throughout] Notation is inconsistent: the text uses 'ln J_z' and 'J_z' interchangeably, and Figure 1 labels the axis 'J_z' while the text and Eq. (1) use 'ln J_z'. Please standardize.
  5. [Sec. 1 and Sec. 2.3] Minor language issues: 'an age-J_z relations' should be 'an age–J_z relation'; 'the low-α disk' is sometimes written 'low-α disk' without the article; in Sec. 4 the phrase 'If these stars are not the result of systematics... they may indicate either parallel disk formation...' is incomplete ('either' without a second option).

Circularity Check

1 steps flagged

The subgiant-age 'validation' is substantially in-sample because Eq. (1) is calibrated on the same Xiang & Rix subgiant ages; independent benchmarks exist but the headline ~30% accuracy claim is partly built in.

specific steps
  1. fitted input called prediction [Section 2.4 (Eq. 1); Section 3, Figure 5; Section 4.1]
    "Subgiant ages provide not only a sample of accurate stellar ages for studying kinematic age relations, but also an independent validation set to test our method. ... Not surprisingly, our ensemble kinematic ages show the smallest bias relative to the subgiant ages, since the lnJz–age relation is calibrated on this sample."

    Equation (1) is constructed by fitting a 5th-order polynomial to the moving median of lnJz as a function of Xiang & Rix (2022) subgiant age, with the metallicity scaling also minimized against those same moving medians. Section 3 then presents the agreement with those subgiant ages (MED=0.9 Gyr, MAD=2.6 Gyr, ~30%) as a validation, and even calls the sample an 'independent validation set'. This is not an independent prediction: it is an in-sample residual of the calibration. The paper itself concedes in Section 4.1 that the smallest bias is expected because the relation is calibrated on this sample. Thus the headline accuracy claim is partly forced by construction and cannot be counted as external confirmation.

full rationale

The central methodological chain is: (i) compute median lnJz for stellar-parameter ensembles, (ii) calibrate an lnJz–age–[Fe/H] relation using Xiang & Rix (2022) subgiant ages (Section 2.4, Eq. 1), and (iii) apply that relation to subgiants and to 1.5M LAMOST stars. The main circularity is that the Section 3 comparison against subgiant ages is not an independent test: the calibration target and the validation set are the same catalog. The reported agreement (MED 0.9 Gyr, MAD 2.6 Gyr, ~30%) quantifies how well Eq. (1) reproduces the moving medians it was fitted to, not how well the method predicts unseen ages. The paper is transparent about this in Section 4.1, but the Section 3 language ('independent validation set') overstates the evidential value. A secondary tuning step—bin-size selection by minimizing chi-squared against 100 randomly selected subgiant ages (Section 2.2)—makes the subgiant comparison even more in-sample, though the effect is modest. The paper does include genuinely independent checks: APOKASC–3 asteroseismic ages, open clusters, gyrochronology, wide binaries, and isochrone ages. Those provide real external support for the method and keep the overall circularity score from being higher. However, the headline accuracy claim is presented first through the subgiant comparison, so the partially circular validation is load-bearing for that claim. The paper's own identified breakdown regions (ages >12.5 Gyr and the ~7.5 Gyr metal-poor low-alpha region) and the lower-main-sequence caveat are limitations, not circularities, but they further weaken the 'robust population-level tool across the full HR diagram' framing. Overall: one central validation step reduces by construction; independent external benchmarks prevent the score from rising above 6.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The method introduces no new physical entities. Its entire weight rests on a calibrated empirical relation, with free parameters for the polynomial and metallicity scaling, and a series of domain assumptions about coevality, universality, and the Galactic potential. The most fragile assumptions are those that assert the relation's universality across populations that demonstrably deviate (old high-alpha, metal-poor low-alpha, lower MS).

free parameters (4)
  • 5th-order polynomial coefficients in Eq. 1 = a0=-9.9, a1=30.8, a2=-30.6, a3=15.1, a4=-3.4, a5=0.3
    Fitted to the moving median of lnJz versus age for subgiants from Xiang & Rix (2022). These coefficients define the age scale.
  • Metallicity scaling in Eq. 1 = 0.34 [Fe/H] + 1.16
    Linear scaling selected to minimize chi-square against the moving medians in [Fe/H] bins. It is a free fit parameter.
  • Group bin sizes for subgiant calibration = minimum bin sizes 10-200, maximum 50-500; adaptive expansion up to 200%
    Bin sizes were optimized via grid search against a random sample of 100 subgiant ages; the choice is a free tuning parameter, though the paper reports insensitivity.
  • Running median window (0.3 Gyr) and step (0.1 Gyr) = 0.3 Gyr / 0.1 Gyr
    Chosen by hand for smoothing the lnJz-age relation; influences the shape of the fitted polynomial.
axioms (6)
  • domain assumption Stars with similar atmospheric and chemical parameters are approximately coeval (Assumption 1, Section 2.2).
    This is the foundational premise of the ensemble method; if false, the median Jz of a parameter group does not correspond to a single age.
  • domain assumption The age-lnJz relation is monotonic and can be parameterized (Assumption 3, Section 2.2).
    The calibration uses a polynomial; a non-monotonic or multi-valued relation would break the age inference.
  • domain assumption The calibrated age-lnJz relation is broadly applicable across stellar populations (Assumption 4, Section 2.2).
    Applied to all LAMOST stars, including high-alpha, low-alpha, and different evolutionary stages; the paper itself shows breakdown regions, indicating this is imperfect.
  • domain assumption Contributions to vertical heating other than age and metallicity average out within ensembles (Assumption 5, Section 2.2).
    Secular heating, mergers, and birth conditions could bias Jz without affecting age; the method requires these to cancel statistically.
  • domain assumption The MilkyWayPotential2022 model and Staeckel Fudge produce correct vertical actions (Section 2.1).
    Jz values are model-dependent; an incorrect gravitational potential would shift the calibration and all derived ages.
  • domain assumption Subgiant ages from Xiang & Rix (2022) are accurate with ~7% median uncertainty (Section 2.1).
    These ages serve as the ground truth for the calibration; systematic errors in them propagate directly into all ensemble kinematic ages.

reviewed 2026-08-01 · how reviews work

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Cite this review

Pith. "Pith review of Ensemble Kinematic Ages for 1.5 Million LAMOST Stars." pith.science (2026). https://pith.science/paper/NYMVVGEV

@misc{pith2026260722309,
  author       = {Pith},
  title        = {Pith review of: Ensemble Kinematic Ages for 1.5 Million LAMOST Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NYMVVGEV}},
  note         = {Machine review of arXiv:2607.22309}
}
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abstract

We present a framework for inferring stellar ages from spectroscopic stellar parameters, calibrated with ensemble kinematics by averaging over the median vertical action, $J_z$, for stars with similar atmospheric and chemical properties, yielding self-consistent age estimates across the Hertzsprung-Russell (HR) diagram. We refer to these ages as ensemble kinematic ages as the age scale is calibrated from the average kinematics of ensembles of stars with similar stellar parameters. Individual stellar kinematics are not used in assigning ages. We validate the method against subgiant ages, achieving an accuracy of ~30%, comparable to [C/N]-based estimates. We find a clear age-$J_z$ relations that enable age inference up to ~10 Gyr for both the high- and low-$\alpha$ disks. Applying this framework to 1.5 million LAMOST stars, we derive ages for subgiants and giants with typical uncertainties of ~2 Gyr. The inferred ages agree well with literature age catalogs, with no significant systematic trends as a function of $\log g$. We also demonstrate the potential of empirical isochrones to calibrate theoretical stellar models. We identify an old (~7 Gyr) population within the low-$\alpha$ disk but draw no firm conclusions. Although ensemble kinematic ages are statistical and sensitive to selection effects, Galactic potential assumptions, and Galactic location, they provide a robust population-level tool for Galactic archaeology, complementing traditional age indicators and extending age estimates across the full HR diagram.

Figures

Figures reproduced from arXiv: 2607.22309 by Marc H. Pinsonneault, Yuxi Lu.

Figure 1
Figure 1. Figure 1: Relation between the subgiant ages (Xiang & Rix 2022) and vertical action (Jz), LAMOST DR5 [Fe/H], [α/Fe], Teff (Xiang et al. 2019), absolute magnitude in 2MASS K band (MK) (Xiang & Rix 2022), and guiding radius (Rg). The stellar parameters on the y-axis are used to infer ensemble kinematic ages. A clear relation between age and Jz is evident. 4. The calibrated age–ln Jz relation is broadly appli￾cable acr… view at source ↗
Figure 2
Figure 2. Figure 2: The ln Jz–age relation for the high-α (left) and low-α (right) Galactic disk populations, using stellar ages from Xiang & Rix (2022). The bottom histograms show the residual after subtracting the median trends and the black points show the running median of the residual. The red and blue solid curves denote the running medians for the high- and low-α disks, respectively, with shaded regions indicating the … view at source ↗
Figure 3
Figure 3. Figure 3: The background gray histogram shows the ln Jz–age relation (same as the top-left panel of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of ensemble kinematic ages with sub￾giant ages. The bottom panels show the residuals, with the running median indicated by red points. The error bars on the red points represent the 1.5*MAD. Ensemble kinematic ages reproduce subgiant ages with a median difference of 0.9 Gyr and a MAD of 2.6 Gyr (∼30%), comparable to the precision of [C/N]-based ages. An increase in bias is ap￾parent for ensemble… view at source ↗
Figure 6
Figure 6. Figure 6: Age–metallicity relation (left), the [Fe/H]–[α/Fe] plane (middle), and the ln Jz–age relation (right), colored by the average absolute difference between subgiant ages and ensemble kinematic ages. The age on the x-axis in the left and right panels corresponds to the subgiant age. White contours show kernel density estimation (KDE) densities computed using SciPy. The regions where the ln Jz–age relation doe… view at source ↗
Figure 7
Figure 7. Figure 7: Top row: Kiel diagram (Teff -logg; left) and the [Mg/Fe]–[Fe/H] plane (right), colored by the average ensemble kinematic age. The overall gradients are broadly consistent with expectations from stellar evolution and chemical evolution models. Boxes in the Kiel diagram indicate the parameters used to define coeval groups for determining ensemble kinematic ages. For lower main-sequence stars, however, Teff a… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of ensemble kinematic ages with independent age estimates: subgiant ages (top left; Xiang & Rix 2022), [C/N] ages from starFlow (top middle; Stone-Martinez et al. 2025), APOKASC–3 asteroseismic ages (top right; Pinsonneault et al. 2025), main-sequence ages from isochrone fitting and gyrochronology, and open-cluster ages (bottom left; Berger et al. 2020; Lu et al. 2024a; Castro-Ginard et al. 2020… view at source ↗
Figure 9
Figure 9. Figure 9: Empirical isochrones constructed with our en￾semble kinematic ages for stars with age = 3, 6, or 9 Gyr, [Fe/H] = −0.3, 0, or 0.3, and [α/Fe] = 0 or 0.2 as indicated by the color and legends. As expected, at the same age, metal-poor stars are hotter, and the effect of [α/Fe] increases towards higher metallicity, agreeing with stellar evolution models Dotter et al. (2026). These empirical isochrones pro￾vide… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between empirical isochrones (points) and MIST isochrones (dashed lines) for stellar populations with ages of 3, 6, and 9 Gyr, [Fe/H] = -0.25, 0.0, +0.25, and [α/Fe] = 0. The errorbars are the 1.5*median absolute deviation of the median Teff . The empirical isochrones look topologically similar to the theory isochrones. An offset exist between the empirical and theory isochrones for the main-se… view at source ↗
Figure 11
Figure 11. Figure 11: Top: Median stellar age in the Galactic R–z plane, showing the expected age stratification, with the thin disk dominated by younger stars and progressively older pop￾ulations at larger distances from the Galactic plane in the thick disk. Bottom: Column normalized age–[Al/Fe] rela￾tions for the full sample (left), dwarfs (log g > 4; center), and giants (log g < 4; right). In all samples, [Al/Fe] decreases … view at source ↗
Figure 12
Figure 12. Figure 12: The difference in ensemble kinematic ages and open cluster ages as a function of logg, colored by the cluster age. The ensemble kinematic ages are inferred for individual cluster members. The dashed line show the linear fit between the residual and logg. There is no strong correlation between the difference in age and logg, meaning we can infer ages consistently across the HR diagram. Notably, a substanti… view at source ↗
Figure 13
Figure 13. Figure 13: [Mg/Fe]–[Fe/H] plane for the full sample (top left), and in ensemble kinematic age bins of 1 Gyr colored by their average guiding radii. The age bins are indicated in the titles. The colored lines show the running median for each age bin. A large population of old stars (>7 Gyr) exists in the parameter space of the low-α disk, which is typically associated with younger populations [PITH_FULL_IMAGE:figure… view at source ↗
Figure 14
Figure 14. Figure 14: Gaussian mixture modeling (GMM) of the ensemble kinematic ages in bins of [Fe/H] and [Mg/Fe]. The bin widths are 0.1 dex and the titles indicate the bin centers. The number of Gaussian components is determined using the Bayesian information criterion (BIC). The black curves show the composite distributions, and the colored histograms show the decomposed components. For most bins where the high- and low-α … view at source ↗
Figure 15
Figure 15. Figure 15: Top row: column-normalized age–[Mg/Fe] (left) and age–[Fe/H] (right) relations. Bottom row: peak locations of the Gaussian mixture model (GMM) components for the ensemble kinematic age distributions in the [Mg/Fe]–[Fe/H] plane (see [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 1, 2026.