Pith. sign in

REVIEW 3 major objections 6 minor 26 references

Simulating Rotating Newtonian Universes

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A rotating universe, with the maximal shear-free rotation allowed by causality, expands more than 1% faster in the equatorial plane than along its polar axis in Newtonian N-body simulations.

desk verdict First 3D N-body simulations of a rotating universe, but the headline 1% anisotropy is probably an artifact of the ad hoc rescaling the authors themselves call unsatisfactory. read the letter →

arxiv 2412.00594 v1 pith:O3P64VOD submitted 2024-11-30 astro-ph.CO physics.comp-ph

Balázs Pál , Tze Goh , Gábor Rácz , István Szapudi This is my paper · ORCID
classification astro-ph.COphysics.comp-ph
keywords rotatinguniverseshear-freerotationcosmologicalanisotropyN-bodysimulationGödelmetricexpansionratecompactifiedsimulationsNewtoniancosmology
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 reports N-body simulations of a universe that rotates as a rigid, shear-free whole, in the spirit of Gödel's rotating spacetime. The central result is that at the maximum angular velocity that avoids closed timelike curves within the horizon, $\omega_0 \approx 10^{-3}$ Gyr$^{-1}$, the cosmic expansion becomes direction-dependent: the equatorial expansion rate exceeds the polar one by more than 1% in both the Einstein–de Sitter and $\Lambda$CDM cosmologies. If correct, this means a global rotation of the kind still allowed by CMB isotropy constraints would leave a measurable imprint on the expansion history, relevant for precision cosmology. The authors use a compactified infinite-universe simulation technique that avoids the toroidal topology of standard N-body boxes, and they measure scale factors in polar sectors versus an equatorial belt to isolate the anisotropy.

What carries the argument

The central object is a rotating Newtonian Friedmann equation with two scale factors, $a_\parallel$ and $a_\perp$, representing expansion parallel and perpendicular to the rotation axis. The simulations use the StePS N-body code, which compactifies the infinite universe via stereographic projection onto a 4D hypersphere, avoiding the periodic toroidal topology that would otherwise suppress global rotation. To flatten the rotating universe, the authors rescale perpendicular velocities by $s = V_{\perp,\mathrm{nr}}^2 / V_{\perp,\mathrm{r}}^2$, restoring the total kinetic energy of the non-rotating case; this rescaling is the step the paper later calls unsatisfactory.

What would settle it

Run the maximal-rotation simulation without applying the perpendicular-velocity rescaling of Sec. 2.3, leaving the naive rotational velocities; if $H_\perp^2 - H_\parallel^2$ then converges to $\omega_0^2$ at the present time, the reported anisotropy is an artifact of the compensation rather than a property of rotating Newtonian cosmologies.

Watch

Extended reading notes

Core claim

The paper's central claim is that a shear-free, rigid rotation of the universe, modeled on the Gödel metric, produces two distinct expansion rates: one along the rotation axis ($a_\parallel$) and one in the equatorial plane ($a_\perp$). In the simulation with the largest permitted rotation, $a_\parallel$ falls below $a_\perp$ by roughly 1% in Einstein–de Sitter and about 2.6% in $\Lambda$CDM at the present time, and the squared Hubble parameters differ by a comparable anisotropy. The authors further find that $H_\perp^2 - H_\parallel^2$ does not converge to the naive expectation $\omega_0^2$, which they interpret as evidence that a curvature-like term is missing from the Newtonian Friedmann equation for a rotating universe, so the exact analytic description is not yet complete.

Load-bearing premise

The load-bearing premise is that rescaling the perpendicular velocities by $s = V_{\perp,\mathrm{nr}}^2 / V_{\perp,\mathrm{r}}^2$ exactly flattens the rotating universe, restoring the non-rotating total kinetic energy; the paper itself concedes this compensation is unsatisfactory and that a curvature-like term is missing, so the 1% anisotropy may be an artifact of that choice.

Editorial extensions

If this is right

  • If a global shear-free rotation exists at its maximal allowed rate, the Hubble expansion is anisotropic at the percent level, so precision distance–redshift surveys must account for a direction-dependent scale factor.
  • The measured difference $H_\perp^2 - H_\parallel^2$ deviates from $\omega_0^2$, meaning the Newtonian Friedmann equation needs an additional curvature-like term; identifying that term would give a closed analytic model for rotating universes.
  • The simulation setup can be extended to perturbed initial conditions, allowing tests of how rotation seeds large-scale structure alongside the expansion anisotropy.
  • The predicted equatorial-vs-polar anisotropy is directly testable with future surveys that map cosmic expansion in different directions, for example via supernova distances or the kinetic Sunyaev–Zel'dovich effect.

Reading between the lines

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

  • Because the paper's curvature compensation is acknowledged to be ad hoc, the reported 1% might be an artifact; a rerun without the kinetic-energy rescaling would distinguish a physical anisotropy from a numerical one.
  • If the missing curvature term is later identified, the same simulations could be re-analyzed to test whether the anisotropy scales exactly as $\omega_0^2$ or has a different dependence, making a sharp prediction for observations.
  • The polar-sector/equatorial-belt measurement scheme could be translated into observable coordinates: a rotating Newtonian universe would produce a dipole-like pattern in the Hubble constant inferred from large-scale structure, which current surveys could search for.
  • The authors' approach suggests that Gödel-type rotation, though shear-free, may still be observationally distinguishable through its distinct expansion history, even if it leaves the CMB temperature isotropic.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This paper presents full 3D Newtonian N-body simulations of a rotating, shear-free universe using the StePS compactified code. The authors set up unperturbed glass initial conditions with a rigid-body angular velocity ω0 about the z-axis, run EdS and ΛCDM cosmologies, and measure scale factors and Hubble parameters in polar sectors (parallel to the rotation axis) and an equatorial belt (perpendicular). For the maximal rotation without closed timelike curves within the horizon, ω0 ≈ 10^-3 Gyr^-1, they report that the perpendicular expansion exceeds the parallel expansion by about 1%, and they interpret the difference through a modified Newtonian Friedmann equation with a curvature-like term. The paper also reports that their initial rescaling prescription used to compensate for this apparent curvature is unsatisfactory, and it defers the full description to future work.

Significance. If the reported anisotropy is robust, the paper is significant: it is the first full 3D numerical realization of a rotating Newtonian universe, it connects to Gödel-type spacetimes and to observational anisotropy claims, and it demonstrates a possible back-reaction of global rotation on the expansion. The use of the StePS code and the stated reproducibility of the simulations are strengths. However, the central quantitative claim, the >1% anisotropy, rests on an ad hoc initial-condition rescaling that the authors themselves call unsatisfactory, and the paper provides no error bars or convergence tests. The qualitative sign of the effect (a∥ < a⊥) appears clear from the figures, but the quantitative precision claimed in the abstract is not yet established.

major comments (3)
  1. [§2.3, Eq. (2), and Fig. 2] The headline >1% anisotropy is not robust because it depends directly on the perpendicular-velocity rescaling s = V⊥,nr² / V⊥,r² applied at z_init = 63. For the maximal case ω0 = 10^-3 Gyr^-1, Ω_init = ω0(1+z_init)² = 4.1 Gyr^-1, while H(z_init) ≈ 35.4 Gyr^-1 in EdS, giving s ≈ 1/(1+(Ω/H)²) ≈ 0.987 and √s ≈ 0.993. Since a(t) in Eq. (3) is normalized to initial distances, this initial 0.7% suppression of perpendicular velocities is imprinted on the final a⊥/a∥ ratio and is of the same order as the reported ~1% anisotropy. The choice z_init = 63 is not justified; evaluating the same prescription at z = 0 gives s ≈ 0.9998, almost no correction. The paper explicitly concedes in §4 that this method is unsatisfactory and that a curvature-like term is missing from the Newtonian Friedmann equation. The quantitative central claim can therefore not currently be separated from the choice of rescaling prescription. The authors should present results without the rescaling, test sensitivity to z_init, and ideally derive the correction from the equations of motion rather than imposing it ad hoc.
  2. [§3, Figs. 2 and 3] The claim of 'approximately 1%' anisotropy is made without any error bars or uncertainty quantification. Each cosmology is simulated once, and the spread across opening angles is shown only as a family of curves. The reported deviation is close to the size of the initial-condition rescaling effect discussed above, so the absence of statistical or systematic error estimates is load-bearing for the precision claim. At minimum, the authors should state the variance across the opening-angle ensembles and, if possible, run multiple realizations with different glass configurations to assess particle-shot-noise effects.
  3. [§4, Eq. (4), and Fig. 3] The relation H⊥² = H∥² + Ω² is asserted without derivation, and Fig. 3 explicitly shows that the simulation does not converge to the expected value ω0² at the present time, which the authors attribute to a missing curvature-like term. Because this relation is used to justify the functional form of the fit c1/a∥² + c2/a∥ and to interpret the back-reaction, the lack of a derivation is a substantive gap. The authors should derive the modified Friedmann equation from the Newtonian equations in the rotating frame, or at least provide the explicit form of the missing term, before using Eq. (4) to interpret the simulation results.
minor comments (6)
  1. [§2.3, Eq. (1)] The quantities V⊥,nr² and V⊥,r² are described as means of squared velocities, but the notation does not make this explicit. Please define them as ensemble averages or add overbars.
  2. [§3 and Fig. 3] The text states that H²∥ - H²⊥ is calculated, while Eq. (4) implies H⊥² > H∥² and the figure caption uses an absolute value. Please make the sign convention consistent throughout and state whether Fig. 3 plots |H²∥ - H²⊥| or H²⊥ - H²∥.
  3. [Fig. 3 caption] The caption text is garbled in places (e.g., '|H2 H2 |', missing superscripts, and axis labels). Please regenerate the figure with clearer mathematical notation and legible axis labels.
  4. [Table 1] The particle number '15 × 216' is ambiguous. If it means 15 × 2^16, please write it in that form or give the integer value.
  5. [Abstract and §1] The abstract refers to a 'Gödel-like metric', but the simulations are Newtonian. Please clarify in the introduction whether the Gödel metric is only a motivation for the velocity field or whether a relativistic correspondence is being claimed.
  6. [§4] The sentence 'H²⊥ - H²∥ does not converge to ω²0 at present' needs a clearer statement of the expected time dependence: since Ω decays as a^-2, the expected present-day value is ω0², so the mismatch shown in Fig. 3 should be stated explicitly as a discrepancy with Eq. (4).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity — the reported >1% anisotropy is a measured N-body output, not a fitted target; the Sec. 2.3 rescaling is a stated initial-condition choice, and the Sec. 4 limitation is an honesty caveat, not a self-referential derivation.

full rationale

The paper's central claim (anisotropy between polar and equatorial expansion rates exceeding 1%) is obtained by integrating N-body trajectories and then measuring scale factors and Hubble parameters from particle positions and velocities. Equation (3) defines a(t) as a mass-weighted ratio of distances; no term in that definition is set equal to the claimed anisotropy, and no output quantity is fed back into the input parameter s. The perpendicular-velocity rescaling in Eq. (2), s = V_perp,nr^2 / V_perp,r^2, is an initial-condition prescription chosen to conserve total kinetic energy; it is computed from initial velocity moments before the simulation runs, not fitted to the final anisotropy, so it does not fall under 'fitted input called prediction.' The c1/a^2 + c2/a curve in Fig. 3 is explicitly presented as a best fit to the data, not as a predicted relation, and the paper openly notes that the square root of H^2_perp - H^2_parallel does not converge to omega0, which is a falsifiable mismatch rather than a construction. The only self-citations are to the open-source StePS code and the compactified-simulation method (Racz et al. 2018, 2019); these are independently published, publicly available tools, not an unverified uniqueness theorem or an ansatz smuggled in by citation. Section 4 concedes that the curvature-compensation method is 'unsatisfactory' and that a curvature-like term is missing from the Newtonian Friedmann equation; while this is a genuine limitation affecting physical robustness and interpretation, it is not circularity, because the simulation output is not defined to equal the rescaling factor or the missing term. The skeptic concern that the initial rescaling already imprints a comparable velocity anisotropy is a legitimate model-robustness criticism, but it does not exhibit an equation in the paper that reduces the prediction to its input by construction. Therefore no circular step is identified, and the appropriate score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central result rests on four assumptions: the adequacy of Newtonian rigid rotation as a proxy for Gödel-like rotation, the faithfulness of the StePS compactification, the validity of the perpendicular velocity rescaling used to flatten the simulation, and the no-CTC bound on ω0. In addition, the reported anisotropy depends on the chosen values of ω0 and the rescaling s, and the interpretation uses a fitted curve with unreported coefficients. No new entities are introduced.

free parameters (3)
  • ω0 (present-day angular velocity) = 0, 1e-5, 5e-5, 1e-4, 5e-4, 1e-3 Gyr^-1
    Chosen values for the present-day angular velocity; the maximal value 1e-3 Gyr^-1 is used for the central claim and is set by the no-CTC condition in Sec. 2.1.
  • s (perpendicular velocity rescaling) = not reported; computed from initial velocities
    Rescaling factor for perpendicular velocities in Sec. 2.3, chosen to match the non-rotating total kinetic energy; the authors later state this compensation is unsatisfactory.
  • c1, c2 (fit coefficients) = not reported
    Coefficients in the fitted curve c1/a∥^2 + c2/a∥ for the H^2 difference in Sec. 4; values and uncertainties are not given.
assumptions (4)
  • domain assumption Newtonian gravity with a rigid, shear-free global rotation adequately models a Gödel-like rotating universe.
    The simulation is Newtonian and rotation is imposed as rigid-body motion; the connection to the Gödel metric is stated as inspiration, not derived (Sec. 2).
  • domain assumption The StePS stereographic compactification faithfully represents the infinite universe without boundary artifacts.
    The code and its compactification are taken from Rácz et al. (2018, 2019) without convergence or resolution checks in this paper.
  • ad hoc to paper The perpendicular velocity rescaling s exactly compensates the apparent curvature from rotation.
    Introduced in Sec. 2.3 as the 'obvious solution,' but Sec. 4 says this naive method is unsatisfactory and a curvature-like term is missing.
  • domain assumption The no-CTC condition is equivalent to Ω ≪ H0√a, giving ω0 ≈ 1e-3 Gyr^-1.
    Sec. 2.1 states this is 'approximately equivalent' to having no closed time-like curves within the Newtonian simulation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Simulating Rotating Newtonian Universes." pith.science (2026). https://pith.science/paper/O3P64VOD

@misc{pith2026241200594,
  author       = {Pith},
  title        = {Pith review of: Simulating Rotating Newtonian Universes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O3P64VOD}},
  note         = {Machine review of arXiv:2412.00594}
}
abstract

We present the results of a novel type of numerical simulation that realizes a rotating Universe with a shear-free, rigid body rotation inspired by a G\"{o}del-like metric. We run cosmological simulations of unperturbed glasses with various degrees of rotation in the Einstein-de Sitter and the $\Lambda$CDM cosmologies. To achieve this, we use the StePS N-body code capable of simulating the infinite Universe, overcoming the technical obstacles of classical toroidal (periodic) topologies that would otherwise prevent us from running such simulations. Results show a clear anisotropy between the polar and equatorial expansion rates with more than $1\%$ deviation from the isotropic case for maximal rotation without closed timeline curves within the horizon, $\omega_{0} \approx 10^{-3}$ Gyr$^{-1}$; a considerable effect in the era of precision cosmology.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

26 extracted references · 10 canonical work pages

  1. [1]

    doi:10.1093/mnras/213.4.917

    Barrow JD, Juszkiewicz R, Sonoda DH (1985) Universal rotation - How large can it be? Monthly Notices of the Royal Astronomical Society 213:917--943. doi:10.1093/mnras/213.4.917

    doi:10.1093/mnras/213.4.917 1985

  2. [2]

    Visualization of the G\"odel universe

    Buser M, Kajari E, Schleich WP (2013) Visualization of the G \"o del universe . New Journal of Physics 15(1):013063. doi:10.1088/1367-2630/15/1/013063, https://arxiv.org/abs/1303.4651 arXiv:1303.4651 [gr-qc]

    work page Pith review arXiv 2013

  3. [3]

    Monthly Notices of the Royal Astronomical Society 162:307

    Collins CB, Hawking SW (1973) The rotation and distortion of the Universe . Monthly Notices of the Royal Astronomical Society 162:307. doi:10.1093/mnras/162.4.307

    work page doi:10.1093/mnras/162.4.307 1973

  4. [4]

    The Astrophysical Journal 886(1):37

    Daly RA (2019) Black Hole Spin and Accretion Disk Magnetic Field Strength Estimates for More Than 750 Active Galactic Nuclei and Multiple Galactic Black Holes . The Astrophysical Journal 886(1):37. doi:10.3847/1538-4357/ab35e6, https://arxiv.org/abs/1905.11319 arXiv:1905.11319 [astro-ph.HE]

    arXiv 2019

  5. [5]

    Astrophysical Journal 292:371--394

    Davis M, Efstathiou G, Frenk CS, et al (1985) The evolution of large-scale structure in a universe dominated by cold dark matter . Astrophysical Journal 292:371--394. doi:10.1086/163168

    doi:10.1086/163168 1985

  6. [6]

    Annalen der Physik 369(3):253--287

    Ewald PP (1921) Die Berechnung optischer und elektrostatischer Gitterpotentiale . Annalen der Physik 369(3):253--287. doi:10.1002/andp.19213690304

    doi:10.1002/andp.19213690304 1921

  7. [7]

    doi:10.1038/158549a0

    Gamow G (1946) Rotating Universe? Nature 158(4016):549. doi:10.1038/158549a0

    work page doi:10.1038/158549a0 1946

  8. [8]

    Reviews of Modern Physics 21(3):447--450

    G \"o del K (1949) An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation . Reviews of Modern Physics 21(3):447--450. doi:10.1103/RevModPhys.21.447

    doi:10.1103/revmodphys.21.447 1949

Show all 26 references
  1. [9]

    Monthly Notices of the Royal Astronomical Society 142:129

    Hawking S (1969) On the rotation of the Universe . Monthly Notices of the Royal Astronomical Society 142:129. doi:10.1093/mnras/142.2.129

    1969 doi

  2. [10]

    Astrophysical Journal Supplement 75:231

    Hernquist L, Bouchet FR, Suto Y (1991) Application of the Ewald Method to Cosmological N-Body Simulations . Astrophysical Journal Supplement 75:231. doi:10.1086/191530

    1991 doi

  3. [11]

    U ber eine station \

    Lanczos K (1924) \"U ber eine station \"a re Kosmologie im Sinne der Einsteinschen Gravitationstheorie . Zeitschrift fur Physik 21(1):73--110. doi:10.1007/BF01328251

    1924 doi

  4. [12]

    Physical Review D 108(12):123533

    Mc Conville R, \'O Colg \'a in E (2023) Anisotropic distance ladder in Pantheon+supernovae . Physical Review D 108(12):123533. doi:10.1103/PhysRevD.108.123533, https://arxiv.org/abs/2304.02718 arXiv:2304.02718 [astro-ph.CO]

    2023 arXiv

  5. [13]

    Astronomy & Astrophysics 636:A15

    Migkas K, Schellenberger G, Reiprich TH, et al (2020) Probing cosmic isotropy with a new X-ray galaxy cluster sample through the L _ X -T scaling relation . Astronomy & Astrophysics 636:A15. doi:10.1051/0004-6361/201936602, https://arxiv.org/abs/2004.03305 arXiv:2004.03305 [as...

    2020 arXiv

  6. [14]

    doi:10.1140/epjs/s11734-021-00199-6, https://arxiv.org/abs/2106.03119 arXiv:2106.03119 [astro-ph.CO]

    Mohayaee R, Rameez M, Sarkar S (2021) Do supernovae indicate an accelerating universe? European Physical Journal Special Topics 230(9):2067--2076. doi:10.1140/epjs/s11734-021-00199-6, https://arxiv.org/abs/2106.03119 arXiv:2106.03119 [astro-ph.CO]

    2021 arXiv

  7. [15]

    General Relativity and Gravitation 24(2):121--128

    Obukhov YN (1992) Rotation in cosmology . General Relativity and Gravitation 24(2):121--128. doi:10.1007/BF00756780

    1992 doi

  8. [16]

    arXiv e-prints astro-ph/0008106

    Obukhov YN (2000) On physical foundations and observational effects of cosmic rotation . arXiv e-prints astro-ph/0008106. doi:10.48550/arXiv.astro-ph/0008106, https://arxiv.org/abs/astro-ph/0008106 arXiv:astro-ph/0008106 [astro-ph]

    2000 doi arXiv

  9. [17]

    Nature 240(5379):298--299

    Pathria RK (1972) The Universe as a Black Hole . Nature 240(5379):298--299. doi:10.1038/240298a0

    1972 doi

  10. [18]

    Planck Collaboration , Ade PAR, Aghanim N, et al (2016) Planck 2015 results. XVIII. Background geometry and topology of the Universe . Astronomy & Astrophysics 594:A18. doi:10.1051/0004-6361/201525829, https://arxiv.org/abs/1502.01593 arXiv:1502.01593 [astro-ph.CO]

    2016 arXiv

  11. [19]

    Planck Collaboration , Aghanim N, Akrami Y, et al (2020) Planck 2018 results. VI. Cosmological parameters . Astronomy & Astrophysics 641:A6. doi:10.1051/0004-6361/201833910, https://arxiv.org/abs/1807.06209 arXiv:1807.06209 [astro-ph.CO]

    2020 arXiv

  12. [20]

    Monthly Notices of the Royal Astronomical Society 477(2):1949--1957

    R \'a cz G, Szapudi I, Csabai I, et al (2018) Compactified cosmological simulations of the infinite universe . Monthly Notices of the Royal Astronomical Society 477(2):1949--1957. doi:10.1093/mnras/sty695, https://arxiv.org/abs/1711.04959 arXiv:1711.04959 [astro-ph.CO]

    2018 arXiv

  13. [21]

    Astronomy and Computing 28:100303

    R \'a cz G, Szapudi I, Dobos L, et al (2019) StePS: A multi-GPU cosmological N-body Code for compactified simulations . Astronomy and Computing 28:100303. doi:10.1016/j.ascom.2019.100303, https://arxiv.org/abs/1811.05903 arXiv:1811.05903 [astro-ph.CO]

    2019

  14. [22]

    doi:10.1103/PhysRevLett.117.131302, https://arxiv.org/abs/1605.07178 arXiv:1605.07178 [astro-ph.CO]

    Saadeh D, Feeney SM, Pontzen A, et al (2016) How Isotropic is the Universe? Physical Review Letters 117(13):131302. doi:10.1103/PhysRevLett.117.131302, https://arxiv.org/abs/1605.07178 arXiv:1605.07178 [astro-ph.CO]

    2016 arXiv

  15. [23]

    Astrophysical Journal 143:689

    Silk J (1966) Local Irregularities in a G \"O DEL Universe . Astrophysical Journal 143:689. doi:10.1086/148551

    1966 doi

  16. [24]

    Monthly Notices of the Royal Astronomical Society 147:13

    Silk J (1970) The instability of a rotating universe . Monthly Notices of the Royal Astronomical Society 147:13. doi:10.1093/mnras/147.1.13

    1970 doi

  17. [25]

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

    ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year archivePrefix primaryClass adsurl adsnote version label extra.labe...

  18. [26]

    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 dupl...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.