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Tracing the Milky Way: Calibrating chemical ages with high-precision Kepler data

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Two abundance ratios, [Ce/Mg] and [Zr/Ti], calibrated on 68 Kepler giants with precise asteroseismic ages, can be transferred to large spectroscopic surveys to date hundreds of thousands of Milky Way stars and recover the age structure of…

desk verdict A careful calibration of [Ce/Mg] and [Zr/Ti] as chemical clocks, worth refereeing, but the birth-radius dependence of the [Ce/Mg] slope is a real soft spot that needs confronting. read the letter →

arxiv 2506.15546 v2 pith:ZNXBWEJ5 submitted 2025-06-18 astro-ph.GA astro-ph.SR

G. Casali , J. Montalbàn , A. Miglio , L. Casagrande , L. Magrini , C. Chiappini , A. Bragaglia , M. Matteuzzi
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K. Brogaard A. Stokholm V. Grisoni M. Tailo E. Willett
This is my paper · ORCID
classification astro-ph.GAastro-ph.SR
keywords chemicalclocksstellaragesasteroseismologyredgiantss-processelementsalphaGalacticarchaeologyAPOGEE
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 aims to turn the chemical composition of red giant stars into ages for hundreds of thousands of Milky Way stars, where asteroseismic ages are unavailable. It builds a calibration set of 68 bright giants in the Kepler field with high-precision optical abundances and asteroseismic ages better than ten percent, then selects the abundance ratios [Ce/Mg] and [Zr/Ti] as the tightest chemical clocks. Fitting these ratios against age and metallicity, the paper derives empirical relations that reproduce the input ages to about seven percent accuracy, and applies them to roughly 270,000 APOGEE stars and 1,500 Gaia-ESO stars. The resulting chemical ages separate the low- and high-alpha sequences by age, recover the age-metallicity relation, show the Milky Way disc flaring, and identify a population of old, metal-rich stars. A sympathetic reader would care because this offers a practical route to statistical ages for millions of giants, provided the calibrated relations hold across the disc.

What carries the argument

The central objects are the chemical-clock ratios $\mathrm{[Ce/Mg]}$ and $\mathrm{[Zr/Ti]}$, logarithmic abundance ratios of a slow-neutron-capture (s-process) element to an $\alpha$-element. The mechanism they exploit is nucleosynthetic delay: s-process elements such as Ce and Zr are released mainly by asymptotic-giant-branch stars on timescales of roughly 0.5 to 7 Gyr, while $\alpha$-elements such as Mg and Ti are released promptly by Type II supernovae, so the ratio declines steadily with stellar age. The load-bearing calibration is the linear model of equation (2), $[\mathrm{s}/\alpha] = m_1\,\mathrm{Age} + m_2\,[\mathrm{Fe/H}] + c$, fitted with a Markov-chain Monte Carlo procedure that also yields an intrinsic scatter term; the fits are repeated in bins of guiding radius and birth radius to test whether the age slope changes across the disc. What carries the argument is the precision of the 68-star calibrator sample: high-resolution spectra with $R \sim 67\,000$--$115\,000$ and asteroseismic ages from individual mode frequencies, which together reduce the scatter of the [Ce/Mg] relation from about 0.15 dex (using catalog abundances) to about 0.08 dex.

What would settle it

Take a sample of giants with independent asteroseismic ages from individual mode frequencies that were not used in the calibration---for example, additional Kepler giants from the same catalogue---and compare their measured $[\mathrm{Ce}/\mathrm{Mg}]$ and $[\mathrm{Zr}/\mathrm{Ti}]$ with the ages predicted by equation (2); a systematic residual that depends on $\alpha$-enhancement, Galactocentric radius, or metallicity beyond $[\mathrm{Fe/H}]$, or a typical bias larger than about 3 Gyr in the oldest regime, would falsify the transfer of the relations to the broader disc.

Watch

Extended reading notes

Core claim

The paper's central claim is that, with high-precision abundances and ages from individual oscillation frequencies, $\mathrm{[Ce/Mg]}$ and $\mathrm{[Zr/Ti]}$ are sufficiently tight functions of age and metallicity---intrinsic scatters of 0.08 and 0.01 dex, respectively---to serve as empirical chemical clocks across the full chronochemical history of the disc. The relations, written as $[\mathrm{s}/\alpha] = m_1\,\mathrm{Age} + m_2\,[\mathrm{Fe/H}] + c$, reproduce the asteroseismic calibration ages with roughly 7% accuracy and an absolute age deviation of about 2.95 Gyr. Applied to APOGEE and Gaia-ESO, they separate low- and high-$\alpha$ sequences in age, recover the age-metallicity relation, reveal disc flaring in the Galactocentric-radius versus vertical-height plane, and identify a population of old, metal-rich stars whose inferred birth radii point to the inner disc. The paper also demonstrates that calibrating with lower-precision APOGEE abundances raises the intrinsic scatter to about 0.15 dex, degrading chemical ages more than using lower-precision seismic ages does.

Load-bearing premise

The linear relation between $[\mathrm{Ce}/\mathrm{Mg}]$ or $[\mathrm{Zr}/\mathrm{Ti}]$ and age plus metallicity, calibrated on 68 bright giants in the solar neighbourhood, is assumed to hold unchanged for all field stars across the Milky Way disc, including stars outside the calibrated metallicity range $[-0.8, 0.2]$ dex; if the real relation has non-linearities, population-dependent offsets, or radial dependence not captured by the $[\mathrm{Fe/H}]$ term, the derived chemical ages will be systematically biased.

Editorial extensions

If this is right

  • If the calibrated relations hold, chemical ages can be assigned to roughly 270,000 APOGEE giants and about 1,500 Gaia-ESO stars, extending age information to populations too faint for asteroseismology.
  • The chemical ages separate the low- and high-$\alpha$ sequences cleanly: high-$\alpha$ stars cluster near 11 Gyr with a narrow spread, while low-$\alpha$ stars span from about 2 Gyr to ages as old as the high-$\alpha$ sequence.
  • Recovering the age-metallicity relation suggests that old stars show a broad range of metallicities, with stars at both $[\mathrm{Fe/H}] < -0.6$ and $>0.2$ dex consistently old, pointing to radial migration as a key mixing process.
  • The $\mathrm{R_{GC}}$--$z$ plane, coloured by chemical age, shows disc flaring---young stars stay close to the plane while the vertical spread widens at larger radii---supporting an inside-out formation scenario for the Galaxy.
  • The paper finds a population of old, metal-rich ([Fe/H] > 0) stars, mostly with thin-disc kinematics and super-solar metallicities; their inferred birth radii are concentrated in the inner disc, suggesting they migrated outward.
  • Higher-precision abundances improve the chemical-clock calibration more than higher-precision ages do, so future gains in survey age precision will come primarily from improving abundance measurements.

Reading between the lines

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

  • If the [Ce/Mg] and [Zr/Ti] relations transfer without recalibration to surveys with different spectral coverage and line lists, the same approach could in principle extend to other large spectroscopic datasets that include neutron-capture lines, giving a uniform age scale across multiple surveys.
  • The paper's finding that the [Ce/Mg]-age slope steepens toward larger birth radii, if confirmed at larger sample sizes, would imply that chemical-age-based studies of radial migration need to account for birth-radius-dependent calibrations before interpreting apparent metallicity gradients.
  • The identification of old, metal-rich stars as migrated inner-disc objects is testable: a subset of APOGEE stars with asteroseismic ages from individual modes, outside the 68-star calibration set, should show the same age-metallicity pattern, providing an independent check of the transfer assumption.
  • A direct prediction of the calibration is that stars sharing the same [Fe/H] and [Ce/Mg] should have the same age regardless of kinematic population; this could be tested with open clusters spanning a range of Galactocentric radii and metallicities.
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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

3 major / 5 minor

Summary. The paper calibrates empirical chemical clock relations [Ce/Mg] and [Zr/Ti] against stellar age and metallicity using 68 Kepler red giants with high-resolution HARPS-N/FIES spectroscopy and asteroseismic ages from individual mode frequencies (AIMS) at roughly 8% typical precision. The relations are fitted with a linear model in age and [Fe/H] (Eq. 2), in bins of guiding radius Rg and birth radius Rb, with parameters in Table 4. The authors then apply the Rg-binned and unbinned relations to roughly 270,000 APOGEE DR17 stars and about 1,500 Gaia-ESO stars, obtaining chemical ages that reproduce the age separation of the low- and high-alpha sequences, an age-metallicity relation, disc flaring, and the presence of old metal-rich and old metal-poor low-alpha populations.

Significance. If the transfer of the 68-star calibration to field surveys is valid, the paper provides a large sample of chemical ages for field stars and demonstrates the importance of high-precision calibration data. A particularly valuable result is the quantitative demonstration that APOGEE-quality abundances degrade the intrinsic scatter of the relation (about 0.15 dex versus 0.08 dex), a cautionary result for survey-level chemical clocks. However, the central claim that the calibration transfers to APOGEE and Gaia-ESO rests on an untested assumption about the universality of the [Ce/Mg]-age relation across birth radii, and the recovery test used to quote accuracy and precision is performed on the calibrators themselves. These issues limit the significance of the field-star results until they are addressed.

major comments (3)
  1. [Section 3.1 and Table 4; Section 4] The [Ce/Mg]-age slope shows a 3-sigma dependence on birth radius: m1 = -0.018 +/- 0.006 dex/Gyr for Rb < 6 kpc versus -0.049 +/- 0.008 dex/Gyr for Rb > 7 kpc. In the transfer to APOGEE in Section 4, the authors apply the Rg-binned or no-binning relations, whose slopes are intermediate, without quantifying the systematic age bias that this introduces for field stars with a broad Rb distribution. The statement in Section 4 that the Rb-binned relations cannot be used because Rb requires an age is correct, but it does not establish that the adopted relation is unbiased. I ask the authors to quantify this bias, for example by computing chemical ages for their 68 calibrators with the extreme Rb-binned relations and comparing to the asteroseismic ages, or by estimating the expected bias using the APOGEE Rg and [Fe/H] distributions together with the Lu et al. (2024) birth-radius prescription. Without such a test, the recovered disc flaring, age-metallicity relation, and old metal-rich star populations could be artifacts of applying an averaged relation.
  2. [Section 3.2 and Section 5] The recovery test in Section 3.2 is performed on the same 68 stars used to build the relations, as the authors state: it compares chemical ages against 'input asteroseismic ages used to build the relations.' This measures self-consistency rather than predictive accuracy on independent data, yet the abstract and Section 5 present the resulting accuracy and precision (7% accuracy, 60-70% precision) as properties of the method. I request either an independent validation, for example using asteroseismic ages from APOKASC-3 stars not in the calibration sample or open clusters with known ages, or a clear statement in the abstract and conclusions that the quoted accuracy is in-sample and that the field-star results rely on the qualitative reproduction of known age trends rather than on independently validated absolute ages.
  3. [Section 4.3 and Figure 16] The birth radii Rb of the old super metal-rich stars are computed using the chemical ages derived from the same [Ce/Mg] relation whose birth-radius dependence is ignored in the transfer. Since the Rb estimate depends on the age through the Lu et al. (2024) prescription, and the age estimate depends on the assumed [Ce/Mg]-age slope, the conclusion that these stars 'show their origin from the inner disc' may be circular. I ask the authors to cross-check this conclusion using an independent age source for a subset (for example asteroseismic ages from the literature) or to demonstrate that the inferred Rb distribution is robust when the slope is varied across the 1-sigma range of the no-binning or Rg-binned values in Table 4.
minor comments (5)
  1. [Section 4, first paragraph] The paper states that chemical ages for stars outside the calibration metallicity range [-0.8, 0.2] dex are extrapolated, but it does not report how many APOGEE stars fall outside this range or how the extrapolated ages behave. A brief quantification would help the reader assess the impact of the extrapolation on the field-star results.
  2. [Section 2.2] The revised solar silicon abundance is based on the analysis of a single HARPS solar spectrum; the authors report excellent agreement but do not describe the S/N or line list used. A short note on the robustness of this revision would strengthen the justification for the 0.07 dex adjustment.
  3. [Section 2.3] The comparison between AIMS and PARAM ages shows a mean normalized difference of -0.72 and the paper notes that APOKASC-3 ages are younger by up to 1.7 Gyr at the oldest ages. The authors attribute this to possible mass overestimation in APOKASC-3, but a brief discussion of the impact of systematic age-scale offsets on the absolute calibration of the chemical clocks would be useful.
  4. [Throughout] There are several typos and grammatical errors: 'deference' should be 'difference' (Section 4), 'worst' should be 'worse' (Section 5), 'Montalbàn' is inconsistent with 'Montalbán', 'corrisponging' should be 'corresponding' (page 10), and 'the difference less than 1σ among the parameters' (Section 5) is ungrammatical. A careful proofread is needed.
  5. [Data availability] The paper states that data will be shared upon reasonable request, but for reproducibility of the MCMC fits and the derived age catalog of about 270,000 APOGEE stars, a public release of the fit parameters and the chemical-age catalog, for example as a machine-readable table, would be highly valuable.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor in-sample recovery test is self-consistency, but the main application to independent surveys is not circular.

  1. fitted input called prediction [Section 3.2, Eq. (2) and Fig. 11]
    "Finally, for the same 68 Kepler stars we performed a recovery test comparing chemical ages inferred from [Ce/Mg] against input asteroseismic ages used to build the relations."

    The chemical ages are computed from the same Eq. (2) relation that was fitted using the very same asteroseismic ages as the dependent variable. The resulting accuracy and precision, quantified via Eq. (3), therefore measure how well the fitted relation reproduces its own training data, not how well it predicts independent ages. The paper is transparent about this, explicitly saying 'input asteroseismic ages used to build the relations,' and it does not use this recovery test as the primary demonstration of transferability. The subsequent application to APOGEE and Gaia-ESO uses abundances from independent surveys and does not use asteroseismic ages for the target stars, so the main external validation remains non-circular.

full rationale

The central calibration is empirical: Eq. (2) is fitted to 68 Kepler giants with asteroseismic ages, and the paper clearly labels the in-sample check as a 'recovery test' against the input ages. This is the only step that is circular by construction, and it is a minor internal-consistency check rather than the paper's principal claim. The transfer to APOGEE and Gaia-ESO uses abundances from those independent surveys and recovers features such as the low-/high-alpha age separation and disc flaring that are not explicit inputs to the fitted relation; these are genuine external checks. The age-metallicity relation and old metal-rich population are weaker validation diagnostics because Eq. (2) includes an [Fe/H] term, so part of the recovered trend is inherited from the fitted coefficient rather than discovered from the survey data, but this is a modeling caveat and not a full reduction of the central claim. Overall circularity is low.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim is an empirical calibration; the four fitted parameters per relation are the content of the paper, not hidden inputs. There are no invented entities. The physical basis (nucleosynthetic delay) is adopted from prior literature, and the universality of the relation is the main assumption.

free parameters (4)
  • m1 (age slope) = see Table 4 (e.g., -0.022±0.003 dex/Gyr for [Zr/Ti] no binning)
    Slope of the [s/alpha]-Age relation in Eq. (2), fitted by MCMC to the 68-star sample.
  • m2 ([Fe/H] slope) = see Table 4 (e.g., 0.123±0.048 for [Zr/Ti] no binning)
    Metallicity dependence of the chemical clock, fitted by MCMC; it is the only term accounting for population differences.
  • c (intercept) = see Table 4 (e.g., 0.104±0.022 for [Zr/Ti] no binning)
    Zero-point of the relation, fitted by MCMC.
  • epsilon (intrinsic scatter) = see Table 4 (e.g., 0.009±0.008 for [Zr/Ti] no binning)
    Intrinsic scatter of the relation, a free parameter in the MCMC fit; it quantifies the tightness of the clock.
assumptions (5)
  • domain assumption Nucleosynthetic delay: s-process elements are released by AGB stars over 0.5-7 Gyr, alpha-elements by Type II SNe within 50 Myr, so [s/alpha] trends with age.
    Section 1; this is the physical basis of chemical clocks, adopted from prior literature, and is not tested in this paper.
  • domain assumption Asteroseismic scaling relation for log g (Eq. 1) and the adopted stellar model grid with Delta Y/Delta Z = 1.5 yield unbiased ages.
    Section 2.3; the ages are taken from Montalbán et al. (in prep.) using AIMS with these inputs; details deferred to a companion paper.
  • domain assumption LTE spectral analysis with MARCS model atmospheres and MOOG (FAMA) provides accurate abundances.
    Section 2.1; standard toolchain, no non-LTE corrections applied.
  • ad hoc to paper The relations are universal across the disc, with no hidden dependence on birth radius or kinematics beyond [Fe/H].
    Sections 3.1 and 4; the paper tests consistency across Rg and Rb bins (slopes agree within 1 sigma) but the transfer to APOGEE assumes the unbinned relation applies to stars outside the calibration range. This is the key assumption.
  • domain assumption The Lu et al. (2024) birth radius method and MWPotential2014 are valid for kinematics.
    Section 2.4; used to compute Rg and Rb, not central to the clock calibration but used in the binned analysis.

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Pith. "Pith review of Tracing the Milky Way: Calibrating chemical ages with high-precision Kepler data." pith.science (2026). https://pith.science/paper/ZNXBWEJ5

@misc{pith2026250615546,
  author       = {Pith},
  title        = {Pith review of: Tracing the Milky Way: Calibrating chemical ages with high-precision Kepler data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZNXBWEJ5}},
  note         = {Machine review of arXiv:2506.15546}
}
read the original abstract

Chemical clocks offer a powerful tool for estimating stellar ages from spectroscopic surveys. We present a new detailed spectroscopic analysis of 68 Kepler red giant stars to provide a suite of high-precision abundances along with asteroseismic ages with better than 10 percent precision from individual mode frequencies. We obtained several chemical clocks as ratios between s-process elements (Y, Zr, Ba, La, Ce) and alpha-elements (Mg, Ca, Si, Al, Ti). Our data show that [Ce/Mg] and [Zr/Ti] display a remarkably tight correlation with stellar ages, with abundance dispersions of 0.08 and 0.01 dex respectively and below 3 Gyr in ages, across the entire Galactic chronochemical history. While improving the precision floor of spectroscopic surveys is critical for broadening the scope and applicability of chemical clocks, the intrinsic accuracy of our relations -- enabled by high-resolution chemical abundances and stellar ages in our sample -- allows us to draw meaningful conclusions about age trends across stellar populations. By applying our relations to the APOGEE and Gaia-ESO surveys, we are able to differentiate the low- and high-alpha sequences in age, recover the age-metallicity relation, observe the disc flaring of the Milky Way, and identify a population of old metal-rich stars.

Figures

Figures reproduced from arXiv: 2506.15546 by the authors.

Figure 1
Figure 1. Comparison between the atmospheric parameters and [𝛼/Fe] of APOGEE (APG17) and those found in this work for the sample of Kepler stars. The difference Δ on y-axis is (this work) - APG17. The red dash-dotted line is the average offset [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Comparison between the elemental abundances of APOGEE (APG17) and those found in this work for the sample of Kepler stars. The difference Δ on y-axis is (this work) - APG17. The red dash-dotted line is the average offset. distance). Moreover, the adoption of 𝑅𝑔 instead of the Galactocen￾tric radius 𝑅𝐺𝐶 can mitigate the blurring effect due to epicyclic oscillations around the guiding radius (Schönrich & Binney 2009).… view at source ↗
Figure 3
Figure 3. Uncertainties distribution for the age computed using the individual mode frequencies for our Kepler sample. N is a probability density: each bin displays the number of stars per bin divided by the total number of stars and the bin width. 0 2 4 6 8 10 12 14 16 Age AIMS (Gyr) 0 2 4 6 8 10 12 14 16 Age PARAM (Gyr) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Comparison between asteroseismic ages of our sample of Ke￾pler stars computed using individual mode-frequencies (AIMS) and using 𝜈max and Δ𝜈 by PARAM. Bailer-Jones et al. (2021) 4 , an assumed solar Galactocentric distance 𝑅0 = 8 kpc, a height above the plane 𝑧0 = 0.02…
Figure 6
Figure 6. Figure 6: Chemical clocks [s/𝛼] vs. stellar age for the Kepler sample. Different rows have different s-process elements, while different columns have different 𝛼-elements. The scatter is indicated in each panel [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Radial gradients of [Zr/Ti] (top panels) and [Ce/Mg] (bottom panels) for the Kepler sample. The lines are the running means of different mono-age populations, determined by calculating the average of [Zr/Ti] and [Ce/Mg] for different bins of 𝑅𝑔 (left panels) and 𝑅𝑏 (ri…
Figure 8
Figure 8. Figure 8: [Zr/Ti] (top panels) and [Ce/Mg] (bottom panels) vs. stellar age. The lines are the running means of mono-𝑅𝑔 populations (left panels) and mono- 𝑅𝑏 populations (right panels). their slopes, implying no differences in [Zr/Ti]-age relations among inner, solar and outer r…
Figure 9
Figure 9. Figure 9: [Zr/Ti] vs. stellar age for the Kepler sample in different bins of 𝑅𝑔 (left panels) and 𝑅𝑏 (right panels). The data are colour-coded by metallicity. The dash-dotted line represents the best fit, and the shaded area the 68% confidence interval plus intrinsic scatter. Al…
Figure 10
Figure 10. Figure 10: [Ce/Mg] vs. stellar age for the Kepler sample in different bins of 𝑅𝑔 (left panels) and 𝑅𝑏 (right panels). The data are colour-coded by metallicity. The dash-dotted line represents the best fit, and the shaded area the 68% confidence interval plus intrinsic scatter. A…
Figure 11
Figure 11. Figure 11: The mean (solid line) and standard deviation (shaded area) of Δ/Ageseismo in different age bins, where Δis explained in the legend. Ageseismo is AgeAIMS or AgePARAM depending on the left term of the Δ. The dot￾dashed lines indicate the relative error in ages for an ab…
Figure 12
Figure 12. Figure 12: displays the [𝛼/Fe] vs. [Fe/H] planes for the APOGEE and GES surveys where stars in each panel are colour-coded using the chemical ages. The number of stars for which we found chemical ages is ∼ 270, 000 and 1, 500, respectively. This is one of the largest sample with…
Figure 14
Figure 14. Figure 14: Toomre diagram for the APOGEE stars with [Fe/H] > 0. The kinematically-defined thin-disc, thick-disc stars (determined using the prob￾ability by Reddy et al. 2006) are represented by green, magenta dots, respectively. The dashed lines indicate the total space velocity…
Figure 15
Figure 15. Figure 15: Chemical age distribution of APOGEE stars in different bin of metallicity ([Fe/H] > 0). N is a probability density as in [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: Spatial distribution of the APOGEE super metal-rich stars ([Fe/H] > 0.2) in 𝑅𝑔 and 𝑅𝑏 (computed using the chemical age from [Ce/Mg]) [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]
Figure 19
Figure 19. Figure 19: 𝑧 vs. 𝑅𝐺𝐶 plane for the APOGEE stars with [Fe/H] > −1. The distribution is colour-coded following the chemical ages computed using the [Ce/Mg]-[Fe/H]-age relations. closer to the Galactic centre while younger stars formed in the more distant regions as the disc expand…

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.