Steady state, core, operational optimization of an ARC-like tokamak via plasma composition and shape

A. Ho; A.J. Creely; A. Saltzman; G. Snoep; J. Hall; J. Han; J. Hillesheim; M.S. Anastopoulos Tzanis; N.T. Howard; P. Rodriguez-Fernandez

REVIEW 4 major objections 6 minor 93 references

Steady state, core, operational optimization of an ARC-like tokamak via plasma composition and shape

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Jointly adjusting impurity content, plasma shape, and pedestal density can raise the predicted steady-state fusion power of an ARC-like tokamak from 1140 MW to 1910 MW, a 65% gain, while respecting density and L-H power threshold limits.

desk verdict A solid integrated-modeling optimization for ARC-class tokamaks that makes a credible case for squareness and impurity composition as joint levers, but the headline 65% gain is relative to a squareness-zero baseline, the optimum is pinned by the Greenwald penalty, and the quantitative claim lacks propagated uncertainty. read the letter →

arxiv 2608.10124 v1 pith:2RYDE4WI submitted 2026-08-10 physics.plasm-ph

A. Saltzman , P. Rodriguez-Fernandez , A. Ho , G. Snoep , J. Han , J. Hall , M.S. Anastopoulos Tzanis , J. Hillesheim

show 3 more authors

A.J. Creely P. Snyder N.T. Howard

This is my paper · ORCID

classification physics.plasm-ph

keywords fusionpowertokamakoperationaloptimizationimpuritycompositionplasmashapingpedestalstabilityGreenwalddensitylimitITGturbulencestabilizationBayesian

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the steady-state fusion power of an already-built tokamak design is not fixed by the design itself: impurity content, plasma shape, and pedestal density can be tuned after construction to move performance substantially. Using a coupled, physics-based core-pedestal modeling chain and Bayesian optimization over six operational parameters, it finds an operating point for the ARC V3A reference design that produces 1910 MW, about 65% more than the 1140 MW predicted for the nominal configuration, while staying below 90% of the Greenwald density limit and above the L-H transition power threshold. The central physics is that additional high-charge impurities stabilize the ion-temperature-gradient turbulence that dominates core transport, while stronger elongation, triangularity, and squareness increase plasma volume and, through the peeling-ballooning pedestal stability, allow higher pedestal pressure. If the claim holds, operational tuning alone can capture a large share of the performance gains usually sought by changing the machine's design.

What carries the argument

The load-bearing mechanism is the coupled iteration between core turbulent transport and the pedestal stability boundary. A quasilinear transport model predicts core gradients from drift-wave turbulence, a pedestal model sets the pressure at the top of the H-mode pedestal from peeling-ballooning stability, and the two are iterated to a converged steady state, so that improved core performance (higher $\beta_N$) raises the pedestal through the Shafranov shift, which in turn improves confinement further. Composition enters through $Z_{eff}$ and $f_{main}$: more impurities stabilize the ion-temperature-gradient mode and dilute the fuel, with the two effects nearly canceling for $f_{main}$ but net favorable for $Z_{eff}$. Shape enters through volume, weak turbulent stabilization, and pedestal stability, with elongation, triangularity, and squareness acting on different parts of the peeling-ballooning boundary. The six-dimensional search is driven by Bayesian optimization on a penalized objective, fusion power times penalties for exceeding 90% of the Greenwald density limit or falling below the L-H transition power threshold.

What would settle it

Re-run the six-dimensional optimization with the same model but replace the flat core $Z_{eff}$ profile with a peaked profile representative of tungsten accumulation; if the predicted fusion power at the claimed optimum falls by more than the paper's stated ~34% modeling uncertainty, the flat-profile assumption is the deciding factor. Alternatively, a direct nonlinear gyrokinetic simulation at $Z_{eff}=2.1$, $f_{main}=0.88$, and the optimal shape should confirm the predicted ITG stabilization and temperature peaking; if growth rates are not reduced relative to the nominal case, the central mechanism is absent.

Watch

Extended reading notes

Core claim

Within a coupled modeling framework that self-consistently iterates core turbulence, heating, current diffusion, and pedestal stability to steady state, the paper claims that simultaneously optimizing the effective ion charge $Z_{eff}$, main-ion fraction $f_{main}$, elongation $\kappa$, triangularity $\delta$, squareness $\zeta$, and pedestal density $n_{e,ped}$ raises the maximum fusion power of an ARC V3A-like device from the nominal 1140 MW to 1910 MW. The optimal point is $Z_{eff}=2.1$, $f_{main}=0.88$, $\kappa=1.99$, $\delta=0.60$, $\zeta=0.17$, and $n_{e,ped}=2.18\times10^{20}\,\mathrm{m}^{-3}$, with the Greenwald density constraint binding. The gain is the sum of three coupled effects: impurities stabilize the dominant ion-temperature-gradient turbulence; increased shaping raises plasma volume and, through the peeling-ballooning stability boundary, allows higher pedestal pressure at the same pedestal density; and the resulting higher $\beta_N$ feeds back to further raise the pedestal pressure. Limiting either elongation or squareness to its nominal value still yields roughly a 30% improvement (1537 MW and 1515 MW respectively), so the main result does not depend on the most difficult shape change alone.

Load-bearing premise

The optimization assumes the operator can set the impurity content as a free knob and that the resulting core $Z_{eff}$ profile stays flat across the plasma, because impurity transport is not modeled; if real impurity accumulation makes the profile peaked or hollow, the predicted turbulence stabilization, pedestal pressure, and radiation balance — and with them the 1910 MW optimum — could change substantially.

Editorial extensions

If this is right

The same machine, operated at the optimized composition and shape, is predicted to deliver 1910 MW instead of 1140 MW, a 65% gain, without a predicted reduction in flattop duration.
Holding elongation at the nominal value still gives 1537 MW, and holding squareness at zero still gives 1515 MW, so about 30% of the gain is available even if the most challenging shape changes are infeasible.
The volumetric fusion power density rises from 5.39 MW/m$^3$ toward over 7.75 MW/m$^3$, implying that a future design could produce the same total power from roughly 30% less plasma volume.
Because the Greenwald density limit is the binding constraint, gains would be larger if power-dependent density limits turn out to allow higher densities.
The optimization method is not specific to this device and can be applied to other tokamak designs once the operational ranges are set.

Reading between the lines

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

If real impurity transport produces a peaked core $Z_{eff}$ profile instead of the assumed flat one, the predicted ITG stabilization and pedestal feedback could weaken; a testable check is re-running the optimization with tungsten-consistent peaked profiles to see whether the 1910 MW point survives.
The paper's finding that squareness adds about 25% fusion power over the zero-squareness optimum suggests higher-order shaping parameters should receive design-phase attention comparable to elongation and triangularity, an extension the paper mentions but does not itself optimize for other devices.
The predicted benefit of high $Z_{eff}$ and reduced $f_{main}$ is in principle testable on existing high-field tokamaks by seeded-impurity experiments that look for the same ITG stabilization and elevated pedestal pressure before a reactor is built.

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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

Quick take: this is a serious integrated-modeling paper that deserves a referee. The genuinely new piece is the joint six-parameter Bayesian optimization — composition (Zeff, fmain), shape (kappa, delta, squareness), and pedestal density — for ARC V3A using the MAESTRO framework (TGLF + EPED + NEO + TRANSP). Squareness is a lever that most design optimizations ignore, and the standalone TGLF/EPED scans give a clear mechanism story: impurities stabilize ITG, elongation and triangularity shift peeling/ballooning balances, and squareness buys volume and peeling-branch pressure. The final optimum is evaluated with the full integrated model, not the surrogate, and the workflow uses open-source MITIM-fusion with documented versions. That is real evidence.

Soft spots, in order. First, the quantitative optima (1910 MW) are point values without propagated uncertainty. They quote a 34% relative uncertainty on fusion power from the companion ARC paper, but they do not carry that through to the optimized point. That should be added, even if it means reporting a band rather than a number. Second, the squareness pedestal response relies on an unpublished EPED modification (personal communication, ref [85]). Plausible and consistent with the physics, but not independently checkable; the authors should publish the modification or benchmark it against standard EPED. Third, the density limit is treated with a hard quintic penalty above fG=0.9, and the optimum sits against that constraint. They correctly flag recent power-dependent density limit work as future work, but the robustness of the 65% number to that choice is untested. A sensitivity scan over the density limit model would be the single most valuable addition.

Fourth, the comparison baseline: the 65% is relative to a nominal with squareness set to zero, which is not the actual ARC V3A shape (that has negative squareness). They disclose this, and the 30% gain with kappa fixed is a fairer apples-to-apples statement. But the abstract should not let the 65% stand without the baseline qualifier.

The central physical claim — joint adjustment of composition and shaping, including squareness, can raise predicted fusion power substantially — holds up within the model. The optima at the edges of the hand-set bounds (kappa near 2.0, delta near 0.65, zeta near 0.2) mean the 'global optimum' claim should be softened, but that is a minor point.

Who this is for: anyone doing reactor design or operational scenario optimization with integrated modeling. It deserves peer review. I would send it out, and ask for the uncertainty propagation, a Greenwald sensitivity test, and a clear statement of the baseline in the abstract.

Referee Report

4 major / 6 minor

Summary. The manuscript presents a steady-state core operational optimization of an ARC-like tokamak (ARC V3A geometry) using the MAESTRO integrated modeling framework. The optimization variables are impurity composition (Zeff, fmain), plasma shape (elongation, triangularity, squareness), and pedestal density, with fusion power as the objective and penalties for exceeding 90% of the Greenwald density limit and for falling below the L-H power threshold. The authors first map the space with 1D/2D scans including standalone TGLF and EPED calculations, then perform 6D Bayesian optimization and two 5D variants with elongation or squareness fixed. They report a maximum fusion power of 1910 MW, a 65% increase over their workflow's nominal ARC V3A prediction of 1140 MW, and attribute the gain to ITG stabilization by impurities, improved pedestal pressure from shaping, and increased plasma volume. The paper emphasizes that 0D empirical scaling laws miss these effects and advocates physics-based operational optimization.

Significance. If the quantitative claims are robust, this is a valuable contribution: it provides a high-fidelity, physics-based workflow for operational optimization of a reactor concept, identifies squareness as a meaningful lever, and quantifies how impurity seeding and shaping jointly affect core-pedestal performance. The work is strengthened by evaluating the final optima with the full MAESTRO model rather than with the surrogate, avoiding circularity in the reported objective values, and by explicitly reporting model versions and limitations. However, the headline 65% gain is a point estimate built on specific modeling choices, notably the Greenwald density-limit penalty and a flat Zeff profile, and is not accompanied by propagated uncertainties or sensitivity tests. These issues must be addressed before the central claim can be accepted.

major comments (4)

[Section 5, 'Appropriate uncertainty quantification' paragraph] The manuscript states that a 34% relative uncertainty, taken from [4], 'should be considered applicable to fusion performance predictions made in this paper,' yet Table 1 reports the optimized fusion powers (1910, 1537, 1515, and 1140 MW) as single point values, and the abstract and discussion present the 65% increase as a definitive result. With a 34% uncertainty on each prediction, the reported 65% improvement is not statistically established. The authors should propagate the EPED and TGLF uncertainties through the optimization, or at least through the optimal and nominal points, and report confidence intervals or a probability that the optimized point exceeds nominal.
[Section 4, Eq. (1), and Section 5] The central result is controlled by the density-limit model: the objective applies a quintic penalty for f_G > 0.9, and Section 5 states that 'the plasma performance is limited by the Greenwald density limit constraint,' with the optimal n_e,ped at 2.18e20 m^-3 sitting just below the limit. The paper cites recent power-dependent density-limit models [109-112] but does not test the sensitivity of the 1910 MW optimum, or even the ranking of the 6D versus 5D results, to that alternative. A sensitivity scan with a power-dependent density limit, or at least a variation of the threshold and penalty exponent, is required to support the robustness of the claimed optimum.
[Section 4, Table 1, and Section 3.2] The headline '65% increase' is computed relative to a nominal point with zero squareness (1140 MW, 'assuming no squareness'), whereas the ARC V3A design from [1] has negative squareness and the published performance range in [4] is approximately 900-1300 MW. The authors are transparent about the re-basing, but the abstract and discussion present the 65% figure as an improvement over 'nominal performance predicted by this workflow,' not over the actual published design point. The comparison should also be made to the published ARC V3A prediction or expressed as a range over the [4] uncertainty band, and the text should state explicitly that the denominator is the re-based zero-squareness case.
[Section 2.1 and Section 5] The composition optimization treats Zeff and fmain as operator-set inputs and assumes a fixed, flat Zeff profile throughout the core, with impurity transport not predicted. While the paper cites recent studies [116,117] supporting the flat-Zeff approximation for SPARC and ARC, the predicted optimal composition (Zeff=2.1, fmain=0.88) and the associated ITG-stabilization benefit depend on this assumption. A sensitivity study allowing peaked or hollow Zeff profiles, or an estimate of the effect of impurity transport on the optimum, would materially strengthen the composition-related claims; without it, the composition optimum should be presented as conditional on the flat-profile assumption.

minor comments (6)

[Section 3.1, Figure 3 caption and text] The text refers to 'Subplot (e)' twice for the effective collisionality and for the L-H power ratio; the first should be subplot (d). The same duplicated 'Subplot (e)' appears in the Figure 10 caption and text.
[Figure 8 caption] The caption says 'the composition input into TGLF changed externally' for scans of elongation and triangularity; this should read 'geometry input' or 'shaping parameters.'
[Section 3.1] 'The mapping between Zeff and fmain and lumped impurity charge state and density scan be found' should read '...density can be found.'
[Section 4, Table 1 and following paragraph] The statement 'No reduction in flattop duration is expected' is contradicted by the fixed-squareness case, which has tau_flattop = 842 s versus 1043 s for the nominal case; the text should be reconciled with the table.
[Section 4, Eq. (1)] The text describes the Greenwald constraint as a 'hard' penalty, but Eq. (1) is a continuous quintic penalty active only for f_G > 0.9; please clarify the terminology.
[Table 1] Table 1 does not report f_G and f_LH at the optimum, even though the objective is formulated around these constraints; reporting them would allow readers to verify that the Greenwald limit is indeed the active constraint.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 65% claim is from full MAESTRO evaluations of scanned input variables, not from a fit or self-citation chain.

full rationale

The central claim (1910 MW, 65% above nominal) is produced by evaluating the full MAESTRO model at input vectors (Zeff, fmain, kappa, delta, zeta, ne,ped) selected by Bayesian optimization; none of these inputs is fitted to the output fusion power. The final optimum is explicitly re-evaluated with the full model rather than the surrogate ('as performance predictions are done with the fullMAESTRO model (not a surrogate of it)'), which forecloses the main surrogate-circularity concern. The objective function is a stated engineering constraint (Greenwald penalty, L-H threshold), not a hidden restatement of the predicted quantity. Self-citations to MAESTRO [79], the ARC performance basis [4], and flat-Zeff studies [116,117] provide the modeling tools and uncertainty estimates, but the paper does not derive its predictions from those citations; it runs the codes on scanned inputs. The re-based nominal (zeta=0 instead of ARC V3A's negative squareness) affects the fairness of the 65% percentage but is a baseline choice, not a circular derivation. No step was found where an equation reduces to its own input or a fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The simulation chain rests on several modeling approximations: the lumped-impurity representation of Zeff/fmain, the unpublished EPED-MXH pedestal model for squareness, TGLF-SAT2 as the turbulence model, an independently controllable pedestal density, and a flat Zeff profile. The optimization bounds and penalty exponents are also hand-selected and influence the reported optimum.

free parameters (3)

Optimization variable bounds = Zeff [1.5,2.5], fmain [0.70,0.90], kappa [1.70,2.00], delta [0.45,0.65], zeta [-0.20,0.20], ne,ped [1.9,2.5] x 10^20…
The reported optima for kappa, delta, and zeta sit at or near the upper bounds of these hand-set ranges (Table 1), so the magnitude of the claimed fusion power increase is partly determined by engineering-limit choices rather than an interior optimum.
Greenwald penalty threshold and exponent = f_G > 0.9 penalized with exponent 5; f_LH > 1 required
The objective in Eq. (1) uses a hand-chosen quintic penalty and a 0.9 margin; the Greenwald constraint is active at the optimum, so this choice shapes the reported optimum.
Fixed tungsten and hydrogen concentrations = n_W = 1.5e-5 n_e; n_H = 0.05 n_e
These fixed background impurity levels are assumed for all scans; the lumped impurity is adjusted to reach target Zeff and fmain, so radiation and transport responses depend on these inputs.

assumptions (5)

domain assumption A single lumped impurity species with charge equivalent to Zeff and concentration set by fmain captures the effect of the true impurity mix on core transport, radiation, and pedestal.
Invoked in Section 1.4 and Section 2.1 to map Zeff/fmain to one species; if a real multi-species mix behaves differently, the composition optimization could change.
domain assumption EPED with the MXH boundary parameterization correctly predicts pedestal height and width as functions of elongation, triangularity, and squareness.
The MXH-capable EPED version is a personal communication [85]; the squareness pedestal results (Figures 11-12) rest on this unvalidated model version.
domain assumption TGLF with the SAT2 saturation rule and nbasis_max=6 predicts core turbulent fluxes in ARC-like burning plasmas.
TGLF SAT2 is a reduced quasi-linear model calibrated to nonlinear gyrokinetics; the paper cites a 15% uncertainty from saturation-rule choice, indicating sensitivity.
domain assumption The operator can independently set the pedestal density n_e,ped across the scanned range.
The paper notes (Section 1.3) that in H-mode it may not be feasible to fuel once a pedestal has formed; the optimization treats n_e,ped as a free knob.
domain assumption The Zeff profile is flat in the core and elevated near the edge; impurity transport is not modeled.
Stated in Sections 2.1 and 5; the impurity optimization assumes this profile shape, and impurity modes depending on profile peaking are not included.

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Cite this review

Pith. "Pith review of Steady state, core, operational optimization of an ARC-like tokamak via plasma composition and shape." pith.science (2026). https://pith.science/paper/2RYDE4WI

@misc{pith2026260810124,
  author       = {Pith},
  title        = {Pith review of: Steady state, core, operational optimization of an ARC-like tokamak via plasma composition and shape},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2RYDE4WI}},
  note         = {Machine review of arXiv:2608.10124}
}

read the original abstract

Impurity composition, plasma shape, and pedestal density all provide strong levers on fusion power. Here, we explore the ways in which their variation changes fusion power and seek to find the optimum of these parameters. The key impacts of these variables are through changes in the core turbulent transport, the density of the fuel species, the pedestal pressure, and the plasma volume. ITG stabilization due to increased amounts of impurities is observed. The dependence of all of these parameters on the pedestal pressure is especially complicated because of the separate impacts on the peeling and ballooning modes, which can each limit the pedestal. Optimization of this multidimensional operating space is enabled by the use of Bayesian optimization, resulting in an operating point similar to ARC V3A with ~30% more fusion power and a higher fusion power density. Increased shaping parameters, including elongation, triangularity, and squareness are all beneficial, as is high Zeff. When elongation is also allowed to vary, a ~65% increase in fusion power can be achieved. While not commonly considered, we find squareness is an important lever on fusion power. The plasma performance is limited by the Greenwald density limit constraint. This workflow developed here and demonstrated with the example of ARC V3A can readily be applied to other tokamak designs.

Figures

Figures reproduced from arXiv: 2608.10124 by the authors.

**Figure 2.** The resulting (a) fusion power and (b) scalar multiplicative factor on the energy confinement [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Additional quantities of interest for the impurity composition scan, varying [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (16 more)

**Figure 4.** Figure 4: Stand-alone TGLF scans at ρ = 0.6 to assess the linear impact on turbulence of changing Zef f at nominal fmain (a, b), fmain at nominal Zef f = 1.5 (c,d), and fmain at Zef f = 2.2. The normalized growth rates are shown in (a) and (c), and the real frequencies, with a n…

**Figure 5.** Figure 5: Impact of Zef f on the pedestal height (ptop) and width (wptop) at different pedestal densities (ne,ped). Higher Zef f causes ballooning modes to begin limiting the pedestal at lower densities. However, for the same density, at higher Zef f , the peeling branch pressur…

**Figure 6.** Figure 6: Impact of βN on the pedestal height (ptop) and width (wptop) at different pedestal densities (ne,ped). Higher βN allows slight increases the pressure on the peeling branch, for the same value of ne,ped as well as increasing the density at which ballooning modes begin t…

**Figure 7.** Figure 7: The resulting (a) fusion power and (b) scalar multiplicative factor on the energy confinement [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: Stand-alone TGLF scans at ρ = 0.6 to assess the linear impact on turbulence of changing κ (a, b) and δ (c,d). All of these simulations were initialized from the output of the nominal (κ = 1.77 and δ = 0.49 at the 99.5% flux surface) MAESTRO simulation, with the composi…

**Figure 9.** Figure 9: Impact of κ and δ on the pedestal height (ptop) and width (wptop) at different pedestal densities (ne,ped). Changes in κ are denoted by changes in color and changes in δ are denoted by changes in shade. Increased elongation shifts the transition from a peeling-limited …

**Figure 10.** Figure 10: Additional quantities of interest for the scan of [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]

**Figure 11.** Figure 11: Impact of squareness (ζ) on the pedestal height (ptop) and width (wptop) at different pedestal densities (ne,ped) for κ = 1.77 and δ = 0.49. For an ARC-like device, increasing absolute value of ζ decreases the density at which the pedestal transitions from peeling lim…

**Figure 12.** Figure 12: The resulting (a) fusion power and (b) scalar multiplicative factor on the energy confinement [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]

**Figure 13.** Figure 13: Input parameter values for each iteration of the full 6D core, steady state operational opti [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

**Figure 14.** Figure 14: Results of full 6D core, steady state operational optimization. Subplot (a) shows the fusion [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]

**Figure 15.** Figure 15: Profiles from scan of fmain at nominal value of Zef f , Zeff = 1.5, from the 2D scan depicted in Figures 2 and 3. The electron and ion temperatures are shown in subplots (a) and (b). The electron and deuterium density are shown in subplots (c) and (d). Reduced fuel io…

**Figure 16.** Figure 16: Profiles of fmain at elevated Zef f , Zeff = 2.2, from the 2D scan depicted in Figures 2 and 3. The electron and ion temperatures are shown in subplots (a) and (b). The electron and deuterium density are shown in subplots (c) and (d). Again, there is a reduction in th…

**Figure 17.** Figure 17: Profiles of Zef f scanned at the nominal value of fmain, fmain = 0.85, from the 2D scan depicted in Figures 2 and 3. The electron and ion temperatures are shown in subplots (a) and (b). The electron and deuterium density are shown in subplots (c) and (d). The inverse …

**Figure 18.** Figure 18: Scan of elongation at δ = 0.50 from the 2D scan depicted in Figures 7 and 10. The electron and ion temperatures are shown in subplots (a) and (b). The electron and deuterium density are shown in subplots (c) and (d). The inverse normalized electron temperature, ion te…

**Figure 19.** Figure 19: Scan of triangularity at κ = 2.0 from the 2D scan depicted in Figures 7 and 10. The electron and ion temperatures are shown in subplots (a) and (b). The electron and deuterium density are shown in subplots (c) and (d). The inverse normalized electron temperature, ion …

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Pith tools

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