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Supernova lightCURVE POPulation Synthesis II: Validation against supernovae with an observed progenitor

T0 review · 4 major / 8 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Light-curve fitting alone recovers type IIP supernova progenitor masses with precision rivaling progenitor imaging.

desk verdict Useful validation of a large-grid lightcurve fitting method for IIP SNe, but the precision claim rests on an uncalibrated 0.25 mag model-error floor. read the letter →

arxiv 1908.07762 v1 pith:6CUQOKHW submitted 2019-08-21 astro-ph.SR astro-ph.HE

J.J. Eldridge , N.-Y. Guo , N. Rodrigues , E.R. Stanway , L. Xiao This is my paper · ORCID
classification astro-ph.SRastro-ph.HE
keywords typeIIPsupernovaesupernovalight-curvefittingprogenitormasspopulationsynthesisexplosionenergynickel-56circumstellarmediumBPASSmodels
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 asks whether a type IIP supernova's light curve alone can reveal the mass of the star that exploded, without ever imaging the star before it died. The authors fit a grid of more than five thousand synthetic light curves, built from single-star progenitor models with varying initial mass, explosion energy, nickel mass and nickel mixing, to eleven supernovae whose progenitors have been directly detected in archival images. For nine of the eleven supernovae the fit is good, and the fitted initial and nickel masses agree with the values inferred from progenitor imaging with comparable uncertainties. The two poor fits suggest the grid is missing some progenitor variety, such as binary interactions or metallicity differences. If this validation is correct, light-curve fitting can substitute for progenitor imaging when the star itself is not resolvable.

What carries the argument

The load-bearing machinery is a grid of 5,346 synthetic V-band light curves computed by the SuperNova Explosion Code (SNEC) from single-star stellar models of the BPASS population synthesis, covering initial masses from 5 to 26 solar masses, explosion energies log(E_exp/ergs) from 50 to 52, nickel masses log(M_Ni/M_sun) from -3 to -1, and three nickel mixing prescriptions. Each observed light curve is fitted to every model by minimising $chi^{2}$, with the explosion epoch also searched and a fixed 0.25 magnitude model error added in quadrature to the photometric uncertainty. The best-fitting model assigns initial mass, explosion energy, nickel mass, mixing parameter and explosion date, with parameter uncertainties read off from the range of the $chi^{2}$ surface in each parameter.

What would settle it

Apply the same fitting grid to a larger sample of type IIP supernovae that have independent mass estimates from late-time nebular spectra or host stellar populations, avoiding any use of pre-explosion imaging. If the fitted masses systematically disagree with those independent estimates by more than the quoted uncertainties, the fixed 0.25 magnitude error is too small and the precision claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that light-curve fitting over a large grid of synthetic models recovers the initial progenitor mass and nickel-56 mass of type IIP supernovae with precision comparable to what is achieved by detecting and modelling the progenitor star in pre-explosion images. The validation is against eleven nearby supernovae with directly observed progenitors; nine of the eleven are well fitted and their derived parameters are consistent with the progenitor-imaging values within the quoted uncertainties. The paper also finds a typical explosion energy of log(E_exp/ergs)=50.52±0.10 for the group, no strong dependence of explosion energy on initial mass, and tentative indications that both nickel mass and nickel mixing depend on the initial progenitor mass. In short, the light curve itself is positioned as a usable probe of the progenitor, not just of the explosion.

Load-bearing premise

The load-bearing premise is that the synthetic light curves never deviate from the true light curve by more than the adopted 0.25 magnitude model error; if the real systematic errors from binary progenitors, differing metallicities, uncertain wind mass loss and the unmodelled final stellar evolution stages are larger, the quoted parameter uncertainties and the claimed precision are not justified.

Editorial extensions

If this is right

  • A well fitted light curve by itself gives an initial progenitor mass that can stand in for a detected progenitor, extending mass measurements to supernovae beyond the local volume where the progenitor is resolvable.
  • The narrow typical explosion energy, log(E_exp/ergs)=50.52±0.10, provides a quantitative prior for core-collapse explosion models.
  • The tentative dependence of nickel mass on initial mass suggests a link from explosion nucleosynthesis to the pre-collapse carbon-oxygen core mass.
  • Including a circumstellar medium tied to the red supergiant wind reproduces the early light-curve brightening without tuning wind parameters supernova by supernova.
  • Two of the eleven supernovae are not well reproduced by any single-star model, marking a clear target for adding binary interactions or metallicity variations to the grid.

Reading between the lines

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

  • If the precision holds in a larger sample, light-curve fitting can measure progenitor masses for type IIP supernovae at distances where photometry is possible but the progenitor is not resolvable, effectively enlarging the statistical sample of core-collapse progenitors by an order of magnitude.
  • The mass-energy degeneracy the paper notes in the chi^2 surfaces might be broken by fitting the same grid to multi-band light curves, since the paper uses only V-band data; this is a testable extension of the same machinery.
  • The 0.25 magnitude model error is a placeholder; re-deriving it by calibrating against supernovae with independent mass anchors would directly test whether the precision claim is robust to the model's known simplifications.
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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 / 8 minor

Summary. The paper presents a supernova lightcurve population synthesis (CURVEPOPS) validation study. The authors compute a grid of 5,346 SNEC supernova lightcurve models from BPASS single-star progenitors, varying initial mass (6-26 M_sun), explosion energy (log E = 50-52 in 0.25 dex steps), nickel mass (10^-3 to 10^-1 M_sun in 0.25 dex steps), and nickel mixing (three boundary fractions). They fit V-band lightcurves of 11 type IIP supernovae that have pre-explosion progenitor detections, using a chi-square statistic with a fixed 0.25 mag model error floor. They compare derived initial masses and nickel masses to progenitor-imaging and literature values, report a mean explosion energy of log(E/erg) = 50.52 +/- 0.10, and suggest correlations of nickel mass and mixing with initial mass. Two objects (SN2005cs, SN2006my) with poor (class C) fits are excluded from the quantitative analysis. The central claim is that, where a good fit is obtained, lightcurve fitting alone yields progenitor and nickel mass estimates with precision comparable to progenitor imaging.

Significance. If the central claim is established, this would be a valuable result: it would show that, for a subset of type IIP supernovae, lightcurve fitting can recover progenitor masses with precision comparable to pre-explosion imaging, and it would constrain the typical explosion energy of these events. The paper has clear strengths: the initial-mass validation against the independent Smartt (2015) progenitor-imaging sample is genuine and generally consistent; the public release of the SNEC input files and model lightcurves is a community resource; and the authors are transparent about many limitations (single-star only, fixed metallicity, coarse nickel-mixing grid, simplified bolometric corrections). However, the quantitative uncertainty estimates are built on an ad hoc and uncalibrated model error floor, the nickel-mass comparison is partly circular, and two of eleven objects are excluded from the population conclusions. These issues are load-bearing for the headline precision claim and must be addressed before the paper can be accepted.

major comments (4)
  1. [Sec. 4.2, Eq. (1)] The model error floor of 0.25 mag is introduced as 'half of the magnitude difference between models of successive explosion energies,' but no justification is given for why this represents a valid statistical error model for the residuals, nor why it should be added in quadrature as an independent Gaussian error. The resulting chi2_min values are far below N_obs for most objects (e.g., SN2003gd chi2_min=21.6 vs N_obs=93; SN2004A chi2_min=7.7 vs N_obs=39; SN2012ec chi2_min=10.0 vs N_obs=46), showing that the adopted sigma_tot dominates as a random-error term while the actual model deficiencies (end-of-plateau shape, early-time CSM features) are systematic and time-correlated. Because the quoted parameter uncertainties in Tables 2 and 3 are all derived from Delta(chi2)=5.89 contours using this sigma_tot, the claimed precision comparable to progenitor imaging is not underpinned by a validated error model. The authors should either calibrate the model error against the residuals of the best-fitting models or explicitly propagate the known systematic uncertainties (single-star assumption, fixed Z and beta, simplified bolometric corrections) into the parameter ranges. This is the central issue for the paper's headline claim.
  2. [Sec. 5 and Sec. 5.2.1] The quantitative conclusions, including the mean explosion energy log(E/erg)=50.52+/-0.10, exclude SN2005cs and SN2006my because their fits are classified as poor (C). SN2005cs, however, is one of the best-observed low-mass IIP supernovae and a canonical object for progenitor studies. The paper states that the poor fits indicate missing model physics, but it does not test how the mean explosion energy or the nickel-mass relation would change if these objects were included with plausible parameters (e.g., from the literature or from the mass-constrained fits). The abstract's phrase 'most of the type IIP supernovae' is based on at most 9 of 11 objects, and the sensitivity of the population conclusions to the excluded objects should be quantified.
  3. [Sec. 5.1 and Tables 2-3] The validation of the recovered nickel mass is partly circular. Many of the 'literature' nickel masses listed in Tables 2-3 are derived from lightcurve modeling with similar one-dimensional explosion-plus-radiation-transport assumptions, sometimes with the same kind of code (e.g., Hendry et al. 2005a, 2006; Smartt et al. 2009; Fraser et al. 2011; Tomasella et al. 2013; Dall'Ora et al. 2014; Bose et al. 2015). The agreement between 'This Work' and 'Literature' in Figure 5 is therefore not a fully independent check on the accuracy of the nickel mass recovery. The authors should explicitly separate which literature nickel masses are independent of lightcurve fitting (e.g., from late-time nebular spectroscopy, as in Jerkstrand et al. 2015b) and base the validation claim on that subset.
  4. [Sec. 5.2.1] The population statement 'most of the type IIP supernovae have an explosion energy of the order of log(E_exp/ergs)=50.52+/-0.10' does not specify the exact sample, weighting, or error propagation used. From Table 2, class A fits alone (SN2003gd, SN2004A, SN2012A, SN2012ec) give a mean near 50.56 with a small scatter, while including class B fits gives a mean near 50.53 but with a larger spread; the individual uncertainty bars are asymmetric and often comparable to the grid spacing. Because the per-object uncertainties from the Delta(chi2) method are unreliable (see the first major comment), the quoted +/-0.10 is not a robust measure of the uncertainty on the typical explosion energy. The authors should state the sample size, the sample standard deviation, and the standard error explicitly, and show how the result changes if class C objects are included.
minor comments (8)
  1. [Sec. 2] There are several typographical issues, including 'codeB PA S S' (missing spaces) and '1050.5erg s-1' in Figure 1 captions, which should read 10^50.5 erg (energy, not power); the same unit error appears in the grid definition in Section 2.
  2. [Eq. (1)] The summation notation is ambiguous; the expression should be written as sum over observed data points i of [(y_model(t_i) - y_obs,i)/sigma_tot]^2, with sigma_tot explicitly defined as the quadrature sum of the photometric error and the 0.25 mag model error.
  3. [Tables 2 and 3] Several table entries are garbled or hard to read, e.g., SN2006my's explosion energy appears as '50.751.13 -0.63' in Table 2, and SN2012aw's initial mass appears as '140.5-2' in Table 3; these need careful reformatting, especially for the asymmetric uncertainties.
  4. [Sec. 4.2] The sentence 'The first magnitude measurement of the SNe is not necessarily the explosion date' should refer to a single supernova ('the SN'), and the phrase 'the difference between minimum and maximum is larger than 10 days' could be restated as 'if the allowed explosion-date range exceeds 10 days.'
  5. [Sec. 5.1] The phrase 'directed in pre-explosion imaging' should be 'detected in pre-explosion imaging.'
  6. [Appendix A] The sentence 'we plot the best fitting model (black line) along with the lightcurves at are within the 1-sigma uncertainty in grey' contains a grammatical error and should read '...along with the lightcurves that are within the 1-sigma uncertainty in grey.'
  7. [Appendix C] The model identifier 'MESAv10398' should be written as 'MESA r10398.'
  8. [Sec. 6] The sentence about constrained and unconstrained fits appears to have the comparison reversed: the text says 'the scatter is less in the latter case' (the unconstrained case), but the constrained fits should have less scatter in mass; the wording should be clarified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the fitted light-curve parameters are validated against independent pre-explosion progenitor imaging, and the self-citations are tool provenance rather than load-bearing circular support.

full rationale

The paper's central validation is genuinely external: unconstrained light-curve fits are compared with progenitor initial masses from Smartt (2015), which come from direct pre-explosion imaging, not from the authors' own models. The CURVEPOPS grid is built from BPASS single-star structures (Eldridge et al. 2017) exploded with the open-source SNEC code, and the fitted quantities (initial mass, explosion energy, nickel mass, nickel mixing) are read off the grid by minimum chi-square against observed light curves; they are not defined in terms of the comparison quantities. The mean explosion energy and the nickel-mass/initial-mass trend are summaries of the fitted grid values, not predictions derived from those same summaries. The fixed 0.25 mag model-error term in Eq. (1) is an a priori uncertainty assumption that affects the claimed precision, but it does not enter the derivation of the best-fit parameters themselves; this is a statistical-calibration concern rather than circularity. The paper's extensive self-citations (paper I, BPASS) supply the model grid and prior motivation, but the load-bearing validation step against Smartt (2015) is independent, so the central claim does not reduce to a self-citation chain. The nickel-mass comparison to literature values is weaker as an independent check because some literature nickel estimates are themselves light-curve-derived, but the paper's nickel fits are not constructed from those literature values, so this is an independence-of-validation caveat rather than a circular derivation step.

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

The central claim rests on the assumed accuracy of the BPASS/SNEC lightcurve models and the noise model used in fitting. The grid steps and the 0.25 mag model error are hand-chosen. No new entities are introduced.

free parameters (5)
  • Model uncertainty sigma_model = 0.25 mag
    Ad hoc error added in quadrature to photometric errors in Eq. 1; estimated as half the magnitude difference between models of successive explosion energies (Section 4.2). It controls all chi^2-based uncertainties and hence the precision claim.
  • Nickel mixing boundary fractions = 0.1, 0.5, 0.9
    Three mixing lengths chosen by hand (Section 2) to represent low/mid/max mixing; the coarse grid inflates uncertainties in the mixing parameter.
  • Explosion energy grid step = 0.25 dex
    Grid spacing from 50 to 52 dex; sets the minimum uncertainty quoted for explosion energy (half grid spacing).
  • Nickel mass grid step = 0.25 dex
    Grid spacing from -3 to -1 dex; sets resolution of nickel mass estimates.
  • Initial mass grid step = 1 Msun
    Integer initial masses from 6 to 26 Msun; minimum mass uncertainty taken as 0.5 Msun (half spacing).
assumptions (5)
  • domain assumption BPASS single-star models evolved to the end of core carbon burning are sufficiently close to core-collapse structure for lightcurve modeling.
    Section 2 states this assumption; Appendix C tests with one MESA model and finds outer structure similar, but late-time lightcurves subject to increased uncertainty.
  • domain assumption Mass-loss rates from de Jager et al. (1988) and wind acceleration beta=5 describe the circumstellar medium around these progenitors.
    Section 2 uses these to set the wind density; they note uncertainties and test factor changes, but the grid itself fixes them.
  • domain assumption All type IIP SNe in the sample arise from single-star progenitors with no significant binary interaction and metallicity Z=0.014.
    Section 2 excludes binary models for computational reasons; Section 6 attributes poor fits to possible binary or metallicity effects.
  • domain assumption SNEC's bolometric corrections to V-band magnitudes are adequate for fitting observed V-band lightcurves.
    Section 5 notes they use simple bolometric corrections and compare photosphere velocities as a partial check.
  • domain assumption The observed V-band lightcurves assembled from the Open Supernova Catalog have accurate distances and extinctions.
    Section 3 lists distances and foreground extinctions from literature; errors on distances are large for some SNe (e.g., SN2004A at 20.3±3.4 Mpc).

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Cite this review

Pith. "Pith review of Supernova lightCURVE POPulation Synthesis II: Validation against supernovae with an observed progenitor." pith.science (2026). https://pith.science/paper/6CUQOKHW

@misc{pith2026190807762,
  author       = {Pith},
  title        = {Pith review of: Supernova lightCURVE POPulation Synthesis II: Validation against supernovae with an observed progenitor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6CUQOKHW}},
  note         = {Machine review of arXiv:1908.07762}
}
read the original abstract

We use the results of a supernova light-curve population synthesis to predict the range of possible supernova light curves arising from a population of single-star progenitors that lead to type IIP supernovae. We calculate multiple models varying the initial mass, explosion energy, nickel mass and nickel mixing and then compare these to type IIP supernovae with detailed light curve data and pre-explosion imaging progenitor constraints. Where a good fit is obtained to observations, we are able to achieve initial progenitor and nickel mass estimates from the supernova lightcurve that are comparable in precision to those obtained from progenitor imaging. For two of the eleven IIP supernovae considered our fits are poor, indicating that more progenitor models should be included in our synthesis or that our assumptions, regarding factors such as stellar mass loss rates or the rapid final stages of stellar evolution, may need to be revisited in certain cases. Using the results of our analysis we are able to show that most of the type IIP supernovae have an explosion energy of the order of log(E_exp/ergs)=50.52+/-0.10 and that both the amount of nickel in the supernovae and the amount of mixing may have a dependence on initial progenitor mass.

Figures

Figures reproduced from arXiv: 1908.07762 by the authors.

Figure 1
Figure 1. Sample synthetic lightcurves, demonstrating how including the circumstellar material of the red supergiant’s wind changes the lightcurve. The solid lines are for lightcurve models with the circumstellar material included as discussed in the text and the dotted lines assume no material surrounding the progenitor star. The dashed line is where the circumstellar material density has been reduced by a factor of 2. While… view at source ↗
Figure 2
Figure 2. Sample synthetic lightcurves, demonstrating how the explosion parameters change the lightcurve. The upper left panel shows how changing the initial mass of star varies the lightcurve when the stellar structure, explosion energy, nickel mass and mixing are kept constant (1050.5erg s−1 , 10−1.5M and mid mixing). In the other panels one of the explosion parameters are varied while the stellar structure and other parame… view at source ↗
Figure 1
Figure 1. We find inclusion of this causes brighter phases [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figures from the paper (32 more)
Figure 3
Figure 3. Figure 3: Light curves of observed supernova in V-band absolute magnitude. SN host details and sources of data are given in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]
Figure 4
Figure 4. Figure 4: A comparison of the progenitor initial mass derived from lightcurve fitting to that derived from analysis of progenitor observations. We show cases where the range of permitted values for lightcurve fitting is constrained by the range found by the progenitor fitting of…
Figure 5
Figure 5. Figure 5: A comparison of the progenitor Nickel-56 mass derived from lightcurve fitting to that derived from analysis of progenitor observations, as described in figure 4 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: The explosion energy derived from lightcurve fitting and its dependence on initial mass, with symbols as described in figure 4. 6 8 10 12 14 16 18 20 Fitted Initial Mass / MO • 0.0 0.2 0.4 0.6 0.8 1.0 Nickel Missing length, X A B C Unconstrained 6 8 10 12 14 16 18 20 F…
Figure 7
Figure 7. Figure 7: The nickel mixing length parameter derived from lightcurve fitting and its dependence on initial mass, with symbols as described in figure 4 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: The nickel mass derived from lightcurve fitting and its dependence on fitted initial mass, with symbols as described in figure 4. Lines show a simple linear relation between the logarithms of initial and nickel mass (dotted) and also a model in which the nickel mass is…
Figure 9
Figure 9. Figure 9: SN2003gd Free-Fit, corner plots showing how χ 2 varies over the 5 parameters as well a plot comparing the observed lightcurves to the matching theoretical models [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: SN2004A Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: SN2004et Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: SN2005cs Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: SN2006my Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: SN2008bk Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]
Figure 15
Figure 15. Figure 15: SN2009md Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]
Figure 16
Figure 16. Figure 16: SN2012A Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p025_16.png]
Figure 17
Figure 17. Figure 17: SN2012aw Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p026_17.png]
Figure 18
Figure 18. Figure 18: SN2012ec Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p027_18.png]
Figure 19
Figure 19. Figure 19: SN2013ej Free-Fit, as in [PITH_FULL_IMAGE:figures/full_fig_p028_19.png]
Figure 20
Figure 20. Figure 20: SN2003gd Constrained, corner plots showing how χ 2 varies over the 5 parameters as well a plot comparing the observed lightcurves to the matching theoretical models [PITH_FULL_IMAGE:figures/full_fig_p030_20.png]
Figure 21
Figure 21. Figure 21: SN2004A Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p031_21.png]
Figure 22
Figure 22. Figure 22: SN2004et Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p032_22.png]
Figure 23
Figure 23. Figure 23: SN2005cs Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p033_23.png]
Figure 24
Figure 24. Figure 24: SN2006my Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p034_24.png]
Figure 25
Figure 25. Figure 25: SN2008bk Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p035_25.png]
Figure 26
Figure 26. Figure 26: SN2009md Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p036_26.png]
Figure 27
Figure 27. Figure 27: SN2012A Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p037_27.png]
Figure 28
Figure 28. Figure 28: SN2012aw Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p038_28.png]
Figure 29
Figure 29. Figure 29: SN2012ec Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p039_29.png]
Figure 30
Figure 30. Figure 30: SN2013ej Constrained, as in [PITH_FULL_IMAGE:figures/full_fig_p040_30.png]
Figure 31
Figure 31. Figure 31: An initially 15.6M stellar model evolved with MESA v10398. The models are taken at the beginning of car￾bon burning, the end of core carbon burning and the final model output before core-collapse. The BPASS models we use are taken after the point of carbon burning com…
Figure 32
Figure 32. Figure 32: Model lightcurves in the V-band for stars with initial masses of 21M and above. Each panel now only shows one stellar initial mass, while the different lightcurves have varying values of β the wind acceleration parameter. Initial mass=21MO • 0 50 100 150 200 Time / da…
Figure 33
Figure 33. Figure 33: As in [PITH_FULL_IMAGE:figures/full_fig_p043_33.png]
Figure 34
Figure 34. Figure 34: As in [PITH_FULL_IMAGE:figures/full_fig_p044_34.png]

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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 14, 2026 · model on record in the stance chip above.