Connecting Planetary Composition with Formation: a New Paradigm Emerges

Alex J. Cridland; Julie Inglis; Mathew Alessi; Ralph E. Pudritz

REVIEW 2 major objections 6 minor 300 references

Connecting Planetary Composition with Formation: a New Paradigm Emerges

T0 review · 2 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This review argues that magnetized disk winds, not disk turbulence, drive protoplanetary disk evolution and thereby shape exoplanet compositions, radii, and orbits.

desk verdict An invited review that gives a clear map of the MHD-wind paradigm, but the headline claim outruns the evidence: the paradigm rests on unmeasured net poloidal flux, and the population-synthesis predictions carry over the authors' own input assumptions. read the letter →

arxiv 2505.22724 v1 pith:UCDJXOHQ submitted 2025-05-28 astro-ph.EP

Ralph E. Pudritz , Alex J. Cridland , Julie Inglis , Mathew Alessi This is my paper

classification astro-ph.EP

keywords planetformationMHDdiskwindsprotoplanetarydisksexoplanetcompositionplanetarymigrationradiusvalleyC/Oratiopopulationsynthesis

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 review argues that a new paradigm for planet formation is emerging in which magnetohydrodynamic (MHD) disk winds, not disk turbulence, are the main transporters of angular momentum in protoplanetary disks, with consequences for accretion, ring and gap formation, disk chemistry, planet migration, and planet composition. The authors assemble exoplanet demographics, ALMA observations of disk structure, kinematics, and layered outflows, JWST disk and atmosphere spectra, plus MHD simulations and population synthesis, to make the case. If the paradigm holds, disk gas flows are laminar and advective rather than viscous and diffusive, and forming planets migrate with wind-driven flows while being captured in traps at ice lines, the dead-zone edge, and the heat transition. The result would be that a planet's atmospheric composition, radius, and orbit become readable records of where it assembled in the disk, testable with observations now underway.

What carries the argument

The argument is carried by two coupled pieces. The first is the vertically averaged disk angular momentum equation (equation 1), whose two source terms are a radial turbulent/Maxwell stress and a vertical wind stress $\sigma_{z,\phi} = B_z B_\phi$; because the vertical term has no radial derivative it drives a laminar advective inflow at speed $v_m = B_\phi B_z/(3\pi\Sigma\Omega)$ rather than a diffusive spreading, and the wind lever arm $\lambda = (r_A/r_0)^2$ sets the mass-loss efficiency $\dot{M}_a/\dot{M}_w = 2(\lambda-1)$ (equation 3). The second is the torque balance for an embedded planet, $\Gamma = \Gamma_{\mathrm{Lindblad}} + \Gamma_{\mathrm{corotation}}$: in wind-dominated disks the corotation torque is replenished on the advective time scale rather than the viscous one, so zero-net-torque 'planet traps' form at the heat transition, the dead-zone edge, and ice lines, and embryos migrate with their traps at the slow advective speed while accreting the local gas and solids. These two pieces convert the wind assumption into concrete predictions for planetary composition, radius, and orbital architecture.

What would settle it

A decisive test is a direct measurement of the large-scale magnetic field threading a protoplanetary disk, for example through Zeeman splitting or Faraday rotation of disk-tracing emission lines, combined with ALMA kinematic limits on turbulent broadening: the paradigm requires a persistent, disk-wide net field and turbulence far too weak to drive the observed accretion ($\alpha \ll 10^{-2}$). Finding no such field, or detecting turbulent broadening at the level of the accretion rate, would point back to viscous transport instead. A second, independent check is the radius valley around M dwarfs, where the paper notes photoevaporation models already fail; if the valley's shape there matches photoevaporation rather than the superposed-population explanation, that leg of the argument gives way.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that a new dynamic paradigm for planet formation is emerging in which MHD disk winds, not disk turbulence, play the central role in angular momentum transport, gap and ring formation, disk astrochemistry, and planet formation and migration. The evidence the review assembles includes measured disk turbulence levels an order of magnitude too low to drive the observed accretion rates; non-ideal MHD simulations in which Ohmic and ambipolar diffusion suppress the magnetorotational instability and launch winds that drive a laminar accretion flow; global simulations in which wind-driven concentration of magnetic flux produces long-lived rings and gaps before any planet exists; three-dimensional planet-disk simulations in which wind torques deepen gaps and shift the migration torque; and population synthesis in which wind-driven evolution reproduces the mass-radius diagram, sends ice-rich mini-Neptunes inward from beyond the ice line, and yields a dry-super-Earth/icy-mini-Neptune mass separation with the signature of the observed radius valley. The atmospheric C/O 'main sequence' connects the final composition to the ratio of solid to gas accretion during formation. The review concludes that these processes leave their mark on the radii, atmospheric composition, and orbital characteristics of exoplanet populations, offering the possibility of future observational tests.

Load-bearing premise

The paradigm rests on one unmeasured premise: protoplanetary disks keep a large-scale magnetic field, spread across the disk, strong enough to launch winds that carry off most of the angular momentum over the disk's multi-million-year lifetime, and the review itself notes that everything depends on 'the amount of magnetic flux that threads it' because if that field is eroded by reconnection or the Hall effect, turbulence-driven viscous transport would reclaim the central role.

Editorial extensions

If this is right

Disk evolution becomes laminar and advective: the wind torque drives inward flow at speed $v_m = B_\phi B_z/(3\pi\Sigma\Omega)$ instead of viscous spreading, so disks stay more compact, dust settles and grows faster, and pebbles drift across a wider range of disk radii.
Rings and gaps can form before planets do: wind-driven magnetic flux concentration creates long-lived dust-trapping pressure bumps that may be the first sites of planet formation.
Planet migration is regulated by traps: embryos are captured at zero-torque radii (heat transition, dead-zone edge, ice lines) and move inward on million-year advective timescales, providing a physical remedy for the factor of 30-300 slowdown that early population synthesis required.
Composition becomes a formation record: the atmospheric C/O main sequence links a planet's final C/O to the ratio of solid to gas accretion, and the radius valley is explained by the superposition of dry super-Earths and ice-rich mini-Neptunes that migrated in from beyond the ice line.
The paradigm is observationally addressable: layered outflows detected from disk radii of 50-90 AU connect winds directly to ring structure, and precise JWST phase-curve measurements of tidally deformed ultra-hot Jupiters can test the core masses predicted by core accretion.

Reading between the lines

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

An extension the paper leaves implicit is quantitative: wind-dominated disks are more compact, so the model predicts a higher fraction of planets ending in short-period orbits than viscous-disk models; the observed hot-Jupiter occurrence rate and the inner pile-up of super-Earths are therefore direct statistical tests of the paradigm.
Because the Hall effect transports magnetic flux inward or outward depending on field polarity relative to disk rotation, the same formation model should yield systematically different migration and compositional outcomes for disks of opposite polarity, a polarity test that no current observation yet discriminates.
The trap framework suggests an inversion strategy the paper does not pursue: a single planet's measured C/O and N/O could be mapped back onto model formation tracks to infer its assembly radius and trap type, turning sparse JWST spectra of individual planets into formation diagnostics.
The radius-valley explanation competes directly with photoevaporation, and the paper itself notes that photoevaporation models fail around M stars; a survey resolving the valley's shape at low stellar masses would discriminate between the two mechanisms.

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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

This is a handbook review chapter, not a new result, so judge it as a synthesis. If you want a readable, well-organized account of the wind-driven picture of planet formation, this is a solid entry point: it connects ALMA ring/gap observations, low-turbulence upper limits, and layered outflows to a coherent story about advective accretion, planet traps, and composition. The torque-map summaries and the discussion of how winds change the corotation torque are genuinely useful, even for people who work in the viscous paradigm.

The soft spots are real but not disqualifying. The core claim—that MHD winds, not turbulence, control disk evolution—rests on the assumption that enough net poloidal flux threads the disk through the multi-Myr planet-forming phase. The review does not hide this; it states that disk evolution depends on the threading Bz and that Eq. (4) must be supplemented with flux back-reaction. But no flux-evolution equation is given, and no direct measurement of Bz is cited. Hall-effect transport can push flux inward or outward depending on field polarity, so a realistic spread of cloud-field orientations likely produces some disks that lose their wind-driving flux early. That makes the categorical abstract phrasing ('and not disk turbulence') stronger than the body's own caveats. This matters, but it is a weakness in the framing of a review, not a fatal internal contradiction.

The population-synthesis section also deserves a flag: the 'C/O main sequence' and ice-fraction results are presented as predictions, but they inherit free parameters (Mw/Ma ~ 0.1, initial C/O = 0.4) from the authors' earlier models. Those are inputs, not outcomes, so the comparison with observed C/O trends is a consistency check, not a falsifiable test. The paper is honest about most of this, but a careful reader should not mistake the Monte Carlo output for an independent confirmation.

Who gets value: graduate students and researchers outside the subfield who want a single, current summary of the wind-dominated paradigm, its observational anchors, and its open questions. As a review, it does its job. As a demonstration that the paradigm is right, it doesn't go beyond the evidence—but it doesn't claim to be a demonstration either. If I were the editor, I would send it to a serious referee, mainly to make sure the abstract is softened to match the body and the flux-evolution limitation is stated more prominently.

Recommendation: accept with revisions. Engage with the content if the review is what you need; just don't cite the abstract as proof of the paradigm.

Referee Report

2 major / 6 minor

Summary. This review, written for the Springer Handbook of Exoplanets (second edition), argues that a new paradigm is emerging in which MHD disk winds, rather than turbulent viscosity, dominate angular momentum transport, gap and ring formation, disk chemistry, planet migration, and the resulting exoplanet compositions. It synthesizes (i) exoplanet demographic observations (M-a and M-R diagrams, radius valley, host-star abundances), (ii) ALMA/JWST observations of disk substructure, kinematics, layered outflows, and molecules, (iii) physical processes in disks (non-ideal MHD, dead zones, ice lines, pebble drift), (iv) migration and planet-trap theory, and (v) the authors' population synthesis models that connect these to C/O ratios, ice fractions, and the radius valley. A roadmap section bundles the paradigm's claims, and the conclusions list testable predictions, including a C/O main sequence and ice-rich origins for the radius valley.

Significance. If the paradigm holds, it would change how disk observations are interpreted and how migration and planetary composition are connected. The review is valuable as a comprehensive, current synthesis: it accurately represents a large body of simulations and observations, includes explicit caveats (low observed turbulence, residual hydrodynamic instabilities, Hall-effect polarity dependence), and makes concrete falsifiable predictions, especially the C/O main sequence and the radius-valley dichotomy. Its primary weakness is that the central claim depends on sustained net poloidal magnetic flux over 3-10 Myr, and the review does not establish or quantify the flux-evolution problem; in addition, the population-synthesis predictions are computed from models with fixed assumptions whose sensitivity is not discussed. These are fixable in a review by reframing the claim as conditional and by adding flux-transport and sensitivity material.

major comments (2)

[Angular momentum transport and disk evolution (Eq. 4)] The review's central claim that MHD disk winds, not turbulence, drive disk evolution over the 3-10 Myr planet-formation epoch requires that a net poloidal magnetic flux Bz thread the disk for that entire period. Equation (4), which underlies the population-synthesis models, contains no evolution equation for Bz; the review itself notes in the population-synthesis section that Eq. (4) 'must be supplemented by equations that consider the back reaction on the magnetic fields.' The Hall-effect paragraph acknowledges that flux transport is polarity-dependent and can be inwards or outwards, but neither quantitative flux-transport timescales nor any replenishment mechanism (for example, ambipolar diffusion, reconnection, or streamer-fed flux injection) is discussed. As written, the 'not disk turbulence' claim is conditional on a premise that is plausible but currently unmeasured. I request a dedicated subsection on poloidal flux evolution and observational constraints (for example, Zeeman or Faraday rotation measurements, or indirect wind diagnostics) that quantifies whether Bz can survive for 3-10 Myr.
[Population synthesis: C/O main sequence and radius valley] The population-synthesis predictions presented as tests of the paradigm—the C/O main sequence and the ice-rich origin of the radius valley—are computed from models that fix the disk-wind mass-loss ratio at Mw/Ma ~ 0.1 (Section 'The effects of MHD disk winds on planetary populations') and the initial global C/O at 0.4 (Section 'Atmospheres'). The review states these values but does not quantify how sensitive the predictions are to them. If the C/O main sequence is governed by the solid-to-gas accretion ratio, its normalization must depend on the initial volatile C/O; the chosen 0.4 value is lower than the protosolar value of ~0.54 and covers only part of the stellar C/O distribution shown in Figure 3. Please add a sensitivity analysis or an explicit statement of which predictions are robust to varying these inputs within observed ranges; otherwise the falsifiability of the C/O main sequence is overstated.

minor comments (6)

[Section heading after 'Planet structure'] The heading 'Panetary structure' should be 'Planetary structure' (page 54 of the manuscript).
[Figure 2(a) discussion] In the text describing Figure 2(a), 'less than 120 solar masses' and '10-25 M_sun' should read Earth masses (M_earth), not solar masses; as printed, these values conflict with the exoplanet masses shown in the figure.
[Figure 19 captions] The captions of Figure 19 contain typos: 'assiciated' should be 'associated', 'tubulent' should be 'turbulent', and the phrase 'for disk wind evolved planetary populations' should be 'for disk-wind-evolved planetary populations.'
[Solid and Ice Lines section] In the subsection on ice lines and grain growth, 'grwoth' should be 'growth' (page 33 of the manuscript).
[Conclusions] In the conclusions, 'promore' should be 'promote' (page 64 of the manuscript), and 'the are ~1 Myr old' in 'Disk formation and initial chemical composition' should be 'they are ~1 Myr old.'
[Figure and text permissions] Several captions and the text spell 'permisson' instead of 'permission' (e.g., Figures 3, 16, and 18); please correct these.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the review's derivation chain is self-contained, with the wind paradigm grounded in independent simulations and the population-synthesis predictions clearly presented as model outputs.

full rationale

This is a review paper rather than a new derivation, and I found no step in which a prediction reduces by construction to its own inputs. The central claim that MHD disk winds rather than turbulence dominate angular momentum transport is supported by externally authored MHD simulations (Bai and Stone 2013; Gressel et al. 2015; Aoyama and Bai 2023) and by independent kinematic and dust-settling observations of low turbulence, so the paradigm does not rest on a self-citation. The population-synthesis section does rely heavily on the authors' own chain of papers (Cridland et al. 2016, 2017a,b, 2019a,b, 2020; Alessi et al. 2017; Alessi and Pudritz 2022), and the assumed wind mass-loss ratio (Mdot_w/Mdot_a ~ 0.1) and initial disk C/O = 0.4 are inputs to those models. However, these inputs are not fitted to the same exoplanet observables that the models are later compared with; they are calibrated to independent outflow observations and adopted chemical initial conditions. The so-called C/O main sequence is a model-generated correlation between atmospheric C/O and the fraction of mass accreted as solids; while this correlation is strongly influenced by the assumed carbon-poor nature of solids relative to gas, it is not presented as an independent empirical discovery and is not used as the sole evidence for the paradigm. The acknowledgment that equation (4) 'must be supplemented by equations that consider the back reaction on the magnetic fields' identifies a missing piece of physics, but missing physics is a completeness or robustness limitation, not a circular argument. No uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in solely via self-citation. The review's claims are therefore not circular, even though the underlying paradigm may be contested on empirical grounds.

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

The ledger lists the key assumptions and parameters the review's argument inherits. The strongest unverified premise is net poloidal magnetic flux throughout the disk, which all wind-launching simulations require. The population synthesis results additionally depend on input parameters (wind mass-loss fraction, alpha_turb, initial C/O) that are chosen or borrowed from fits, and the atmospheric C/O 'predictions' are computed relative to the assumed initial C/O = 0.4.

free parameters (4)

Disk wind mass-loss to accretion ratio (M_w/M_a) = ~0.1
Assumed from observed disk wind rates (Watson et al. 2016; Pascucci et al. 2023) in the population synthesis models of Alessi & Pudritz (2022); sets the wind torque strength in Eqs. (3)-(4).
Turbulent viscosity parameter alpha_turb = 10^-4 to 10^-3 (lognormal draw)
Free parameter in the reviewed disk models; controls gap opening, co-rotation torque saturation, and dust scale height. Values are taken from turbulence upper limits but remain a model input.
Initial global C/O of the disk = 0.4
Set as initial condition in Cridland et al. (2019b, 2020); the predicted atmospheric C/O values, including the C/O main sequence, are evaluated relative to this input.
Envelope opacity kappa_env for gas accretion = 0.001 cm^2 g^-1
Needed for the Kelvin-Helmholtz gas accretion timescale (Eq. 11); the review notes this value is three orders of magnitude lower than typical disk opacity.

assumptions (4)

domain assumption Protoplanetary disks retain a net poloidal magnetic field strong enough to launch MHD winds across the planet-forming region.
Required for wind-driven accretion; the review itself states that disk evolution and accretion depend on the magnetic flux threading the disk (Bai 2016), and direct flux measurements are lacking. See Section 'Angular momentum transport and disk evolution'.
domain assumption Non-ideal MHD effects (ambipolar diffusion, Ohmic resistivity) with the adopted ionization structure suppress MRI and launch laminar winds as in Bai & Stone (2013) and Gressel et al. (2015).
The paradigm rests on these simulations; results depend on grain charge carriers, cosmic ray exclusion, and X-ray/FUV ionization, all of which carry uncertainty. See Section 'Angular momentum transport and disk evolution'.
domain assumption Core accretion is the dominant giant-planet formation mechanism.
Assumed throughout the population synthesis and in the interpretation of the radius valley and atmospheric C/O; gravitational instability is mentioned but not treated as the main channel. See Sections 'Introduction' and 'Planet formation'.
domain assumption Equilibrium thermodynamics adequately describes condensation of refractory materials in the inner disk.
Used to compute core and mantle compositions (Alessi et al. 2017) and to trace ice-line positions; condensation timescales are short relative to disk evolution, supporting the assumption. See Section 'Solids and Ice Lines'.

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Cite this review

Pith. "Pith review of Connecting Planetary Composition with Formation: a New Paradigm Emerges." pith.science (2026). https://pith.science/paper/UCDJXOHQ

@misc{pith2026250522724,
  author       = {Pith},
  title        = {Pith review of: Connecting Planetary Composition with Formation: a New Paradigm Emerges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UCDJXOHQ}},
  note         = {Machine review of arXiv:2505.22724}
}

read the original abstract

Extensive ground and space based surveys have now characterized the properties of thousands of exoplanets; their radii, masses, orbits around their host stars, and the beginnings of accurate measurements of the chemical compositions of their atmospheres and cores. How are these properties linked to their formation in physically and chemically evolving protoplanetary disks wherein they accrete pebbles, planetesimals, and gas as they undergo migration? To address this challenge, our review assembles a large and varied body of exoplanet observations as well as recent Atacama Large Millimeter Array (ALMA) and James Webb Space Telescope (JWST) observations of disk structure, chemistry, kinematics, and winds. The latest advances in theory and MHD simulations that bear on these issues are also reviewed and compared with the observations. Taken together, this review argues that a new dynamic paradigm for planet formation is emerging wherein MHD disk winds and not disk turbulence play a central role in disk evolution and planet formation including: angular momentum transport, gap and ring formation. disk astrochemistry, and planet formation and migration. These processes leave their mark on the resulting atmospheric composition, radii, and orbital characteristics of exoplanet populations, offering the possibility of future observational tests.

Figures

Figures reproduced from arXiv: 2505.22724 by the authors.

**Figure 2.** The M-R diagram for well determined planetary masses and radii (left pan [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** The distribution of C/O and O/H for a wide range of stars with and without [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (23 more)

**Figure 4.** Figure 4: Example cloud-free transmission spectra for a typical hot Jupiter, with prop [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: An example of the variety of known molecules and their structures in proto [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Cumulative distributions of dust mass in PPD populations in star forming [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: The late feeding and early formation of PPDs by streamers and filaments. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: Layered outflow from HL Tau - ALMA observations Figure from Bacciotti [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

**Figure 9.** Figure 9: Disk wind from non-ideal PPDs. Figure from Gressel et al. (2015), repro [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]

**Figure 10.** Figure 10: Global 3D simulation of spontaneously produced ring - gap structure by [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

**Figure 11.** Figure 11: The abundance of carbon (top) and nitrogen (bottom) relatively oxygen [PITH_FULL_IMAGE:figures/full_fig_p027_11.png]

**Figure 12.** Figure 12: Two examples of how chemical and/or physical evolution can shift the C/O [PITH_FULL_IMAGE:figures/full_fig_p028_12.png]

**Figure 13.** Figure 13: A snapshot at t=0.5 Myr of the radial distribution of cumulative solid ma [PITH_FULL_IMAGE:figures/full_fig_p032_13.png]

**Figure 14.** Figure 14: 3D MHD simulation of planet-disk interaction in presences of an MHD [PITH_FULL_IMAGE:figures/full_fig_p038_14.png]

**Figure 15.** Figure 15: Comparison of planet-induced gap opening in viscous vs MHD disk wind [PITH_FULL_IMAGE:figures/full_fig_p043_15.png]

**Figure 16.** Figure 16: Snapshot of Lindblad (left) and co-rotation (right) torque maps at time [PITH_FULL_IMAGE:figures/full_fig_p045_16.png]

**Figure 17.** Figure 17: Snapshot of the total torque for two different viscosities; [PITH_FULL_IMAGE:figures/full_fig_p046_17.png]

**Figure 18.** Figure 18: Snapshots of planetary evolution tracks superposed on torque maps for [PITH_FULL_IMAGE:figures/full_fig_p047_18.png]

**Figure 19.** Figure 19: Planet evolution tracks - for giant planet formation - in the M-a diagram, [PITH_FULL_IMAGE:figures/full_fig_p051_19.png]

**Figure 20.** Figure 20: Population synthesis results for disk wind evolved planetary populations. [PITH_FULL_IMAGE:figures/full_fig_p052_20.png]

**Figure 21.** Figure 21: Ice fraction of simulated planets, as situated in the M-a diagram. Note con [PITH_FULL_IMAGE:figures/full_fig_p053_21.png]

**Figure 22.** Figure 22: The mass-radius (M-R) diagram for a set of Hot Jupiters and sub-Earths. [PITH_FULL_IMAGE:figures/full_fig_p056_22.png]

**Figure 23.** Figure 23: The link between a super-Earth’s size and its internal composition is com [PITH_FULL_IMAGE:figures/full_fig_p058_23.png]

**Figure 24.** Figure 24: Water mass fractions stored in the mantle and core depends on pressure, [PITH_FULL_IMAGE:figures/full_fig_p059_24.png]

**Figure 25.** Figure 25: An example of planet formation tracks (left) and the result of a chemical [PITH_FULL_IMAGE:figures/full_fig_p060_25.png]

**Figure 26.** Figure 26: The C/O main sequence for hot- and warm-Jupiters based on the population [PITH_FULL_IMAGE:figures/full_fig_p062_26.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION add.period duplicate empty 'skip "." * add.blank if FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION ...

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work page Pith review arXiv doi:10.48550/arxiv.2310.03553 2023

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