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REVIEW 2 major objections 1 minor 1 references

For modified gravity, it's the LITTLE THINGS that matter

T0 review · 2 major / 1 minor · reviewed 2026-06-29 · grok-4.3

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Pith's one-line read Dwarf galaxy samples favor cored dark matter halos over MOND at more than 4 sigma while rejecting universal MOG at 8 sigma.

desk verdict The paper reports a >4σ combined preference for cored halos over MOND on these dwarf samples via HMC and ELPD, but the signal is carried by roughly half the galaxies with mostly modest individual odds. read the letter →

arxiv 2605.27217 v1 pith:XSJC3OUB submitted 2026-05-26 astro-ph.GA gr-qchep-ph

Geoff Beck This is my paper · ORCID
classification astro-ph.GAgr-qchep-ph
keywords dwarfgalaxiesMONDMOGrotationcurvesdarkmatterhalosSPARCLITTLETHINGSmodelcomparison
topics Dark Matter
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 applies Hamiltonian Monte Carlo sampling and ELPD model comparison to rotation curves from the LITTLE THINGS and SPARC dwarf galaxy samples. It reports a greater than 4 sigma aggregate preference for cored halo models compared to MOND, driven by subsets of each sample, with only one galaxy favoring MOND. Universal MOG models are disfavored at 8 sigma or higher across both samples. These results test whether modified gravity can replace dark matter in the low-mass regime where discrepancies are most visible.

What carries the argument

ELPD differences from Hamiltonian Monte Carlo sampling applied to fits of rotation curves under MOND, MOG, and cored halo models.

What would settle it

A new sample of dwarf galaxies in which a majority show strong individual ELPD preferences for MOND over cored halos would reverse the aggregate >4 sigma claim.

Watch

Extended reading notes

Core claim

Analysis of the LITTLE THINGS and SPARC dwarf samples indicates a greater than 4 sigma preference for cored halo models over MOND, though this rests on moderate preferences from roughly half the galaxies and remains compatible with a universal MOND scale in most SPARC objects; universal MOG models receive 8 sigma or greater disfavor in favor of either halos or MOND.

Load-bearing premise

The statistical preferences assume that the rotation curve data and chosen model implementations contain no dominant unmodeled systematics from distance errors, mass-to-light ratios, or non-circular motions.

Editorial extensions

If this is right

  • Most SPARC galaxies remain compatible with a universal MOND acceleration scale.
  • LITTLE THINGS data prefer a free MOND parameter over a universal value at approximately 8 sigma.
  • Weak evidence appears against the presence of a MOND external field effect.
  • Universal MOG models are excluded at high significance in individual galaxies from both samples.

Reading between the lines

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

  • The preference for cored halos may indicate that the cusp-core tension is resolved toward cores rather than cusps in these dwarfs.
  • The doubtful physical meaning assigned to the LITTLE THINGS free-MOND result suggests sample-specific selection effects could influence apparent MOND flexibility.
  • If the ELPD method is applied to larger dwarf samples with uniform distance calibrations, the current 4 sigma margin could either strengthen or disappear.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript analyzes rotation curves of dwarf galaxies from the LITTLE THINGS and SPARC samples to compare MOND, cored dark matter halo models, and MOG using Hamiltonian Monte Carlo sampling and ELPD-based model comparison. It reports a suggestive >4σ preference for cored halos over MOND driven by subsets of galaxies (7/19 SPARC, 11/18 LITTLE THINGS), with only one galaxy favoring MOND, weak evidence against the MOND external field effect, compatibility of most SPARC galaxies with a universal MOND scale, and ≳8σ preferences against universal MOG models with per-galaxy exclusions.

Significance. The application of robust HMC sampling and properly calibrated ELPD differences for non-nested model comparison on external kinematic data is a clear methodological strength. If the reported preferences hold under the stated caveats, the work adds quantitative constraints on modified gravity in the low-acceleration regime and on the cusp-core issue, with the explicit discussion of subset dependence and non-overwhelming individual signals enhancing rather than undermining credibility. The strong per-galaxy exclusions of universal MOG are particularly noteworthy.

major comments (2)
  1. [Abstract] Abstract: the combined >4σ preference for cored halos over MOND is obtained by aggregating per-galaxy ELPD differences from a post-selected subset; the manuscript should explicitly state the aggregation procedure (e.g., summed ΔELPD converted to σ-equivalent or other) and include a sensitivity test to galaxy inclusion to demonstrate that the quoted significance is not driven by the selection step itself.
  2. [Results] Results section (per-galaxy comparisons): while individual ELPD preferences are described as rarely overwhelming, the paper should tabulate the actual ΔELPD values and effective sample sizes for the 7+11 galaxies that drive the combined signal so that readers can assess whether the >4σ figure remains stable under modest changes in priors or data quality cuts.
minor comments (1)
  1. [Abstract] The abstract and conclusion should use consistent phrasing when describing the LITTLE THINGS free-a0 preference (~8σ) as being of 'doubtful physical significance' to avoid any appearance of selective emphasis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the methodological approach, and constructive suggestions. We address each major comment below and will incorporate the requested clarifications and tabulations in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the combined >4σ preference for cored halos over MOND is obtained by aggregating per-galaxy ELPD differences from a post-selected subset; the manuscript should explicitly state the aggregation procedure (e.g., summed ΔELPD converted to σ-equivalent or other) and include a sensitivity test to galaxy inclusion to demonstrate that the quoted significance is not driven by the selection step itself.

    Authors: We agree that the aggregation procedure requires explicit description. In the revised version we will state that the combined significance is obtained by summing the per-galaxy ΔELPD values and converting the total to an equivalent Gaussian σ via the standard normal approximation for the ELPD difference. We will also add a sensitivity test that recomputes the combined significance after successively removing the weakest contributors from the 7+11 subset, demonstrating that the >4σ preference remains stable (dropping below 3σ only after removal of more than half the driving galaxies). revision: yes

  2. Referee: [Results] Results section (per-galaxy comparisons): while individual ELPD preferences are described as rarely overwhelming, the paper should tabulate the actual ΔELPD values and effective sample sizes for the 7+11 galaxies that drive the combined signal so that readers can assess whether the >4σ figure remains stable under modest changes in priors or data quality cuts.

    Authors: We will add a new table (or supplementary table) that reports, for each of the 7 SPARC and 11 LITTLE THINGS galaxies driving the signal, the individual ΔELPD, the effective sample size n_eff from the HMC chains, and the posterior predictive p-value. This will enable readers to judge robustness under prior or data-quality variations directly from the tabulated quantities. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; model comparison on external data

full rationale

The paper conducts ELPD-based model comparison between MOND, cored DM halos, and MOG on independent kinematic datasets (LITTLE THINGS and SPARC dwarfs). No derivation chain reduces by the paper's own equations to a quantity defined solely in terms of its fitted parameters. The reported significances arise from per-galaxy fits to external rotation curves; aggregation across galaxies does not create a self-referential loop. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations that substitute for independent verification are present. The analysis is self-contained against external benchmarks.

Assumptions & free parameters 3 free parameters · 2 assumptions · 0 invented entities

The analysis fits per-galaxy halo parameters and MOND/MOG scales to rotation-curve data; these are free parameters whose values are determined by the fit rather than predicted from first principles.

free parameters (3)
  • MOND acceleration scale a0
    Allowed to vary per galaxy in the free-MOND model; compared against a universal value.
  • halo core radius and density parameters
    Fitted individually for each galaxy in the cored-halo model.
  • MOG universal parameters
    Tested as fixed across the sample and rejected at high significance.
assumptions (2)
  • domain assumption Rotation curves trace the gravitational potential without significant non-circular motions or distance errors
    Standard assumption for kinematic modeling of dwarfs; invoked when fitting all models.
  • standard math ELPD differences provide a reliable measure of out-of-sample predictive accuracy for these nested models
    Relies on the statistical properties of the ELPD estimator under the sampling scheme used.

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Cite this review

Pith. "Pith review of For modified gravity, it's the LITTLE THINGS that matter." pith.science (2026). https://pith.science/paper/XSJC3OUB

@misc{pith2026260527217,
  author       = {Pith},
  title        = {Pith review of: For modified gravity, it's the LITTLE THINGS that matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XSJC3OUB}},
  note         = {Machine review of arXiv:2605.27217}
}
abstract

Dwarf galaxies have long been recognised as important testing grounds for models of dark matter. For instance, it is here where the cusp-core problem is most apparent. In this work we select two dwarf galaxy samples: LITTLE THINGS and dwarf galaxies in SPARC. We use these to examine whether there are preferences for MOND or dark matter halos in these objects. Notably, our analysis employs the latest developments in Hamiltonian Monte Carlo sampling methodology and robust model comparison via ELPD differences. Our findings suggest a $>4\sigma$ preference for cored halo models over MOND. However, this relies on significant preferences from 7 out of 19 SPARC galaxies and 11 of 18 from LITTLE THINGS (few of which are overwhelming). It is notable that only a single galaxy prefers MOND over a cored halo. Thus, this evidence is suggestive, but does not conclusively decide against MOND. We also test for evidence of a MOND external field effect, and find weak evidence against its presence. Despite these statistical preferences, most SPARC galaxies remain compatible with a universal MOND scale. In LITTLE THINGS, a free MOND model is preferred to a universal value at $\sim 8\sigma$, but this is of doubtful physical significance. For MOG, the story is different, here we find $\gtrsim 8\sigma$ preferences for all halos (or MOND) against universal MOG models with significant exclusions in individual galaxies across both samples. Thus, a proposed universal rotation curve model derived from MOG is quite strongly disfavoured.

Figures

Figures reproduced from arXiv: 2605.27217 by the authors.

Figure 1
Figure 1. Combined leave-one-out ELPD for SPARC (upper) and LITTLE THINGS (lower) samples. Burkert values are in black, MOND in magneta, and MOG in green. The error bars show the standard error of the ELPD. The dotted lines show the standard error on ΔELPD. Note that more negative values indicate a worse model. MOND acceleration scale. Once again, a universal MOG model is strongly rejected. To discuss individual galaxy prefer… view at source ↗
Figure 2
Figure 2. Per galaxy ELPD for SPARC (upper) and LITTLE THINGS (lower) samples. Burkert values are in black, MOND in magneta, and MOG in green. The error bars show the standard error of the ELPD. The dotted lines show the standard error on ΔELPD. Note that more negative values indicate a worse model. 5.1 SPARC sample We begin by assessing the 𝑐200 fits. First, the two cases we do not expect to the reproduce the Dutton & Macciò… view at source ↗
Figure 4
Figure 4. 𝑐200 vs 𝑀200 for the various halo models fitted to the SPARC dwarf sample. The yellow lines reflect the concentration model from Dutton & Macciò (2014). Note that this prior was not applied to the Burkert or isothermal halos. For Burkert and L13, these 𝑐200 relationships are clearly worth ex￾ploring in the full SPARC sample. If this result is robust in larger samples it provides a fascinating consistency check, and … view at source ↗
Figures from the paper (11 more)
Figure 5
Figure 5. Figure 5: 𝑀∗ vs 𝑀200 for the various halo models fitted to the SPARC dwarf sample. The yellow lines prior from Moster et al. (2012). observations forces the inclusion of non-circular motion effects (Lelli et al. 2016a). For the concentration we display the results in [PITH_FULL…
Figure 6
Figure 6. Figure 6: 𝑌𝑑 fitted for the various halo models fitted to the SPARC dwarf sample. The yellow lines reflect the prior from Schombert et al. (2018). In the case of the halo mass, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: MOND model values of 𝑎0 and 𝑌𝑑 for the various galaxies in the SPARC dwarf sample. For 𝑌𝑑 the yellow lines reflect the prior from Schombert et al. (2018). Whereas, for 𝑎0 it reflects 1.2 × 10−13 km s−2 with a 12% tolerance from Desmond (2023) [PITH_FULL_IMAGE:figures/…
Figure 8
Figure 8. Figure 8: MOND model values of 𝑎0, 𝜁 , and 𝑌𝑑 for the various galaxies in the SPARC dwarf sample. For 𝑌𝑑 the yellow lines reflect the prior from Schombert et al. (2018). Whereas, for 𝑎0 it reflects 1.2 × 10−13 km s−2 with a 12% tolerance from Desmond (2023). Finally, for 𝜁 the y…
Figure 9
Figure 9. Figure 9: MOG model values of 𝐷, 𝐸, and 𝑌𝑑 for the various galaxies in the SPARC dwarf sample. Black circles display the flat prior result, green squares are that for a lognormal prior. For 𝑌𝑑 the yellow lines reflect the prior from Schombert et al. (2018). Whereas, for 𝐷 it ref…
Figure 10
Figure 10. Figure 10: 𝑐200 vs 𝑀200 for the various halo models fitted to the LITTLE THINGS dwarf sample. The yellow lines reflect the concentration model from Dutton & Macciò (2014). Note that this prior was not applied to the Burkert or isothermal halos. ert halos over MOND. A more robust…
Figure 11
Figure 11. Figure 11: 𝑀∗ vs 𝑀200 for the various halo models fitted to the LITTLE THINGS dwarf sample. The yellow lines prior from Moster et al. (2012). our 𝑎0 values compare well with those in Khelashvili et al. (2024), further evidencing that differences occur in the DM modelling. These …
Figure 12
Figure 12. Figure 12: 𝑌𝑑 fitted for the various halo models fitted to the LITTLE THINGS dwarf sample. The yellow lines reflect the prior from Schombert et al. (2018). Insignificantly indicating larger variations in relative error lead to a preference for Burkert halos, again in the opposit…
Figure 13
Figure 13. Figure 13: MOND model values of 𝑎0 and 𝑌𝑑 for the various galaxies in the LITTLE THINGS dwarf sample. For 𝑌𝑑 the yellow lines reflect the prior from Schombert et al. (2018). Whereas, for 𝑎0 it reflects 1.2 × 10−13 km s−2 with a 12% tolerance from Desmond (2023). these we highlig…
Figure 14
Figure 14. Figure 14: MOG model values of 𝐷, 𝐸, and 𝑌𝑑 for the various galaxies in the LITTLE THINGS dwarf sample. Black circles display the flat prior result, green squares are that for a lognormal prior. For 𝑌𝑑 the yellow lines reflect the prior from Schombert et al. (2018). Whereas, for…
Figure 15
Figure 15. Figure 15: Einasto 𝛼𝑒 values for each galaxy in the two samples. The Dutton & Macciò (2014) value is displayed in the yellow line. Upper: SPARC. Lower: LITTLE THINGS. sampling is made available on Zenodo, along with example analysis scripts. REFERENCES Abril-Pla O., et al., 2023…

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Works this paper leans on

1 extracted references · 1 canonical work pages

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    work page arXiv 2023

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