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REVIEW 4 major objections 6 minor 89 references

Gas accretion at high redshift: cold flows all the way

T0 review · 4 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper argues that more than 75% of star-forming gas in massive high-redshift galaxies arrives via cold filamentary accretion.

desk verdict The qualitative cold-flow result is robust, but the abstract's '>75%' headline is definition-dependent, and the paper itself shows why. read the letter →

arxiv 2501.19009 v1 pith:DGEP5JLQ submitted 2025-01-31 astro-ph.GA

Stefan Waterval , Carlo Cannarozzo , Andrea V. Macciò This is my paper · ORCID
classification astro-ph.GA
keywords cold-modeaccretioncoldfilamentsgashigh-redshiftgalaxieshydrodynamicalsimulationsstarformationBayesianhierarchicalmodelcriticalhalomass
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 argues that cold filamentary accretion is the dominant gas-supply channel for massive galaxies at $z\approx2$--$4$. In two suites of cosmological hydrodynamical zoom-in simulations, the authors track individual gas particles across snapshots and classify gas as cold if its maximum past temperature stayed below $2.5\times10^5$ K. For haloes of roughly $10^{12}$--$10^{13}$ solar masses, 91\% of the smooth gas crossing into the galaxy at $z=3.6$ and 71\% at $z=2.0$ never heated beyond that threshold, leading the authors to conclude that more than 75\% of gas participating in star formation at high redshift arrives through cold streams even above $10^{12}$ solar masses. The paper then fits a Bayesian hierarchical double-sigmoid model to the cold fraction as a function of halo mass and redshift, finding a nearly constant critical mass near $10^{11.8}$ solar masses up to $z\approx1.3$ and a critical mass that rises as $\log(1+z)^{1.7}$ above that redshift.

What carries the argument

The central diagnostic is the cold fraction $f_{\rm cold}=\sum m_{\rm cold}/\sum m_j$, computed by tracing each smooth gas particle's maximum historical temperature $T_{\rm max}$ across snapshots separated by roughly 200 Myr and classifying particles with $T_{\rm max}<2.5\times10^5$ K as cold. The supporting model is a double-sigmoid function of virial mass and redshift, $f_{\rm cold}(M_{\rm vir},z)=\tau S_1+(1-\tau)S_2$, where $S_1$ and $S_2$ are sigmoids representing the low-redshift and high-redshift critical-mass regimes and $\tau$ is a transition sigmoid with $z_\tau\approx1.23$. Fitted with a Bayesian hierarchical formalism to 246 independent snapshot measurements, it yields $\log M_{\rm shock}\approx11.83$ and $\log M_{\rm stream}\approx10.94+1.69\log(1+z)$. This machinery converts raw particle histories into a continuous prediction of the cold-to-hot transition mass across cosmic time.

What would settle it

Recompute $f_{\rm cold}$ for the same $z=3.6$ galaxies with the final snapshot included in $T_{\rm max}$; if the galaxy cold fraction falls below 50\%, the claim that more than 75\% of star-forming gas arrives cold does not survive. A complementary observational check would be a survey at $z\approx2$--$3$ that measures cold gas inflow rates and shows they cannot supply the observed star-formation rates.

Watch

Extended reading notes

Core claim

Using maximum historical temperature $T_{\rm max}<2.5\times10^5$ K as the definition of cold, and restricting to smooth gas (particles never bound to a satellite) that crossed the galaxy radius $R_{\rm gal}=0.2R_{\rm vir}$ between the last two snapshots, the paper finds cold fractions of 91\% at $z=3.6$ and 71\% at $z=2.0$ for haloes with $M_{\rm vir}\approx10^{12}$--$10^{13}$ solar masses. The cold fraction for gas crossing the virial radius is much lower (around 40\% and 24\%), so most hot gas entering the halo never reaches the galaxy, while the cold filaments penetrate to the centre. Maps of the simulations show a spatial separation: cold streams occupy a small volume fraction, with hot outflowing gas filling the space between filaments and barely interacting with the inflow. The paper presents this segregation, together with the high galaxy cold fractions, as the reason massive high-redshift galaxies can sustain star-formation rates above 100 solar masses per year.

Load-bearing premise

The headline cold fractions assume a particular operational definition---cold means a particle's maximum historical temperature stayed below $2.5\times10^5$ K with the final snapshot excluded for gas crossing $R_{\rm gal}$, smooth means never bound to a satellite, and $R_{\rm gal}=0.2R_{\rm vir}$---and the paper's own tests show that including the final snapshot drops the $z=3.6$ galaxy cold fraction from 91\% to about 60\%.

Editorial extensions

If this is right

  • If the 75\% cold-fraction claim holds, the fuel for star formation in massive high-redshift galaxies is delivered by unshocked cold streams, and the hot halo gas around these systems is a passive by-product rather than the main supply.
  • The spatial segregation of cold inflow and hot outflow implies that stellar and AGN feedback can vent energy into the inter-filament volume without shutting off the cold gas supply, so quenching must operate through a different mechanism in these galaxies.
  • A nearly constant $M_{\rm shock}\approx10^{11.8}$ solar masses up to $z\approx1.3$ means the cold-to-hot transition mass does not follow halo growth at low redshift, while the rising $M_{\rm stream}$ at higher redshift extends cold accretion to progressively more massive haloes.
  • Because the galaxy cold fraction is much higher than the halo cold fraction, measurements of cold gas at the virial radius would systematically understate the cold fraction of the gas that actually forms stars.

Reading between the lines

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

  • The definitional sensitivity shown in Fig. 9 suggests that reporting cold fractions without stating whether the final snapshot is included in $T_{\rm max}$ is incomplete; standardizing a "cold at entry" versus "cold at arrival" distinction would make cross-simulation and observational comparisons meaningful.
  • If the low volume-filling factor of cold streams persists in higher-resolution runs, random sightline surveys through the circumgalactic medium may miss the dominant cold accretion channel, so non-detections of cold gas should not be taken as evidence against cold-mode accretion.
  • A testable extension is to apply the same Bayesian double-sigmoid machinery to $f_{\rm cold}$ measured at $R_{\rm gal}$ instead of $R_{\rm vir}$; the paper focuses on the virial radius for robustness, but its own results imply the galaxy-level relation would show a different, more redshift-sensitive transition mass.
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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 / 6 minor

Summary. The paper uses cosmological zoom-in simulations from the NIHAO and HELLO suites to quantify how much of the gas accreted onto massive high-redshift galaxies arrives via cold, smooth flows. Gas particles are classified by their maximum historical temperature, with cold accretion defined as Tmax < 2.5e5 K, and cold fractions are computed for particles crossing the galaxy radius Rgal = 0.2 Rvir and the virial radius Rvir. The authors report that at z = 3.6 and z = 2.0 roughly 91% and 71% of the smooth gas entering the galaxy is cold, which the abstract summarizes as 'more than 75%' of the gas participating in star formation. They also present a Bayesian hierarchical double-sigmoid model for fcold(Mvir, z) at the halo radius, inferring a roughly constant critical mass log(Mc) ≈ 11.8 up to z ≈ 1.3 and a rising critical mass thereafter. The qualitative conclusion that cold filamentary accretion dominates at high redshift is supported by particle tracking, temperature maps, and radial-velocity maps, and the paper is transparent about several definitional sensitivities.

Significance. If the quantitative claim holds, the paper provides a direct simulation-based confirmation that cold accretion remains the dominant fuel supply for massive (10^12-10^13 Msun) star-forming galaxies at z ~ 2-4, extending earlier cold-flow results to the high-mass end. The paper's strengths include a clearly specified particle-history methodology, explicit comparison of the Tmax and Tgas criteria and of smooth versus total accretion in the appendices, a Bayesian model comparison via the Bayes factor, and a careful comparison with earlier simulation work. The main value is the empirical fcold(Mvir, z) fitting function and the inference of the redshift-dependent critical mass, which can be tested against future simulations and observations.

major comments (4)
  1. [§3.1, Fig. 9, Table 3] The headline claim in the abstract that 'more than 75% of the total gas participating in the star formation process is accreted via this channel' is not robust to the operational definition of cold gas at the galaxy radius. The fiducial definition excludes the final snapshot from Tmax for particles crossing Rgal (§3.1); Fig. 9 shows that including that snapshot lowers the HELLOz3.6 galaxy cold fraction from roughly 90 per cent to roughly 60 per cent, and Table 3 gives only 71 per cent for HELLOz2.0 even under the fiducial definition. If the criterion is that gas should still be cold when it reaches the star-forming region, the abstract's quantitative claim fails. The authors are transparent about this sensitivity, but the abstract and conclusions still present the number without qualification; please either qualify the claim explicitly (e.g., 'under our fiducial definition') or provide a physical argument for why heating after crossing Rgal should be excluded when discussing gas that participates in star formation.
  2. [§7.1.2, Appendix D] The construction of the independent dataset rests on two assumptions that are not quantitatively justified: that after sigmoid detrending the fcold tracks are stationary, and that the chosen lags (k = 3 for HELLO, k = 7 for NIHAO) make successive selected points statistically independent. The HELLO tracks contain only a handful of snapshots, so the autocorrelation confidence intervals are very wide, as the paper itself notes. Because the 246-point independent sample directly drives the Bayesian inference in §7.2, an overestimated effective sample size would make the posterior uncertainties in Table 5 (e.g., z_tau = 1.23 with its credible interval) appear tighter than warranted. Please demonstrate that the inferred hyperparameters and the Mshock/Mstream evolution are insensitive to reasonable changes in the lag choice, or propagate the uncertainty in the decorrelation lag into the final results.
  3. [Abstract, §7.2, Eq. (11)] The abstract states that the model 'predicts' the critical-mass evolution, but the model is fit to the same fcold(Mvir, z) measurements that it describes; it is an empirical summary, not an independent forecast. In addition, the abstract's 'log(Mc) ∝ log(1+z)^1.7' is inconsistent with Eq. (11), where log Mc,2 = 10.94 + 1.69 log(1+z): the factor 1.7 is a coefficient in a linear relation, not a power-law exponent. Please rephrase to describe the result as a fit and correct the functional-form statement in the abstract and §7.2.
  4. [§7, §8, Fig. 9] The Bayesian model is deliberately fitted to fcold at Rvir (halo accretion), as stated at the end of §7, whereas the abstract's '>75%' headline refers to accretion onto the galaxy at Rgal. The two quantities behave very differently: the galaxy cold fraction is highly sensitive to the definition (Fig. 9, Appendix A), while the halo cold fraction is more robust. Presenting the Rvir-based critical-mass model as a 'robust framework' for the gas participating in star formation conflates the two scales; the text should state explicitly that the model constrains the halo-scale accretion mode and that the galaxy-scale cold fraction is the quantity carrying the larger systematic uncertainty.
minor comments (6)
  1. [Abstract] The word 'accreate' should be 'accrete'.
  2. [§4.1] The phrase 'the gas temperature and radial velocity (two left columns)' should refer to the two right columns in Fig. 2.
  3. [Fig. 7 caption] The caption says 'starting with HELLOz3.6 on the right, HELLOz2.0 in the middle, and NIHAO on the right', which is internally contradictory; the intended order is left, middle, right.
  4. [Table 3 header] The header 'accreted onto the the galaxy' contains a duplicated article.
  5. [§8] The term 'viral mass' should be 'virial mass'.
  6. [Table 2] The entry 'In 2.0 67 110 12' at 3Rvir reads implausibly low compared with the surrounding values and the text's description of ~110 Msun/yr at Rvir; please verify the printed value.

Circularity Check

1 steps flagged · score 2.0 of 10

The paper's cold-fraction measurements are direct reads from particle temperature histories and are not circular; the only mild reduction is that the abstract's 'prediction' of the critical-mass evolution log(Mc) ∝ log(1+z)^1.7 restates the fitted hyperparameter slope log Mz,2 = 1.69 of the Bayesian double-sigmoid fit, which the paper itself reports transparently as a fit.

  1. fitted input called prediction [Abstract; §7.1.1 Eqs. 5-8; §7.2 Eqs. 10-11; Table 5]
    "Abstract: "Our model predicts a relatively constant critical mass (Mc) for cold-to-hot transition up to z∼1.3 and an evolving critical mass log(Mc)∝ log(1+z)1.7 at higher redshift." §7.2 Eq. 11: "log Mc,2≃10.94+1.69log(1+z)", with the 1.69 being the fitted hyperparameter log Mz,2 (Table 5)."

    The 'prediction' of the Mc evolution is not an independent forecast: the model (Eq. 5) is fitted to the fcold(Mvir, z) measurements (§7.1.2, 246 independent points), and Mc is defined as the inflection point of the fitted sigmoids (Eq. 6). The claimed exponent 1.7 is exactly the fitted slope xz,2 = 1.69±0.19 of Eq. 8, so 'log(Mc) ∝ log(1+z)^1.7' is a restatement of the fitted hyperparameter, not a prediction against unseen data. Similarly, the 'relatively constant' Mshock restates log Mz,1 = -0.18±0.60, a fitted slope consistent with zero. The circularity is mild because the paper is transparent — it says it 'leverages a Bayesian hierarchical formalism to model the continuous evolution of fcold' — and because the resulting Mc curve is later checked against external data (Daddi et al.

full rationale

The central quantitative content of this paper is measured, not derived from a model. The cold fractions (91% and 71% for galaxy accretion at z=3.6 and z=2.0, and 40%/24% for halo accretion; Table 3) are computed by tracing each accreted smooth gas particle's full temperature history against a fixed Tcutoff = 2.5e5 K (§3.1, Eq. 2). These are direct, definition-stated measurements from the simulations and therefore cannot be circular: no fitted parameter enters the headline claim. The abstract's 'more than 75%' statement is a fair summary of the 91% and 71% sample averages, though it pools two redshifts and is sensitive to the operational choice of excluding the final snapshot from Tmax; Fig. 9 shows that including the final snapshot lowers the HELLOz3.6 galaxy value from ~90% to ~60%. This is a disclosed robustness/sensitivity issue, not circularity — the paper states the definition, shows the sensitivity, and in §7 explicitly redirects the modelling to halo accretion because it is less definition-dependent. The one genuine reduction found is the abstract's use of 'predicts' for the critical-mass evolution: log(Mc,2) = 10.94 + 1.69 log(1+z) is the double-sigmoid fit's own hyperparameter (Table 5, Eq. 11), so the '1.7' exponent is a fit summary rather than an independent forecast. The paper is transparent about this, frames §7 as modelling/describing the evolution, and validates the functional form externally against Dekel & Birnboim (2006), Daddi et al. (2022a), van de Voort et al. (2011a), and Correa et al. (2018a), so the step is statistically forced but openly reported. Self-citations (Waterval et al. 2024 for the HELLO suite) are present but not load-bearing: HELLO's physics is described in §2.1, it shares its code and feedback with the externally published NIHAO suite (Wang et al. 2015), and the paper's numbers are benchmarked against several independent groups. No uniqueness theorem is imported from the authors, and the two-regime (double-sigmoid) ansatz is not smuggled in: it is motivated by the external Dekel & Birnboim (2006) theory and is explicitly tested against a single-sigmoid alternative in Appendix C, with a decisive Bayes factor (ln B ≈ −16) favouring the double-sigmoid model. Overall, the derivation chain — particle histories → fcold measurements → Bayesian fit → Mc(z) law → external comparison — is self-contained at the measurement stage, with only the 'prediction' language overstating what is a transparent fit output.

Assumptions & free parameters 12 free parameters · 5 assumptions · 0 invented entities

The paper's quantitative model rests on a set of fitted hyperparameters (11 free parameters plus a hand-set kappa_tau) and on several definitional choices (Tmax threshold, smooth-particle criterion, double-sigmoid form). The measured cold fractions themselves are direct outputs of simulations, but their interpretation as 'gas participating in star formation' assumes the subgrid physics and the temperature cutoffs are meaningful.

free parameters (12)
  • log M0,1 = 11.83 (+0.06, -0.09)
    Normalisation of the low-redshift critical mass Mshock in Eq. 8; fitted to the simulation snapshots.
  • log Mz,1 = -0.18 (+0.60, -0.36)
    Redshift slope of Mshock in Eq. 8; fitted.
  • log M0,2 = 10.94 (+0.11, -0.12)
    Normalisation of the high-redshift critical mass Mstream in Eq. 8; fitted.
  • log Mz,2 = 1.69 (+0.19, -0.18)
    Redshift slope of Mstream; this is the 1.7-ish exponent quoted in the abstract; fitted.
  • kappa0,1 = -3.60 (+0.66, -0.67)
    Steepness normalisation of the low-z sigmoid; fitted.
  • kappaz,1 = 2.40 (+3.00, -4.20)
    Redshift slope of steepness for S1; fitted.
  • kappa0,2 = -2.65 (+0.20, -0.19)
    Steepness normalisation of the high-z sigmoid; fitted.
  • kappaz,2 = 1.50 (+0.23, -0.25)
    Redshift slope of steepness for S2; fitted.
  • z_tau = 1.23 (+0.38, -0.29)
    Transition redshift between Mshock and Mstream regimes; fitted.
  • sigma0 = 0.08 (+0.01, -0.01)
    Intrinsic scatter normalisation at z=0; fitted.
  • sigmaz = -0.04 (+0.02, -0.02)
    Redshift slope of intrinsic scatter; fitted.
  • kappa_tau = -10 (fixed by hand)
    Steepness of the transition sigmoid tau; set empirically, not sampled.
assumptions (5)
  • domain assumption The GASOLINE2 subgrid model (ESF, SN blast waves, AGN Bondi accretion) accurately captures the thermal history of gas particles relevant for accretion mode classification.
    Section 2.1; if feedback is mis-modeled, the cold/hot balance could be systematically wrong, as the paper itself notes when comparing with Correa et al. (2018a).
  • domain assumption Tmax < 2.5e5 K is a valid discriminator between cold and hot accretion.
    Section 3; adopted from Kereš et al. (2005); the paper shows results depend on this choice.
  • ad hoc to paper The double-sigmoid functional form (Eq. 5) captures the true two-regime evolution of the critical mass.
    Section 7.1.1; motivated by Dekel & Birnboim (2006), but the specific shape is chosen by the authors and not derived.
  • ad hoc to paper The autocorrelation analysis assumes stationarity after sigmoid detrending and that lags k=7 (NIHAO) and k=3 (HELLO) yield statistically independent data points.
    Appendix D; the validity of this independence assumption determines the effective sample size of 246 points.
  • domain assumption Smooth accretion excludes any particle ever bound to a halo other than the main one.
    Section 3.1; this operational definition affects fcold as shown in Appendix A.

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Cite this review

Pith. "Pith review of Gas accretion at high redshift: cold flows all the way." pith.science (2026). https://pith.science/paper/DGEP5JLQ

@misc{pith2026250119009,
  author       = {Pith},
  title        = {Pith review of: Gas accretion at high redshift: cold flows all the way},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DGEP5JLQ}},
  note         = {Machine review of arXiv:2501.19009}
}
read the original abstract

We study in detail how massive galaxies accrete gas through cosmic time using cosmological hydrodynamical simulations from the High-z Evolution of Large and Luminous Objects (HELLO) and the Numerical Investigation of a Hundred Astrophysical Objects (NIHAO) projects. We find that accretion through cold filaments at high redshift (z ~ 2-4) is a key factor in maintaining the high star formation rates (> 100 Msun/yr) observed in these galaxies, and that more than 75% of the total gas participating in the star formation process is accreted via this channel at high z even in haloes well above 10^12 Msun. The low volume occupancy of the filaments allows plenty of space for massive gas outflows generated by the vigorous star formation and AGN activity, with the cold incoming gas and the hot outflowing gas barely interacting. We present a model based on a Bayesian hierarchical formalism that accurately describes the evolution of the cold fraction accretion with redshift and halo mass. Our model predicts a relatively constant critical mass (Mc) for the cold-to-hot transition up to z ~ 1.3 and an evolving critical mass log(Mc) proportional to log(1+z)^1.7 at higher redshift. Overall, our findings provide deeper insight into the cosmic evolution of gas accretion modes and offer a robust framework for understanding how cold accretion contributes to galaxy growth across different epochs.

Figures

Figures reproduced from arXiv: 2501.19009 by the authors.

Figure 1
Figure 1. Mass-weighted temperature average of the particles accreted onto Rvir in the hot mode (red) and cold mode (blue) calculated for each galaxy at each snapshot. The left (right) panel shows the results for HELLOz3.6 (HELLOz2.0) galaxies. The horizontal dashed line indicates Tcutoff and the x’s in the hot tracks mark the two last snapshots. 4 VISUAL INSPECTION In this section, we begin with a qualitative visual inspecti… view at source ↗
Figure 2
Figure 2. Large-scale maps of the distribution of DM, gas, gas temperature and gas radial velocity for three example galaxies, one from each sample (HELLOz3.6, HELLOz2.0, and NIHAO, from top to bottom). The first column is an RGB image of the DM where the hue is associated with the velocity dispersion and the brightness to the mass surface density. The second column shows the gas surface density. The third and fourth columns … view at source ↗
Figure 3
Figure 3. Temperature-density diagrams of three example galaxies (same as [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Smooth inflowing radial mass accretion rates of DM (scaled by Ωb/Ωm) and gas for HELLOz3.6 (left), HELLOz2.0 (middle), and NIHAO (right) galaxies. The continuous curves represent the median rates from all galaxies within the respective sample, while the shaded regions …
Figure 5
Figure 5. Figure 5: Specific inflowing smooth gas accretion rates onto the halo for our galaxies (squares, HELLOz3.6; circles, HELLOz2.0; triangles, NIHAO) calculated within a shell encompassing 0.95– 1 Rvir. We compare our galaxies to previous results from the litera￾ture (Ocvirk et al. …
Figure 6
Figure 6. Figure 6: Smooth gas mass accretion rates for HELLOz3.6 (left), HELLOz2.0 (middle), and NIHAO (right) separated in three components (top panels): inflowing gas (green), outflowing gas (purple) and net (in − out; black). Shaded regions encompass the 16th and 84th percentiles. The…
Figure 7
Figure 7. Figure 7: Tmax distribution for particles that crossed Rgal (top) and Rvir (bottom) in the last snapshot. Each histogram represents the combination of the Tmax distributions across all galaxies in their respective samples, weighted by the particle mass. Tmax is defined as the hi…
Figure 8
Figure 8. Figure 8: Fraction fcold of gas accreted onto the galaxy (left) and the halo (right) whose temperature never exceeded Tcutoff, plotted against the virial mass of the galaxy. Each marker represents fcold of one galaxy, colour-coded by the parent sample (HELLOz3.6, blue squares; H…
Figure 9
Figure 9. Figure 9: Same as the left panel of [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Cold fraction evolutionary tracks from particles crossing the galaxy (top) and the halo (bottom) for HELLOz3.6 (left), HELLOz2.0 (middle), and NIHAO (right) colour-coded by redshift. Additionally, each panel contains the other two samples in grey. Dots represent all s…
Figure 11
Figure 11. Figure 11: Evolution of fcold as a function of Mvirin six different redshift bins. Each panel contains the model evaluated at the redshift bin’s midpoint, displayed as a dashed line and the 1σ uncertainty region, delimited by the 16 per cent and the 84 per cent of the distributi…
Figure 12
Figure 12. Figure 12: Visual representation of the continuous evolution of our fcold−Mvir relation for log(Mvir/M⊙) ∈ [10.5,13.0] and z ∈ [0,5]. the temperature criterion (Tmaxor Tgas; first versus second column), does not appear to significantly alter the overall distribution of fcold val…
Figure 13
Figure 13. Figure 13: Evolution of fcold as a function of Mvir from our model at fixed z = {0,1,2,3,4} compared to previous works. Each panel contains the model evaluated at one redshift (continuous, blue) compared to results from Ocvirk et al. (2008) (dashed, green), van de Voort et al. (…
Figure 14
Figure 14. Figure 14: Evolution of Mshock and Mstream inferred from our simu￾lations compared with theoretical predictions (Dekel & Birnboim 2006), simulations (Ocvirk et al. 2008), and recent observations (Daddi et al. 2022a). The dashed line represents an extrapola￾tion of Mshock (Mstrea…

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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 9, 2026 · model on record in the stance chip above.