From Stellar Halos to Intracluster Light: the physics of the Intra-Halo Stellar Component in cosmological hydrodynamical simulations

Charlotte Welker; Chris Power; Christophe Pichon; Claudia del P. Lagos; Pascal J. Elahi; Rodrigo Ca\~nas; Yohan Dubois

REVIEW 2 major objections 4 minor 1 cited by

From Stellar Halos to Intracluster Light: the physics of the Intra-Halo Stellar Component in cosmological hydrodynamical simulations

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Using an adaptive phase-space definition, the diffuse stellar component can be measured consistently from Milky Way-mass halos to galaxy clusters; its mass fraction grows with total stellar mass and, below group masses, tracks the central…

desk verdict Adaptive phase-space definition of diffuse stellar material is a real new tool; the paper's quantitative scatter claims need a shot-noise subtraction before they can stand. read the letter →

arxiv 1908.02945 v1 pith:2TV2TVDB submitted 2019-08-08 astro-ph.GA

Rodrigo Cañas , Claudia del P. Lagos , Pascal J. Elahi , Chris Power , Charlotte Welker , Yohan Dubois , Christophe Pichon This is my paper · ORCID

classification astro-ph.GA

keywords intra-halostellarcomponenthalointraclusterlightcosmologicalhydrodynamicalsimulationsphase-spacegalaxyfinderkinematicsmergersformation

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 introduces and applies an adaptive, shape-independent way to identify the diffuse stellar component in cosmological hydrodynamical simulations: the collection of stars too kinematically hot and phase-space distant to belong to any galaxy. Using this Intra-Halo Stellar Component (IHSC) definition in the Horizon-AGN simulation, it claims that the IHSC mass fraction grows with total stellar mass on average, while its scatter shrinks from roughly two orders of magnitude at Milky Way masses to about 0.3 dex at group masses. The main physical driver of that scatter below $\sim10^{12}\,M_\odot$ is the central galaxy's kinematic morphology: rotation-supported galaxies have IHSC fractions below 0.1%, whereas dispersion-supported systems reach about 5%. If correct, this gives observers a measurable proxy, $V/\sigma$, for the assembly history encoded in diffuse starlight, and unifies the study of stellar halos and intracluster light under one definition.

What carries the argument

The central object is an adaptive phase-space Friends-of-Friends search that identifies galaxies as six-dimensional phase-space overdensities. The IHSC is defined as all stellar particles not linked to any galaxy in that search, meaning kinematically hot, diffuse background stars and tidal debris. The user-set parameter $f_{l_x,6D}=0.4$ sets the phase-space density threshold separating galaxy from IHSC, and the paper shows that the shapes and slopes of the resulting mass relations are robust to this choice, with only the normalization shifting. The observational proxy that carries the physical argument is the central galaxy's $V/\sigma$, the ratio of rotational velocity to velocity dispersion, because it encodes merger history in a single measurable number.

What would settle it

Measure $V/\sigma$ and the diffuse stellar fraction for a sample of $M_{*,\mathrm{tot}}\sim10^{11}\,M_\odot$ galaxies: the paper predicts that rotation-supported galaxies stay below $f_{M_*,\mathrm{IHSC}}\sim0.1\%$, so finding many high-$V/\sigma$ systems with diffuse fractions above 1% would falsify the claimed anti-correlation.

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Extended reading notes

Core claim

The central discovery is that the same adaptive phase-space criterion identifies the diffuse stellar component across the full mass range, and that the resulting $f_{M_*,\mathrm{IHSC}}$ versus $M_{*,\mathrm{tot}}$ relation has a mass-dependent scatter with two distinct regimes. For $M_{*,\mathrm{tot}}<10^{12}\,M_\odot$, the diffuse fraction is strongly anti-correlated with the central galaxy's stellar rotation-to-dispersion ratio $V/\sigma$; high-$V/\sigma$ galaxies sit at $f_{M_*,\mathrm{IHSC}}<0.1\%$, while low-$V/\sigma$ galaxies reach about 5%, and this correlation is the strongest among all halo and galaxy properties examined. At $M_{*,\mathrm{tot}}>10^{12}\,M_\odot$, all centrals are dispersion-supported, and the diffuse fraction instead tracks the dynamical state of the system, quantified by the mass ratio of the largest satellite to the central galaxy; cluster-scale systems reach 10 to 20 percent by $z\sim1$ and then evolve weakly, though the paper cautions that the cluster sample is small. The paper interprets the low-mass regime as reflecting the diversity of accretion histories: quiescent, rotation-supported galaxies simply do not have much stripped stellar material, while dispersion-supported galaxies have experienced active merger histories. A further robustness claim is that the power-law slopes relating IHSC mass, central-galaxy mass, and satellite stellar mass are essentially independent of the user-set phase-space density threshold; only the normalization changes.

Load-bearing premise

The load-bearing premise is that the chosen phase-space density threshold identifies the same physical component that observers measure as stellar halos and intracluster light, because the threshold is calibrated to match those observations rather than derived independently.

Editorial extensions

If this is right

At a fixed total stellar mass below $10^{12}\,M_\odot$, measuring the central galaxy's $V/\sigma$ predicts the diffuse stellar fraction: high rotation means under 0.1 percent, low rotation about 5 percent.
The large observed scatter in stellar-halo mass fractions of Milky Way-like galaxies, about 2 dex, is not pure noise but encodes distinct accretion histories, and should correlate with kinematic morphology once dispersion-supported galaxies are included.
At group and cluster scales the diffuse component reaches 10 to 20 percent of all stars by $z\sim1$ and then stays nearly constant, so the intracluster-light fraction should be a weak function of cluster mass at late times; the paper flags this as tentative because of the small simulated cluster sample.
Because the slope between IHSC mass and satellite stellar mass is about unity and is independent of the phase-space threshold, observational measurements made with different surface-brightness limits should recover the same slope and differ mainly in normalization.

Reading between the lines

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

If the $V/\sigma$ correlation survives in observational samples, surveys that already measure galaxy kinematics could statistically infer halo mass fractions without directly detecting the faint diffuse light.
The same phase-space definition could be applied to other cosmological hydrodynamical simulations; a testable prediction is that the near-unity slope of the IHSC mass versus satellite mass relation is robust across feedback implementations, while the normalization carries information about the subgrid physics.
The paper's tentative flat evolution at cluster scales suggests a concrete forecast: with dozens of simulated clusters, the intracluster-light fraction should remain within 10 to 20 percent with no monotonic redshift trend, whereas strong evolution would indicate missing physics or a resolution effect.
Current Milky Way-mass observational samples are dominated by rotationally supported galaxies, so the apparent tension with the simulated relation may disappear once ellipticals with similar stellar masses are measured and found to have systematically higher diffuse fractions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The useful thing here is the method. Defining the Intra-Halo Stellar Component as the kinematically hot material that 6DFOF phase-space linking leaves unassigned to galaxies is genuinely adaptive and shape-independent, and the paper applies it across roughly three decades in halo mass in one simulation. Two results earn credit: the M_IHSC-M_sats power-law slope is nearly independent of the linking parameter flx,6D, and V/sigma of the central galaxy is the strongest scatter driver of the IHSC fraction at fixed stellar mass below 10^12 Msun. The paper is also careful in several respects—it flags resolution with particle-number lines, tests flx,6D from 0.1 to 0.8, compares against spherical apertures, and follows individual merger histories. The cluster results are explicitly tentative, which is honest.

The soft spots are two. First, the reader's circularity flag is real: flx,6D = 0.4 is adopted because it makes the predicted f-M* relation match the observed stellar halo and ICL fractions. The text says so plainly in Section 3.1, but the abstract and conclusions still present the resulting normalization as a prediction. It is a calibration. That said, the qualitative mass dependence and the power-law slopes survive changes in flx,6D, so this is a moderate concern, not a fatal one.

Second, the stress-test concern lands harder. The quoted 2 dex scatter at M* ~ 10^11 Msun is probably inflated by particle shot noise. Horizon-AGN stellar particles are ~3e6 Msun, so at f ~ 1e-4 you are working with a handful of particles. The blue lines in Fig. 2 mark 100 and 10 particles, but the paper never subtracts a Poisson floor before attributing the scatter to growth mechanisms in Section 3. The low-f tail and the high-V/sigma branch of Fig. 9 sit exactly where discreteness is order unity. The qualitative V/sigma anti-correlation may survive subtraction, but the headline claim—scatter decreasing from 2 dex to 0.3 dex—is not secure as presented.

This is not a fatal flaw in the method. The parameter-sensitivity tests, the comparison to spherical apertures, and the stability of the mass relations make a convincing case that the phase-space definition is better behaved across mass. The paper deserves peer review, but revision should quantify and subtract the shot-noise floor, present the flx,6D calibration as calibration, and add error bars to fits and sub-sample medians. I'd bring this to reading group, and I'd cite it if I worked on stellar halos or ICL.

Referee Report

2 major / 4 minor

Summary. The paper introduces an adaptive phase-space definition of the diffuse stellar component, which the authors call the Intra-Halo Stellar Component (IHSC), and applies it to the Horizon-AGN cosmological hydrodynamical simulation. The IHSC is defined as stellar particles not linked to galaxies by a 6D friends-of-friends search, so it represents the kinematically hot, diffuse stellar background around galaxies, groups, and clusters. Using this definition, the paper reports the z = 0 f_M*,IHSC-M*_tot relation, characterizing its slope, normalization, and the mass dependence of its scatter; it then studies correlations of the scatter with the number of satellites, the central-to-satellite mass ratio, the central galaxy's V/sigma, and sSFR. The paper also follows individual systems through cosmic time with merger trees, distinguishing quiescent and merger-rich evolutionary paths and discussing the tentative behavior of galaxy clusters. The central quantitative claims are that f_M*,IHSC increases with total stellar mass on average, that the scatter decreases from roughly 2 dex at M*_tot ~ 1e11 Msun to about 0.3 dex at group masses, and that V/sigma of the central galaxy is the strongest predictor of f_M*,IHSC at fixed mass for M*_tot below about 1e12 Msun.

Significance. If the results are robust, the paper provides a useful unifying framework: the same adaptive, shape-independent definition applies to stellar halos, intra-group light, and intracluster light, which is a genuine improvement over fixed or variable spherical apertures. The stability of the M_IHSC-M_sats power-law slopes across flx,6D = 0.1-0.8 is a credible and falsifiable prediction, and the V/sigma anti-correlation at Milky-Way and group masses gives observers a concrete kinematic proxy for the diffuse stellar mass fraction. The authors are also transparent about the parameter choice that sets the normalization and about the limited cluster sample. The main significance risk is quantitative: part of the reported scatter and of the low-f_M*,IHSC population rests on systems with very few IHSC particles, and the paper does not quantify this counting-noise floor before presenting its headline numbers.

major comments (2)

[Section 3, Fig. 2; Section 4.3, Fig. 9] The paper quotes a scatter of about 2 dex at M*_tot around 1e11 Msun and uses the low-f_M*,IHSC tail (f < 0.1%) to support the V/sigma anti-correlation, but at these masses a large part of that range contains only tens of IHSC particles. With the stated stellar particle mass of ~3e6 Msun, f_M*,IHSC = 1e-4 at M*_tot = 1e11 Msun corresponds to about 3 particles, and f_M*,IHSC = 1e-3 at M*_tot = 3e10 Msun corresponds to about 10 particles. The blue dashed and dot-dashed lines in Fig. 2 mark the N_IHSC = 100 and N_IHSC = 10 boundaries, but these boundaries are not applied as cuts and no Poisson or jackknife uncertainty in f_M*,IHSC is propagated into the scatter or into the sub-sample medians in Figs. 7-10. The text identifies resolution effects only at M*_tot < 1e10 Msun, yet the same discreteness affects low-f systems at higher masses. Please add a quantitative noise-floor analysis: for example, compute Monte Carlo uncertainties from the IHSC particle counts, show how the scatter-versus-mass trend and the Fig. 9 medians change when N_IHSC >= 100 or N_IHSC >= 1000 cuts are imposed, and verify explicitly that the 2-dex-to-0.3-dex claim and the V/sigma anti-correlation survive such cuts.
[Section 3.1 and Section 3.2] The parameter flx,6D = 0.4 is adopted in Section 3.1 specifically because it makes the simulated f_M*,IHSC-M* relation agree with the observed stellar-halo and ICL fractions of Merritt et al. (2016), Harmsen et al. (2017), and Morishita et al. (2017). Given that, the statement in Section 3.2 that the method 'predicts' IHSC mass fractions in agreement with observations is circular for the normalization: those anchor points are matched by construction. The shape of the relation, the slope of M_IHSC-M_sats in Fig. 4, and the V/sigma-dependent ordering in Fig. 9 are genuine predictions, but the absolute normalization is not. Please state this distinction explicitly and avoid phrasing that presents the agreement at the calibration points as an independent success.

minor comments (4)

[Fig. 9 caption] The caption contains two typographical errors: 'as labellled' should read 'as labelled', and 'the medians of each sub-sample do nor overlap' should read 'do not overlap'.
[Section 4.2, Fig. 8 caption] The word 'fracton' in the caption text should be 'fraction'.
[Section 5.1.1] The sentence 'At z = 2.12 these systems have total stellar masses between M*_tot~1e10 and 1e10.5 and a f_M*,IHSC ~0.03' is slightly ambiguous; clarify that the ~0.03 value refers to the same redshift.
[Section 4.3] The discussion of the 2D versus 3D V/sigma difference is noted in the text, but it would help the observational reader to state whether the reported V/sigma values are the 3D values and to indicate the expected size of the projection-induced scatter.

Circularity Check

1 steps flagged · score 6.0 of 10

IHSC mass-fraction normalization is calibrated to the same observations it is later said to 'predict'; the mass-dependence shape and V/sigma trends are independent.

fitted input called prediction [Section 3.1, parameter choice after Fig. 3; invoked again in Section 3.2]
"In this study we adopt flx,6D = 0.4, because it predicts a fM∗,IHSC− M∗ relation that is in better agreement with the estimated stellar halo mass fractions for Milky Way-like galaxies from Merritt et al. (2016) and Harmsen et al. (2017), and recent ICL mass estimations of Morishita et al. (2017)."

The only user-set parameter of the phase-space definition, flx,6D, sets the density threshold that separates galaxies from the IHSC (Eq. 7). The paper explicitly chooses flx,6D = 0.4 so that the simulated f_M*,IHSC-M* relation matches the observed stellar-halo and ICL fractions. Therefore the later statement in Section 3.2 that 'Only our method is capable of predicting IHSC mass fractions that are in agreement with observations' is not an independent prediction: the normalization agreement is imposed by the choice of flx,6D. The qualitative shape of the relation and the V/sigma correlation are not reduced in this way, but the quantitative 'agreement with observations' claim is circular by construction.

full rationale

The identified circular step is real but partial. Equation (7) makes flx,6D the single free linking-length parameter controlling how much stellar material is assigned to galaxies versus the IHSC, and Section 3.1 states that the adopted value 0.4 was selected precisely because it makes f_M*,IHSC match the observed stellar-halo fractions of Merritt et al. (2016) and Harmsen et al. (2017) and the ICL fractions of Morishita et al. (2017). Consequently, Section 3.2's claim that the method 'is capable of predicting IHSC mass fractions that are in agreement with observations' presents a calibrated normalization as a prediction. This is the classic fitted-input-called-prediction pattern. However, I do not treat the mass-dependence itself as circular: Fig. 3 shows that the increasing-then-flattening shape and the decreasing scatter survive for flx,6D values from 0.1 to 0.8, and the slopes of the M_IHSC-M*_ctrl and M_IHSC-M*_sats relations vary by less than 5% (Fig. 4). The V/sigma anti-correlation in Section 4.3 is also independent of the calibration, because V/sigma is measured from central-galaxy stellar particles and is not used to set flx,6D. The paper's self-citations to Canas et al. (2019) and Elahi et al. (2019) describe the structure-finder code and are not invoked as a uniqueness theorem or as the load-bearing physical argument. The explicit caveat about the small number of clusters in Horizon-AGN is an honest limitation, not circularity. The shot-noise and particle-count concerns raised by the skeptic are correctness and robustness risks rather than constructional circularity, so they do not increase this score. Overall, one central 'prediction' reduces by construction to the calibration of the IHSC threshold, while the main physical interpretation retains substantial independent content: score 6.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central quantitative claim (f_M*,IHSC normalization and its agreement with observations) rests on one free parameter, flx,6D, calibrated to the very observational points the paper later says it predicts. The qualitative shape of the relation is robust to this parameter, but the zero-point is not. Additional domain assumptions are the realism of Horizon-AGN's feedback physics and the reliability of the observational anchors. No new physical entities are introduced.

free parameters (2)

flx,6D (velocity-space linking length scaling for 6DFOF field search) = 0.4 (adopted)
User-defined phase-space density threshold separating galaxies from the IHSC. Chosen to match observed stellar halo and ICL mass fractions from Merritt et al. (2016), Harmsen et al. (2017), and Morishita et al. (2017). Directly sets the normalization of f_M*,IHSC.
b (3DFOF linking length parameter) = 0.2
Standard friends-of-friends value; sets the outer boundary of systems (3DFOF objects). Affects which particles are included in the system and hence in the IHSC estimate.

assumptions (4)

ad hoc to paper The IHSC can be defined operationally as stellar particles not linked to galaxies by a fixed phase-space density threshold; this boundary corresponds to the physically diffuse, kinematically hot component.
Section 2.2.3. The definition depends on the arbitrary threshold flx,6D; no independent physical criterion fixes the galaxy/IHSC boundary.
domain assumption Horizon-AGN's subgrid prescriptions for star formation, supernovae, and AGN feedback produce a stellar distribution realistic enough for IHSC mass fractions and their scatter to be meaningful.
The paper uses Horizon-AGN outputs without independent validation of the diffuse stellar component; prior work validated galaxy properties broadly.
domain assumption The observational estimates of stellar halo and ICL mass fractions used for calibration (Merritt et al. 2016, Harmsen et al. 2017, Morishita et al. 2017) are reliable truth anchors.
Section 3.1. These measurements themselves carry definitional and systematic uncertainties, but they are used to set flx,6D.
domain assumption A constant mass-to-light ratio makes f_M*,IHSC comparable to observed light fractions.
Footnote 1. Comparisons to ICL and stellar-halo surface brightness observations assume this.

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Cite this review

Pith. "Pith review of From Stellar Halos to Intracluster Light: the physics of the Intra-Halo Stellar Component in cosmological hydrodynamical simulations." pith.science (2026). https://pith.science/paper/2TV2TVDB

@misc{pith2026190802945,
  author       = {Pith},
  title        = {Pith review of: From Stellar Halos to Intracluster Light: the physics of the Intra-Halo Stellar Component in cosmological hydrodynamical simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2TV2TVDB}},
  note         = {Machine review of arXiv:1908.02945}
}

abstract

We study the Intra-Halo Stellar Component (IHSC) of Milky Way-mass systems up to galaxy clusters in the Horizon-AGN cosmological hydrodynamical simulation. We identify the IHSC using an improved phase-space galaxy finder algorithm which provides an adaptive, physically motivated and shape-independent definition of this stellar component, that can be applied to halos of arbitrary masses. We explore the IHSC mass fraction-total halo's stellar mass, $f_{M*,IHSC}-M*$, relation and the physical drivers of its scatter. We find that on average the $f_{M*,IHSC}$ increases with $M_{*,tot}$, with the scatter decreasing strongly with mass from 2 dex at $M_{*,tot}\sim10^{11}M_\odot$ to 0.3 dex at group masses. At high masses, $M_{*,tot}>10^{11.5}M_\odot$, $f_{M*,IHSC}$ increases with the number of substructures, and with the mass ratio between the central galaxy and largest satellite, at fixed $M_{*,tot}$. From mid-size groups and systems below $M_{*,tot}<10^{12}M_\odot$, we find that the central galaxy's stellar rotation-to-dispersion velocity ratio, V/{\sigma}, displays the strongest (anti)-correlation with $f_{M*,IHSC}$ at fixed $M_{*,tot}$ of all the galaxy and halo properties explored, transitioning from $f_{M*,IHSC}$<0.1% for high V/{\sigma}, to $f_{M*,IHSC}\sim5$% for low V/{\sigma} galaxies. By studying the $f_{M*,IHSC}$ temporal evolution, we find that, in the former, mergers not always take place, but if they did, they happened early (z>1), while the high $f_{M*,IHSC}$ population displays a much more active merger history. In the case of massive groups and galaxy clusters, $M_{*,tot}>10^{12}M_\odot$, a fraction $f_{M*,IHSC}\sim$10-20% is reached at $z\sim1$ and then they evolve across lines of constant $f_{M*,IHSC}$ modulo some small perturbations. Because of the limited simulation's volume, the latter is only tentative and requires a larger sample of simulated galaxy clusters to confirm.

Figures

Figures reproduced from arXiv: 1908.02945 by the authors.

**Figure 1.** Projected stellar mass density of all the stellar particles inside 3DFOF objects (first and third row), and its IHSC as identified using velociraptor (second and fourth row). 3DFOF total stellar mass, M∗,tot, central galaxy stellar mass, M∗,ctrl, and IHSC mass fraction fM∗,IHSC = M∗,IHSC/M∗,tot are shown for each object. Circles show 30 and 100 kpc apertures commonly used in the literature to separate the central ga… view at source ↗

**Figure 2.** Mass fraction in the Intra-Halo Stellar Component (IHSC), fM∗,IHSC , as identified by velociraptor, as a function of total stellar mass M∗,tot at z = 0 for all systems in the HorizonAGN simulation, shown as black dots. Blue dashed and dotdashed lines delimit regions where the IHSC at a given M∗,tot is composed by ≤ 100 and ≤ 10 particles, respectively. See text for more details. large dispersion observed at these … view at source ↗

**Figure 3.** Mass fraction in the IHSC fM∗,IHSC (top left), and mass content in the IHSC and central as estimated using flx,6D = {0.1, 0.2, 0.4, 0.6, 0.8}, coloured as labelled. Solid lines represent the median fM∗,IHSC for each M∗,tot bin and shaded regions delimit the 16th and 84th percentile of the distribution in that bin; vertical dot-dashed line indicate the M∗,tot where measurements are considered not to be affected by r… view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Stellar mass content of the IHSC as a function of the central galaxy stellar mass (left panel), and the total stellar mass in satellite galaxies (right panel) as estimated using flx,6D = {0.1, 0.2, 0.4, 0.6, 0.8}, as labelled. Solid lines represent the median fM∗,IHSC …

**Figure 5.** Figure 5: IHSC mass as a function of the total stellar mass in satellites with stellar masses > 108 , 109 , and 1010 M , for flx,6D = 0.4. Solid lines shows the median in each mass bin, and shaded regions delimit the 16th and 84th percentiles. Similarly to [PITH_FULL_IMAGE:figu…

**Figure 7.** Figure 7: fM∗,IHSC − M∗ relation separating it into sub-samples of systems with different total number of satellites, Nsats. Solid lines show the median of the distribution, and shaded regions delimit the 1σ and 2σ, respectively. Colours show the sub-samples using different Nsat…

**Figure 8.** Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

**Figure 11.** Figure 11: Evolution of Milky Way-mass systems with low fM∗,IHSC . Top left panel. Evolutionary paths of a sample of galaxies (thin magenta lines) from z = 2.12 (square symbols) to z = 0 (triangle symbols). In blue is highlighted the path of object A, with its location at each s…

**Figure 12.** Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]

**Figure 13.** Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]

**Figure 14.** Figure 14: Temporal evolution of the fM∗,IHSC − M∗ relation from z = 2.12 to z = 0.02, as labelled. Gray points are the measurements for individual systems; solid lines indicate the median fM∗,IHSC per mass bin, and dashed line indicates the median at z = 0 for reference. Diagon…

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write newline

" 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.

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