Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 29

The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.

Vitamin D, Its Role in Recovery after Muscular Damage Following Exercise

Caballero-García, Alberto, Córdova-Martínez, Alfredo, Vicente-Salar, Néstor, Roche, Enrique, Pérez-Valdecantos, Daniel·2021·Nutrients

Abstract

Aside from its role in bone metabolism, vitamin D is a key immunomodulatory micronutrient. The active form of vitamin D (1,25(OH)D) seems to modulate the innate immune system through different mechanisms. The vitamin is involved in the differentiation of monocytes into macrophages, increasing the phagocytic and chemotactic functions of these cells. At the same time, vitamin D enables efferocytosis and prevents immunopathology. In addition, vitamin D is involved in other processes related to immune function, such as inflammation. Regarding muscle tissue, vitamin D plays an active role in muscle inflammatory response, protein synthesis, and regulation of skeletal muscle function. Two mechanisms have been proposed: A direct role of 1,25(OH)D binding to vitamin D receptors (VDRs) in muscle cells and the modulation of calcium transport in the sarcoplasmic reticulum. This second mechanism needs additional investigation. In conclusion, vitamin D seems to be effective in cases of deficiency and/or if there is a great muscular commitment, such as in high intensity exercises.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3390/nu13072336

Cites

6 of 6 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 6 references

Research works printed but not linked: 95

  1. Morton, 2012, Seasonal Variation in Vitamin D Status in Professional Soccer Players of the English Premier League, Appl. Physiol. Nutr. Metab., 37, 798, 10.1139/h2012-037 · DOI
  2. Beck, 2014, Vitamin D and Skeletal Muscle Function in Athletes, Curr. Opin. Clin. Nutr. Metab. Care, 17, 539, 10.1097/MCO.0000000000000105 · DOI
  3. Garay, 2007, Calcitriol Derivatives with Two Different Side-Chains at C-20. Part 4: Further Chain Modifications that Alter VDR-Dependent Monocytic Differentiation Potency in Human Leukemia Cells, Bioorg. Med. Chem., 15, 4444, 10.1016/j.bmc.2007.04.034 · DOI
  4. Ahmed, 2009, Low Serum 25 (OH) Vitamin D Levels (<32 ng/mL) Are Associated with Reversible Myositis-Myalgia in Statin-Treated Patients, Transl. Res., 153, 11, 10.1016/j.trsl.2008.11.002 · DOI
  5. Singh, 2018, Treatment of Vitamin D Deficiency and Comorbidities: A Review, J. Assoc. Physicians India, 66, 75
  6. Holick, 2007, Vitamin D Deficiency, N. Engl. J. Med., 357, 266, 10.1056/NEJMra070553 · DOI · Paper page
  7. Baeke, 2010, Vitamin D: Modulator of the Immune System, Curr. Opin. Pharmacol., 10, 482, 10.1016/j.coph.2010.04.001 · DOI · Paper page
  8. Hewison, 2011, Vitamin D and Innate and Adaptive Immunity, Vitamins & Hormones, Volume 86, 23, 10.1016/B978-0-12-386960-9.00002-2 · DOI
  9. Xu, 1993, 1,25-Dihydroxyvitamin D3 Exerts Opposing Effects to IL-4 on MHC Class-II Antigen Expression, Accessory Activity, and Phagocytosis of Human Monocytes, Scand. J. Immunol., 38, 535, 10.1111/j.1365-3083.1993.tb03237.x · DOI
  10. Willis, 2010, Vitamin D and Athletes, Curr. Sports Med. Rep., 9, 220, 10.1249/JSR.0b013e3181e7dd45 · DOI · Paper page
  11. Willis, 2012, Vitamin D Status and Biomarkers of Inflammation in Runners, J. Sports Med., 3, 35
  12. Campbell, 2006, Muscle Strength and Vitamin D in Older People, Gerontology, 52, 335, 10.1159/000094981 · DOI
  13. Ceglia, 2008, Vitamin D and Skeletal Muscle Tissue and Function, Mol. Asp. Med., 29, 407, 10.1016/j.mam.2008.07.002 · DOI · Paper page
  14. Dinarello, 2003, Anti-Cytokine Therapeutics and Infections, Vaccine, 21, S24, 10.1016/S0264-410X(03)00196-8 · DOI
  15. Prineas, 1965, Myopathy in Metabolic Bone Disease, Br. Med. J., 1, 1034, 10.1136/bmj.1.5441.1034 · DOI
  16. Dalakas, 2010, Immunotherapy of Myositis: Issues, Concerns and Future Prospects, Nat. Rev. Rheumatol., 6, 129, 10.1038/nrrheum.2010.2 · DOI
  17. Ceglia, 2013, Vitamin D and Its Role in Skeletal Muscle, Calcif. Tissue Int., 92, 151, 10.1007/s00223-012-9645-y · DOI · Paper page
  18. Irani, 1976, Electromyography in Nutritional Osteomalacic Myopathy, J. Neurol. Neurosurg. Psychiatry, 10, 686, 10.1136/jnnp.39.7.686 · DOI
  19. Barker, 2013, Higher Serum 25-Hydroxyvitamin D Concentrations Associate with a Faster Recovery of Skeletal Muscle Strength after Muscular Injury, Nutrients, 5, 1253, 10.3390/nu5041253 · DOI
  20. Stratos, 2013, Vitamin D Increases Cellular Turnover and Functionally Restores the Skeletal Muscle after Crush Injury in Rats, Am. J. Pathol., 182, 895, 10.1016/j.ajpath.2012.11.006 · DOI
  21. Paulsen, 2012, Leucocytes, Cytokines and Satellite Cells: What Role Do They Play in Muscle Damage and Regeneration Following Eccentric Exercise?, Exerc. Immunol. Rev., 18, 42
  22. Warren, 1999, Measurement Tools Used in the Study of Eccentric Contraction-Induced Injury, Sports Med., 27, 43, 10.2165/00007256-199927010-00004 · DOI · Paper page
  23. Choi, 2013, Vitamin D3 Supplementation Modulates Inflammatory Responses from the Muscle Damage Induced by High-Intensity Exercise in SD Rats, Cytokine, 63, 27, 10.1016/j.cyto.2013.03.018 · DOI
  24. Pojednic, 2015, Vitamin D Receptor Protein Is Associated with Interleukin-6 in Human Skeletal Muscle, Endocrine, 49, 512, 10.1007/s12020-014-0505-6 · DOI
  25. Lund, 1979, Myopathy in Bone Loss of Ageing: Improvement by Treatment with 1 Alpha-Hydroxycholecalciferol and Calcium, Clin. Sci., 56, 157, 10.1042/cs0560157 · DOI · Paper page
  26. Srikuea, 2012, VDR and CYP27B1 Are Expressed in C2C12 Cells and Regenerating Skeletal Muscle: Potential Role in Suppression of Myoblast Proliferation, Am. J. Physiol. Cell Physiol., 303, C396, 10.1152/ajpcell.00014.2012 · DOI
  27. Foo, 2009, Low Vitamin D Status Has an Adverse Influence on Bone Mass, Bone Turnover, and Muscle Strength in Chinese Adolescent Girls, J. Nutr., 139, 1002, 10.3945/jn.108.102053 · DOI
  28. Wacker, 2013, Vitamin D—Effects on Skeletal and Extraskeletal Health and the Need for Supplementation, Nutrients, 5, 111, 10.3390/nu5010111 · DOI · Paper page
  29. Brech, 2017, Serum 25-Hydroxyvitamin D Levels Are Associated with Functional Capacity but Not with Postural Balance in Osteoporotic Postmenopausal Women, Clinics (Sao Paulo), 72, 11, 10.6061/clinics/2017(01)03 · DOI
  30. Barker, 2012, Different Doses of Supplemental Vitamin D Maintain Interleukin-5 without Altering Skeletal Muscle Strength: A Randomized, Double-Blind, Placebocontrolled Study in Vitamin D Sufficient Adults, Nutr. Metab., 9, 16, 10.1186/1743-7075-9-16 · DOI
  31. Barker, 2013, Circulating Pro-Inflammatory Cytokines Are Elevated and Peak Power Output Correlates with 25-Hydroxyvitamin D in Vitamin D Insufficient Adults, Eur. J. Appl. Physiol., 113, 1523, 10.1007/s00421-012-2582-7 · DOI
  32. Schleithoff, 2006, Vitamin D Supplementation Improves Cytokine Profiles in Patients with Congestive Heart Failure: A Double-Blind, Randomized, Placebo-Controlled Trial, Am. J. Clin. Nutr., 83, 754, 10.1093/ajcn/83.4.754 · DOI · Paper page
  33. Barker, 2014, Vitamin D Sufficiency Associates with An Increase in Anti-Inflammatory Cytokines after Intense Exercise in Humans, Cytokine, 65, 134, 10.1016/j.cyto.2013.12.004 · DOI
  34. Visser, 2003, Low Vitamin D and High Parathyroid Hormone Levels as Determinants of Loss of Muscle Strength and Muscle Mass (Sarcopenia): The Longitudinal Aging Study Amsterdam, J. Clin. Endocrinol. Metab., 88, 5766, 10.1210/jc.2003-030604 · DOI · Paper page
  35. Wyon, 2014, The Influence of Winter Vitamin D Supplementation on Muscle Function and Injury Occurrence in Elite Ballet Dancers: A Controlled Study, J. Sci. Med. Sport, 17, 8, 10.1016/j.jsams.2013.03.007 · DOI · Paper page
  36. Close, 2013, The Effects of Vitamin D(3) Supplementation on Serum Total 25 [OH] D Concentration and Physical Performance: A Randomised Dose-Response Study, Br. J. Sports Med., 47, 692, 10.1136/bjsports-2012-091735 · DOI · Paper page
  37. Carswell, 2018, Influence of Vitamin D Supplementation by Sunlight or Oral D3 on Exercise Performance, Med. Sci. Sports Exerc., 50, 2555, 10.1249/MSS.0000000000001721 · DOI · Paper page
  38. Koundourakis, N.E., Androulakis, N.E., Malliaraki, N., and Margioris, A.N. (2014). Vitamin D and Exercise Performance in Professional Soccer Players. PLoS ONE, 9. · DOI
  39. Mielgo-Ayuso, J., Calleja-González, J., Urdampilleta, A., León-Guereño, P., Córdova, A., Caballero-García, A., and Fernandez-Lázaro, D. (2018). Effects of Vitamin D Supplementation on Haematological Values and Muscle Recovery in Elite Male Traditional Rowers. Nutrients, 10. · DOI · Paper page
  40. Hamilton, 2014, Vitamin D Concentration in 342 Professional Football Players and Association with Lower Limb Isokinetic Function, J. Sci. Med. Sport, 17, 139, 10.1016/j.jsams.2013.03.006 · DOI · Paper page
  41. Agergaard, 2015, Does Vitamin-D Intake during Resistance Training Improve the Skeletal Muscle Hypertrophic and Strength Response in Young and Elderly Men?—A Randomized Controlled Trial, Nutr. Metab. (Lond), 12, 32, 10.1186/s12986-015-0029-y · DOI
  42. Pinto, 2019, The Proinflammatory Effects of Chronic Excessive Exercise, Cytokine, 119, 57, 10.1016/j.cyto.2019.02.016 · DOI
  43. Peake, 2015, Cytokine Expression and Secretion by Skeletal Muscle Cells: Regulatory Mechanisms and Exercise Effects, Exerc. Immunol. Rev., 21, 8
  44. Feghali, 1997, Cytokines in Acute and Chronic Inflammation, Front. Biosci., 2, 12, 10.2741/A171 · DOI · Paper page
  45. Dinarello, 2000, Proinflammatory Cytokines, Chest, 118, 503, 10.1378/chest.118.2.503 · DOI · Paper page
  46. Cerqueira, 2020, Inflammatory Effects of High and Moderate Intensity Exercise—A Systematic Review, Front. Physiol., 10, 1550, 10.3389/fphys.2019.01550 · DOI · Paper page
  47. Allen, 2015, Exercise and the Regulation of Inflammatory Responses, Prog. Mol. Biol. Transl. Sci., 135, 337, 10.1016/bs.pmbts.2015.07.003 · DOI
  48. Moldoveanu, 2001, The Cytokine Response to Physical Activity and Training, Sports Med., 31, 115, 10.2165/00007256-200131020-00004 · DOI · Paper page
  49. Gleeson, 2011, The Anti-Inflammatory Effects of Exercise: Mechanisms and Implications for the Prevention and Treatment of Disease, Nat. Rev. Immunol., 11, 607, 10.1038/nri3041 · DOI · Paper page
  50. Martin, 2004, Protection against Muscle Damage in Competitive Sports Players: The Effect of the Immunomodulator AM3, J. Sports Sci., 22, 827, 10.1080/02640410410001716742 · DOI
  51. Monserrat, 2006, Effects of AM3 (Inmunoferon) on Increased Serum Concentrations of Interleukin-6 and Tumour Necrosis Factor Receptors I and II in Cyclists, J. Sports Sci., 24, 565, 10.1080/02640410500141158 · DOI
  52. Sureda, 2015, Modulation of TNF-α, TNF-α Receptors and IL-6 after Treatment with AM3 in Professional Cyclists, J. Sports Med. Phys. Fitness, 55, 345
  53. Fernández-Lázaro, D., Mielgo-Ayuso, J., Seco-Calvo, J., Córdova-Martínez, A., Caballero-García, A., and Fernandez-Lazaro, C.I. (2020). Modulation of Exercise-Induced Muscle Damage, Inflammation, and Oxidative Markers by Curcumin Supplementation in a Physically Active Population: A Systematic Review. Nutrients, 12. · DOI
  54. Carrera-Quintanar, L., Funes, L., Herranz-López, M., Martínez-Peinado, P., Pascual-García, S., Sempere, J.M., Boix-Castejón, M., Córdova, A., Pons, A., and Micol, V. (2020). Antioxidant Supplementation Modulates Neutrophil Inflammatory Response to Exercise-Induced Stress. Antioxidants, 9. · DOI
  55. Sureda, 2007, Intense Physical Activity Enhances Neutrophil Antioxidant Gene Expression. Immunocytochemistry Evidence for Catalase Secretion, Free Rad. Res., 41, 874, 10.1080/10715760701416459 · DOI
  56. Wang, 2002, The Role of NF-KappaB in the Regulation of Cell Stress Responses, Int. Immunopharmacol., 2, 1509, 10.1016/S1567-5769(02)00058-9 · DOI · Paper page
  57. Baumann, 1994, The Acute Phase Response, Immunol. Today, 15, 74, 10.1016/0167-5699(94)90137-6 · DOI · Paper page
  58. Kammuler, 1995, Recombinant Human Interleukin-6: Safety Issues of a Pleiotropic Growth Factor, Toxicology, 105, 91, 10.1016/0300-483X(95)03128-3 · DOI
  59. Pedersen, 2000, Exercise and the Immune System: Regulation, Integration, and Adaptation, Physiol. Rev., 80, 1055, 10.1152/physrev.2000.80.3.1055 · DOI · Paper page
  60. Suzuki, 2002, Systemic Inflammatory Response to Exhaustive Exercise, Cytokine Kinetics. Exerc. Immunol. Rev., 8, 6
  61. Billiau, 1996, Interferon Gamma: Biology and Role in Pathogenesis, Adv. Immunol., 62, 61, 10.1016/S0065-2776(08)60428-9 · DOI · Paper page
  62. Viti, 1985, Effect of Exercise on Plasma Interferon Levels, J. Appl. Physiol., 59, 426, 10.1152/jappl.1985.59.2.426 · DOI
  63. Ruggiero, 1986, Induction of Synthesis of Tumor Necrosis Factor Alpha by Interferon Gamma, J. Immunol., 136, 2445, 10.4049/jimmunol.136.7.2445 · DOI · Paper page
  64. Lowenstein, 1992, Nitric Oxide, a Novel Biologic Messenger, Cell, 70, 705, 10.1016/0092-8674(92)90301-R · DOI · Paper page
  65. Kanda, 2013, Eccentric Exercise-Induced Delayed-Onset Muscle Soreness and Changes in Markers of Muscle Damage and Inflammation, Exerc. Immunol. Rev., 19, 72
  66. Tidball, 2005, Inflammatory Processes in Muscle Injury and Repair, Am. J. Physiol. Regul. Integr. Comp. Physiol., 288, R345, 10.1152/ajpregu.00454.2004 · DOI · Paper page
  67. Toumi, 2006, The Role of Neutrophils in Injury and Repair Following Muscle Stretch, J. Anat., 208, 459, 10.1111/j.1469-7580.2006.00543.x · DOI
  68. Baskurt, 2011, Nitric Oxide, Erythrocytes and Exercise, Clin. Hemorheol. Microcirc., 49, 175, 10.3233/CH-2011-1467 · DOI
  69. Clarkson, 2000, Antioxidants: What Role Do They Play in Physical Activity and Health?, Am. J. Clin. Nutr., 72, 637S, 10.1093/ajcn/72.2.637S · DOI · Paper page
  70. Ceglia, 2011, Serum 25-Hydroxyvitamin D Concentration and Physical Function in Adult Men, Clin. Endocrinol., 74, 370, 10.1111/j.1365-2265.2010.03926.x · DOI
  71. Remelli, F., Vitali, A., Zurlo, A., and Volpato, S. (2019). Vitamin D Deficiency and Sarcopenia in Older Persons. Nutrients, 11. · DOI · Paper page
  72. Grimaldi, 2013, 25(OH) Vitamin D Is Associated with Greater Muscle Strength in Healthy Men and Women, Med. Sci. Sports Exerc., 45, 157, 10.1249/MSS.0b013e31826c9a78 · DOI
  73. Marantes, 2011, Is Vitamin D a Determinant of Muscle Mass and Strength?, J. Bone Miner. Res., 26, 2860, 10.1002/jbmr.510 · DOI
  74. Houston, 2012, Health ABC Study. 25-Hydroxyvitamin D Status and Change in Physical Performance and Strength in Older Adults: The Health, Aging, and Body Composition Study, Am. J. Epidemiol., 176, 1025, 10.1093/aje/kws147 · DOI
  75. Bischoff, 1999, Muscle Strength in the Elderly: Its Relation to Vitamin D Metabolites, Arch. Phys. Med. Rehab., 80, 54, 10.1016/S0003-9993(99)90307-6 · DOI · Paper page
  76. Sohl, 2013, Vitamin D Status Is Associated with Functional Limitations and Functional Decline in Older Individuals, J. Clin. Endocrinol. Metab., 98, E1483, 10.1210/jc.2013-1698 · DOI
  77. Cannell, 2009, Athletic Performance and Vitamin D, Med. Sci. Sports Exerc., 41, 1102, 10.1249/MSS.0b013e3181930c2b · DOI · Paper page
  78. De la Puente Yagüe, M., Collado, L., Ciudad-Cabañas, M.J., and Cuadrado-Cenzual, M.A. (2020). Role of Vitamin D in Athletes and Their Performance: Current Concepts and New Trends. Nutrients, 12. · DOI · Paper page
  79. Steinacker, 2004, New Aspects of the Hormone and Cytokine Response to Training, Eur. J. Appl. Physiol., 91, 382, 10.1007/s00421-003-0960-x · DOI
  80. Hennigar, 2017, Nutritional Interventions and the IL-6 Response to Exercise, FASEB J., 31, 3719, 10.1096/fj.201700080R · DOI
  81. Brandenburg, 2012, The Role of Vitamin D in Cardiovascular Disease: From Present Evidence to Future Perspectives, Atherosclerosis, 225, 253, 10.1016/j.atherosclerosis.2012.08.005 · DOI
  82. Kim, D.H., Meza, C.A., Clarke, H., Kim, J.S., and Hickner, R.C. (2020). Vitamin D and Endothelial Function. Nutrients, 12. · DOI · Paper page
  83. Jain, 2016, 1,25(OH)2D3 Inhibits Oxidative Stress and Monocyte Adhesion by Mediating the Upregulation of GCLC and GSH in Endothelial Cells Treated with Acetoacetate (ketosis), J. Steroid Biochem. Mol. Biol., 159, 94, 10.1016/j.jsbmb.2016.03.002 · DOI
  84. Andrukhova, 2014, Vitamin D Is a Regulator of Endothelial Nitric Oxide Synthase and Arterial Stiffness in Mice, Mol. Endocrinol., 28, 53, 10.1210/me.2013-1252 · DOI · Paper page
  85. 2012, Relevance of Vitamin D in Muscle Health, Rev. Endocr. Metab. Disord., 13, 71, 10.1007/s11154-011-9200-6 · DOI
  86. Hamilton, 2011, Vitamin D and Athletic Performance: The Potential Role of Muscle, Asian J. Sports Med., 2, 211, 10.5812/asjsm.34736 · DOI
  87. DeLuca, 2004, Overview of General Physiologic Features and Functions of Vitamin D, Am. J. Clin. Nutr., 80, 1689S, 10.1093/ajcn/80.6.1689S · DOI · Paper page
  88. Haussler, 2008, Vitamin D Receptor: Molecular Signaling and Actions of Nutritional Ligands in Disease Prevention, Nutr. Rev., 66, S98, 10.1111/j.1753-4887.2008.00093.x · DOI · Paper page
  89. Li, 2018, Vitamin D Prevents Lipid Accumulation in Murine Muscle through Regulation of Pparγ and Perilipin-2 Expression, J. Steroid Biochem. Mol. Biol., 177, 116, 10.1016/j.jsbmb.2017.10.010 · DOI
  90. Hamilton, 2010, Vitamin D and Human Skeletal Muscle, Scand. J. Med. Sci. Sports, 20, 182
  91. Salminen, 2015, Vitamin D Status and Physical Function in Older Finnish People: A One-Year Follow-Up Study, Arch. Gerontol. Geriatr., 61, 419, 10.1016/j.archger.2015.08.014 · DOI
  92. Ryan, 2016, 1alpha,25-Dihydroxyvitamin D3 Regulates Mitochondrial Oxygen Consumption and Dynamics in Human Skeletal Muscle Cells, J. Biol. Chem., 291, 1514, 10.1074/jbc.M115.684399 · DOI
  93. Ogan, 2013, Vitamin D and the Athlete: Risks, Recommendations, and Benefits, Nutrients, 5, 1856, 10.3390/nu5061856 · DOI · Paper page
  94. Carlberg, 2018, The Concept of the Personal Vitamin D Response Index, J. Steroid Biochem. Mol. Biol., 175, 12, 10.1016/j.jsbmb.2016.12.011 · DOI
  95. Holick, 2011, Endocrine Society. Evaluation, Treatment, and Prevention of Vitamin D Deficiency: An Endocrine Society Clinical Practice Guideline, J. Clin. Endocrinol. Metab., 96, 1911, 10.1210/jc.2011-0385 · DOI · Paper page

Metadata

Authors
Caballero-García, A., Córdova-Martínez, A., Vicente-Salar, N., Roche, E., & Pérez-Valdecantos, D.
Venue
Nutrients
Publisher
MDPI AG
Published
2021-07-08
Volume
13
Issue
7
Pages
2336
ISSN
2072-6643
Cited by
29
References
6
Language
en

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.