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Survey of Surveys. II. Stellar parameters for 23 millions of stars

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A photometric neural network, seeded with previous estimates and trained on a PASTEL-recalibrated spectroscopic reference, predicts stellar parameters for tens of millions of stars and claims its largest accuracy gain exactly where…

desk verdict A genuinely useful catalog with a novel 'refine, don't predict from scratch' approach, but the headline metal-poor accuracy gain is partly inherited from PASTEL, and the validation independence is weaker than the abstract suggests. read the letter →

arxiv 2507.05901 v1 pith:DIVP7G4A submitted 2025-07-08 astro-ph.SR

A. Turchi , E. Pancino , A. Avdeeva , F. Rossi , M. Tsantaki , P. M. Marrese , S. Marinoni , N. Sanna
show 11 more authors
G. Fanari D. Alvarez Garay M. Echeveste S. Nedhath S. Rani E. Reggiani S. Saracino L. Steinbauer G. Thomas F. Gran G. Guiglion
This is my paper · ORCID
classification astro-ph.SR
keywords SurveyofSurveysstellarparametersmachinelearningmulti-layerperceptronmetal-poorstarsglobularclustersphotometricGaiaDR3
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

The paper sets out to show that photometric surveys can yield stellar parameters accurate enough for large-scale Galactic archaeology, provided the machine-learning model does not start from scratch. Its recipe is to take existing estimates (Gaia DR3 Teff and logg, Andrae et al. (2023) [Fe/H]) and refine them with a multi-layer perceptron trained on SoS-Spectro, a homogenized spectroscopic reference that was itself recalibrated on the high-resolution PASTEL database. The result is a catalog of around 19 million ML-derived parameters, validated on globular clusters where the mean [Fe/H] offset drops to +0.08 dex with 0.10 scatter, compared with +0.43 (Andrae et al.), +0.78 (Gu et al.), and +0.14 (Zhang et al.). A reader should care because metal-poor stars are precisely where photometric ML methods have historically been least trustworthy, and the claimed improvement is concentrated there.

What carries the argument

The load-bearing mechanism is the two-stage calibration chain. First, a linear correction (Eq. 2) rescales SoS-Spectro's homogenized survey parameters to the PASTEL high-resolution system, reducing the low-gravity, low-metallicity deviations by more than a factor of two. Second, a multi-layer perceptron (a stacked neural network with 18 hidden layers, batch normalization, dropout, and Leaky ReLU activations) learns to map photometric and astrometric features—absolute magnitudes in both reddened and dereddened forms, distance, Gaia DR3 gspphot values, Andrae et al. (2023) [Fe/H], and error estimates—onto those recalibrated labels. The seeding with previous parameter estimates and the missing-value flags are what allow the network to act as a refiner rather than a from-scratch predictor. Errors are computed per star by summing in quadrature the training error (MLP versus SoS-Spectro on the test set) and a repeatability error from ten differently initialized trainings.

What would settle it

Measure NLTE-corrected high-resolution metallicities for stars in the 20 globular clusters used here (e.g., NGC 7078/M15, NGC 6397) and compare them with both PASTEL and the SoS-ML predictions; if the NLTE values fall systematically below PASTEL by more than about 0.1 dex, the claimed metal-poor validation is an artifact of the reference. A second, cheaper check: the paper already shows median [Fe/H] residuals of roughly 0.6 dex versus PASTEL and SAGA for [Fe/H] below -2, so verifying whether those extreme stars' true metallicities match the catalog would delimit the claim's validity range.

Watch

Extended reading notes

Core claim

The central claim is that two ingredients, a high-resolution-calibrated reference catalog and the use of pre-existing parameter estimates as input features, are what make photometric stellar parameters accurate. SoS-Spectro is built from five spectroscopic surveys (APOGEE, GALAH, Gaia-ESO, RAVE, LAMOST) and recalibrated to PASTEL through the linear correction $\Delta f = a + b\,T_{\rm eff}^{\rm SoS} + c\,\log g^{\rm SoS} + d\,[{\rm Fe/H}]^{\rm SoS}$ (Eq. 2), which more than halves the deviations at low log g and low [Fe/H]. A multi-layer perceptron then predicts each parameter separately from features that include distance, reddened and dereddened absolute magnitudes, Gaia gspphot temperatures and gravities, Andrae et al. (2023) metallicities, and their errors, with flags to handle missing values. On the test sample the predictions reproduce SoS-Spectro to medians of about 50 K in Teff, 0.08 dex in logg, and 0.07 dex in [Fe/H]; merged with SoS-Spectro, the released catalog covers about 23 million stars. The paper argues that the improved low-metallicity behavior is visible in the globular cluster comparison, where its [Fe/H] residuals are much smaller and better centered than those of the other ML catalogs, and that this stems from the PASTEL recalibration and from refining rather than replacing previous estimates.

Load-bearing premise

The low-metallicity training labels are assumed trustworthy because SoS-Spectro was recalibrated against the PASTEL database; if PASTEL's metallicities for metal-poor giants are systematically biased, the improved globular-cluster agreement is partly inherited rather than newly established.

Editorial extensions

If this is right

  • If the claim holds, photometric surveys alone can supply usable stellar parameters for tens of millions of stars, extending spectroscopic-quality metallicity measurements to full-sky Gaia and multi-band samples.
  • The metal-poor regime, where previous ML catalogs show offsets of +0.14 to +0.78 dex against globular clusters, becomes accessible for studies of the halo and accreted populations.
  • The refine-don't-reinvent strategy, using existing parameter estimates as inputs, can be applied to any future parameter set as survey pipelines improve.
  • The catalog provides a homogeneous 23-million-star reference spanning the SDSS and SkyMapper footprints, useful for cluster studies and asteroseismic comparisons.
  • Future releases can absorb newer survey reductions (APOGEE DR17, GALAH DR4, LAMOST DR10), since the current SoS-Spectro exhibits wavy biases against them at the 10-150 K, 0.1-0.3 dex level.

Reading between the lines

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

  • If PASTEL's metal-poor giant metallicities carry systematics (the paper explicitly cannot decide whether PASTEL or the surveys are at fault), part of the globular-cluster agreement is inherited from the reference rather than produced by the ML method; a comparison against independent NLTE abundances of the same clusters would separate the two.
  • The same seeding recipe with asteroseismic logg as an additional input feature could plausibly fix the residual 0.14 dex gravity offset seen against APOKASC-3, since the paper's own validation shows the offset mirrors the SoS-Spectro versus PASTEL logg disagreement for giants.
  • The persistent ~0.6 dex median residual for [Fe/H] below -2 versus PASTEL and SAGA, even after training enrichment, suggests the low-metallicity improvement is real in the globular-cluster range (-2.3 to -0.7) but should not be extrapolated to the extremely metal-poor regime.
  • The method's dependence on distance and reddening input quality implies the accuracy claims hold where those are reliable; applying the catalog to heavily reddened or crowded fields should be done with the provided train-area flags.
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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 / 4 minor

Summary. The paper presents the second data release of the Survey of Surveys project: a recalibrated spectroscopic catalog (SoS-Spectro) and a new photometric machine-learning catalog (SoS-ML) containing Teff, log g, and [Fe/H] for about 23 million stars. The ML method is a multilayer perceptron trained on SoS-Spectro labels, using Gaia astrometry and photometry, SDSS or SkyMapper photometry, and Gaia/Andrae parameter estimates as input features. The paper reports test-set errors of about 50 K, 0.07 dex, and 0.08 dex for Teff, log g, and [Fe/H], and validates the results against other ML catalogs, globular and open clusters, APOKASC asteroseismic gravities, and spectral types. The central claim is that SoS-ML improves precision and accuracy relative to other ML catalogs, especially in the metal-poor range, based on the globular cluster comparison.

Significance. If the low-metallicity accuracy claim holds, the catalog is a valuable community resource: it is public, covers about 19 million stars with ML parameters and an additional 3.75 million with spectroscopic parameters, and it includes a careful error budget that combines a training error and a repeatability error derived from ten independent trainings. The authors are also appropriately cautious in several places, explicitly acknowledging that the reference catalog has its own biases and that the APOKASC log g comparison shows a residual 0.14 dex offset. However, the decisive evidence for the headline metal-poor improvement is not yet independent: PASTEL is used both to calibrate the training labels and to augment the metal-poor training sample, and the overlap between PASTEL and the Harris (1996) globular cluster metallicities used for validation is not quantified. The paper would be materially strengthened by an external validation sample that was not used in any calibration or training step.

major comments (4)
  1. [Sect. 3.1, 4.3, 6.4] The low-metallicity accuracy claim rests on a benchmark that is not independent of the training labels. SoS-Spectro is recalibrated against PASTEL via Eq. (2) in Sect. 3.1, and the metal-poor training sample is augmented with 406 PASTEL stars in Sect. 4.3; the headline validation in Sect. 6.4 then compares ML [Fe/H] with Harris (1996) globular cluster metallicities. The paper does not quantify how many cluster stars or underlying literature measurements are shared between PASTEL and Harris, and the authors themselves note up to 2 dex disagreement between PASTEL and all spectroscopic surveys for metal-poor giants (Sect. 3.1). As a result, the +0.08 dex offset and 0.10 dex scatter reported in Fig. 8 may represent a realignment to the PASTEL scale rather than an independent accuracy gain. Please quantify the PASTEL-Harris overlap and re-validate on an external sample not used in any calibration step, or explicitly downgrade the claim to consistency with PASTEL.
  2. [Sect. 6.3 and Tables 2-3] Andrae et al. (2023) [Fe/H] is used as an input feature (Tables 2 and 3), and the same catalog is then used as a comparison benchmark in Fig. 7 (bottom-right panel). The excellent median agreement (-0.02 dex, MAD 0.08) is therefore partly by construction and cannot serve as independent evidence for accuracy. The text in Sect. 6.3 even uses this agreement, combined with the cluster comparison, to argue that the method improves on Andrae et al.; please separate the input-dependence discussion from the validation and rely on the cluster, asteroseismic, and spectral-type comparisons for claims of improvement over Andrae et al.
  3. [Appendix C.3] The log g validation against APOKASC-3 shows a median offset of 0.14 dex for giants, with error bars barely touching the 1:1 line, and the authors attribute this to the PASTEL-based calibration. Since the catalog reports formal log g errors of about 0.07-0.08 dex (Table 5), the systematic offset is larger than the quoted precision. The broad abstract statement of 'substantial improvements ... in terms of precision and accuracy' should be restricted to [Fe/H] or supported by a log g validation that reaches the claimed accuracy; otherwise the error bars in Table 5 should be recalibrated to include this systematic component.
  4. [App. D.1 and Fig. 8] The comparison with Gu et al. (2025) for globular clusters is based on only two clusters (NGC 7078 and NGC 7089), as stated in Appendix D.1; the mean offset +0.78 and scatter 0.25 shown in Fig. 8 therefore rest on very limited data and should not be given equal weight in the cross-catalog comparison. Either compute the Gu et al. statistics on a larger cluster sample or explicitly mark this panel as preliminary.
minor comments (4)
  1. [General] There are several typographical errors, including 'di fferent' in the Abstract and Introduction, 'Suveys' in the Introduction, and 'Trainig' in the caption of Fig. 4; these should be corrected.
  2. [Sect. 3.1] The text describes Eq. (2) as a 'three-parameter linear fit', but the equation has four fitted coefficients (a, b, c, d) corresponding to three predictors plus an intercept; please rephrase as a linear fit with three predictors plus an intercept.
  3. [Sect. 6.2 and App. C.1] The acronym for the SAGES catalog appears as 'SAGE' in Sect. 6.2 and as 'SAGA' in Appendix C.1; please use a single consistent name.
  4. [Sect. 5.2] The quality cuts on the ML errors (eML on log g > 1.0 dex, eML on [Fe/H] > 1.0 dex) are very loose, and only the total number of removed stars (1557) is reported; please also report how many stars are removed by each individual cut so readers can judge the impact of these thresholds.

Circularity Check

2 steps flagged · score 5.0 of 10

Low-metallicity validation shares its scale with the PASTEL-calibrated training labels, and the Andrae [Fe/H] comparison is degenerate because Andrae [Fe/H] is an input feature; the core photometric ML derivation is otherwise independent.

  1. fitted input called prediction [Sect. 3.1 (Eq. 2), Sect. 4.3, Appendix C.1 (Fig. C.1), Sect. 6.4]
    "We thus enriched the SoS-Spectro reference sample by adding metal-poor stars from the PASTEL catalog, given the good agreement with the recalibrated SoS-Spectro. ... We also compared our [Fe/H] results with data from open and globular clusters (see also Sect. 6.4) and observed the same trend as in the PASTEL comparison."

    The low-metallicity labels are calibrated to PASTEL via Eq. 2 and then augmented with PASTEL stars as labels (139 SDSS and 267 SM stars with [Fe/H] < -1, Sect. 4.3). The low-metallicity validation (Appendix C.1, Fig. C.1) uses PASTEL as the reference, so part of the reported after-augmentation improvement (median [Fe/H] residual 0.86 -> 0.61 dex for [Fe/H] < -2) is the network reproducing PASTEL labels that were in its training set. The headline globular-cluster validation (Sect. 6.4, Harris 1996) is presented as the decisive evidence, but the paper itself links it to PASTEL ('observed the same trend as in the PASTEL comparison'), and Harris is likewise a literature compilation of high-resolution spectroscopy with plausible, unquantified source overlap with PASTEL.

  2. other [Tables 2-3 (feature mh_andrae), Sect. 2.1, Sect. 6.3, Fig. 7 (bottom row)]
    "The bottom row of Fig. 7 shows the comparison. While the [Fe/H] values agree extremely well, as expected since we used them as input parameters to the ML prediction, we observe a large spread."

    Andrae et al. (2023) [Fe/H] (mh_andrae) is a listed input feature for both the SDSS and SkyMapper networks (Tables 2-3), selected specifically because it agrees with the SoS-Spectro labels (Sect. 2.1). The bottom row of Fig. 7 therefore compares the network output against one of its own inputs, so the reported agreement (median -0.02 dex, MAD 0.08 dex) is largely a by-construction property of the model, not an independent accuracy check. The paper acknowledges this in a clause ('as expected'), yet the conclusions still count the comparison among the validations ('we compare extremely well with other ML catalogs in the literature'), making a part of the presented validation display degenerate even though it is not the central claim.

full rationale

The core derivation is a genuine regression: the MLP maps photometric, astrometric, and Gaia/Andrae features to SoS-Spectro labels, and the globular-cluster validation uses Harris (1996) values that were never inputs to the training, so the work is not circular by construction in its main pipeline. However, two load-bearing checks are partially self-referential. First, the low-metallicity accuracy claim rests on a scale that the paper itself built: SoS-Spectro was recalibrated to PASTEL (Eq. 2), PASTEL stars were added as training labels (Sect. 4.3), and PASTEL then serves as the low-metallicity validation reference (App. C.1); the cluster validation is explicitly described as showing 'the same trend as in the PASTEL comparison,' and Harris compilations plausibly share sources with PASTEL, so the '+0.08 vs +0.14/+0.43/+0.78' improvement over other ML catalogs is partly inherited from the calibration target. Second, the Andrae et al. [Fe/H] agreement is degenerate because mh_andrae is an input feature, though the paper honestly flags it as expected. In the paper's favor, it explicitly acknowledges that the reference catalog has its own biases that the MLP will 'faithfully reproduce', reports the unresolved PASTEL-versus-survey disagreement for metal-poor giants, and provides independent checks (APOKASC log g, spectral types) that are not circular. These genuine independent elements and the paper's transparency keep the circularity partial rather than total; the score reflects that the headline low-metallicity validation axis is not demonstrably independent of the calibration and enrichment inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The catalog's accuracy is carried by two fitted objects: the 12 coefficients of the PASTEL recalibration (Eq. 2, Table 1) and the hand-tuned MLP. The paper assumes PASTEL is the external truth, including for metal-poor giants where its own comparison shows up to 2 dex logg disagreement, and assumes the five-survey SoS average is a valid label after recalibration. It further assumes reddening maps, Bailer-Jones distances, and one-to-one cross-matching preserve accuracy. No new physical entities are introduced; SoSid is a catalog identifier. All such choices are disclosed, but they cap the achievable accuracy: the MLP cannot beat the reference labels.

free parameters (6)
  • PASTEL calibration coefficients for Teff (a, b, c, d) = a=112, b=-6.66e-3, c=-28.1, d=-40.7
    Eq. 2, Table 1. Linear fit of SoS-Spectro minus PASTEL residuals to Teff, logg, [Fe/H] over about 15,000 measurements; rescales the training labels before ML training.
  • PASTEL calibration coefficients for logg = a=0.159, b=-2.21e-5, c=-0.00242, d=-0.0689
    Table 1, same fit as Teff. These coefficients propagate PASTEL's giant logg systematics into the labels.
  • PASTEL calibration coefficients for [Fe/H] = a=0.0769, b=-3.84e-7, c=-0.0186, d=-0.0262
    Table 1, same fit. Directly affects the headline low-metallicity [Fe/H] claim.
  • MLP architecture and training schedule = 18 hidden layers (80-160 units), Leaky ReLU, batch norm, dropout, MAE for first 1/5 of epochs then SMAPE with…
    Sect. 4.1. Hand-chosen hyperparameters; no systematic tuning or ablation is reported, yet they set the reported prediction errors.
  • Astrometric and magnitude quality cuts = G>18 mag, parallax_error>0.1, astrometric_sigma5d_max>0.1, teff_gspphot>9000 K, vbroad>30 km/s, ruwe>1.4…
    Sect. 2.1. Adopted after initial tests because about 13% of stars were giants spectroscopically but main-sequence in the CMD; the cuts shaped the training and application samples.
  • Very metal-poor training enrichment threshold = [Fe/H] < -1 dex; 139 SDSS and 267 SM stars from PASTEL
    Sect. 4.3. Adds PASTEL stars to the training labels to mitigate the metal-poor deficiency; these same stars overlap the PASTEL validation benchmark.
assumptions (5)
  • domain assumption PASTEL is a reliable external reference for stellar parameters, including for metal-poor giants.
    Sect. 3.1. The recalibration (Eq. 2) assumes PASTEL is the truth; the paper itself reports up to 2 dex logg disagreement between PASTEL and each survey for metal-poor giants and says 'it is difficult to decide whether the problem lies in PASTEL or in the surveys.'
  • domain assumption The SoS-Spectro five-survey average is a valid training label once recalibrated on PASTEL.
    Sect. 3. The homogenization is a simple average of five surveys with only LAMOST Teff and RAVE [Fe/H] calibrated (Tsantaki et al. 2022); the MLP reproduces SoS-Spectro, so label biases propagate to predictions, acknowledged in Sect. 4.3.
  • domain assumption Photometric magnitudes, Gaia astrometry, and reddening maps suffice to predict the three stellar parameters at the claimed accuracy.
    Sects. 2 and 4.2. The feature set assumes reddening corrections (Schlegel et al. 1998 maps, SDSS AB coefficients) and absolute magnitudes from Bailer-Jones et al. distances are accurate enough, including at high reddening values up to 500 mag in the g band before filtering.
  • domain assumption One-to-one cross-matching between catalogs preserves an unbiased sample.
    Sect. 2.2. Dropping all stars with multiple counterparts removes binaries and crowded-field stars; a clean-sample strategy that restricts the catalog's applicability but is not tested for induced sample biases.
  • standard math Standard statistical and ML machinery behaves as expected on this dataset.
    Sect. 4. Background methods: MLP training with backpropagation, SMAPE loss, batch normalization, dropout, treeKDE density estimation, MAD rescaling with k about 1.4826.

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Pith. "Pith review of Survey of Surveys. II. Stellar parameters for 23 millions of stars." pith.science (2026). https://pith.science/paper/DIVP7G4A

@misc{pith2026250705901,
  author       = {Pith},
  title        = {Pith review of: Survey of Surveys. II. Stellar parameters for 23 millions of stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DIVP7G4A}},
  note         = {Machine review of arXiv:2507.05901}
}
read the original abstract

In the current panorama of large surveys, the vast amount of data obtained with different methods, data types, formats, and stellar samples, is making an efficient use of the available information difficult. The Survey of Surveys is a project to critically compile survey results in a single catalogue, facilitating the scientific use of the available information. In this second release, we present two new catalogs of stellar parameters (Teff, logg, and [Fe/H]). To build the first catalog, SoS-Spectro, we calibrated internally and externally stellar parameters from five spectroscopic surveys (APOGEE, GALAH, Gaia-ESO, RAVE, and LAMOST) and externally on the PASTEL database. The second catalog, SoS-ML catalog, is obtained by using SoS-Spectro as a reference to train a multi-layer perceptron, which predicts stellar parameters based on two photometric surveys, SDSS and SkyMapper. As a novel approach, we build on previous parameters sets, from Gaia DR3 and Andrae et al. (2023), aiming to improve their precision and accuracy. We obtain a catalog of stellar parameters for around 23 millions of stars, which we make publicly available. We validate our results with several comparisons with other machine learning catalogs, stellar clusters, and astroseismic samples. We find substantial improvements in the parameters estimates compared to other Machine Learning methods in terms of precision and accuracy, especially in the metal-poor range, as shown in particular when validating our results with globular clusters. We believe that there are two reasons behind our improved results at the low-metallicity end: first, our use of a reference catalog, the SoS-Spectro, which is calibrated using high-resolution spectroscopic data; and second, our choice to build on pre-existing parameter estimates from em Gaia and Andrae et al., rather than attempting to obtain our predictions from survey data alone.

Figures

Figures reproduced from arXiv: 2507.05901 by the authors.

Figure 1
Figure 1. Photometric passbands of Gaia (top panel), SDSS (middle panel), and SkyMapper (bottom panel), obtained from the SVO filter profile service (Rodrigo et al. 2024, http://svo2.cab.inta-csic. es/theory/fps/). (2023) instead of mh_gspphot from Gaia DR3 because we no￾ticed that they agree with the SoS-Spectro metallicities sensi￾bly better than the Gaia ones. Specifically we observe an over￾all RMSE which is better by 0.1… view at source ↗
Figure 2
Figure 2. Sky distribution of our sample selections, after the cross-match with Gaia and all quality selections (Sect. 2), in an Aitoff projection of RA and Dec. The color scale refers to the density of points (blue is minimum density and red maximum) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Comparison of the SoS-Spectro atmospheric parameters (Tsantaki et al. 2022, after calibration) with the literature compilation of high￾resolution studies in the PASTEL database (Soubiran et al. 2016), for ≃15 000 measurements, corresponding to ≃14 000 unique stars in common. See Sect. 3 for details. Lighter color corresponds to higher data density per pixel. Grey points in the background represents the uncorrected d… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Distribution of ML prediction errors on the Test dataset in the SM sample case (blue) and the SDSS sample case (red). The y scale indicates the logarithm of the fraction of the Trainig dataset in each bin (total of 100 bins) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Comparison between the ML predictions obtained on the intersection between SDSS and SM training+test sample and SM sample (55696 stars). Lighter color corresponds to higher data density per pixel. each accounting for around 9-10 million stars after applying the relevan…
Figure 6
Figure 6. Figure 6: Kiel Diagram for the final catalog, colored with the estimated errors on the three parameters. From left to right: Teff, log g and [Fe/H]. The diagram is divided in small hexagonal bins and the color represents the average of the error inside the bin [PITH_FULL_IMAGE:…
Figure 7
Figure 7. Figure 7: Comparison of atmospheric parameters predicted by our ML approach (abscissae) and literature ML catalogs (ordinates). The left plots show Teff comparisons, the middle ones log g, and the right ones [Fe/H]. The top row shows the comparison with Zhang et al. (2023), the …
Figure 8
Figure 8. Figure 8: Comparison of metallicity predictions for globular (top row) and open clusters (bottom row). Our results are shown in purple in the leftmost panels, the ones by Andrae et al. (2023) in blue in the center-left panels, the ones by Gu et al. (2025) in red in the center-ri…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.