Here the proofs corrections in the order they appear. Page 1, added highlighted text "di Pisa" is OK. agreed to all other changes Page 3, in paragraph 2 (starting with Galactic magnetic fields...), after the sentence "There has long been a debate about the origin of such magnetic fields: are they primordial or dynamo-generated, or perhaps a combination of the two?", put here the marginnote, \begin{marginnote}[] \entry{Dynamos}{convert kinetic energy into magnetic energy} \end{marginnote} from page 7. Page 3, in paragraph 2, 2 lines below, suggested change ok, i.e., change "there has been a shift in attention from" --> "attention has shifted from" Page 3, in paragraph 4, middle, suggested change ok, i.e., change "effect in question is what is referred to as the" --> "effect in question has been termed the" Page 3, in paragraph 4 (starting with "At the time of the..."), middle, to before the 2nd sentence (starting with "Specifically, the mean-field..." move and modify marginnote "catastrophic quenching" from page 15 to here, and merge with that on page 4: \entry{Catastrophic quenching means}{$\alpha\to0$ as $\Rm\to\infty$, so it limits the large-scale field at large $\Rm$} Page 3, in paragraph 4, middle, suggested change ok, i.e., delete: "``Catastrophic'' can mean that the coefficient $\alpha$ goes to zero as $\Rm$ goes to infinity." Page 4: omit marginnote "Large magnetic ..." Page 4, Sec 2.1, paragraph 2, middle, suggested change ok, i.e., change "commonly referred to as primordial" --> "commonly termed the primordial" Page 4, Sec 2.1, paragraph 2, middle, suggested change *not* ok. The term "face-on" is established in galactic physics; "head-on" is never used. Page 4, Sec 2.1, paragraph 2, middle, suggested change ok, i.e., change "contrasted this with the axisymmetric" --> "contrasted BSS with an axisymmetric" Page 4, it is ok to remove italics from boldfaced symbols such as A, B, and \hat{z}. Page 5, text box, the subscript "e" in "n_e" in the mathematical expression for RM should then also be made roman. Page 5, the original sketch did not include the axisymmetric spiral, so we must not credit them for everything. Also, a sketch like this has been recreated many times by others. We do give credit to the authors of the original paper, but asking for permission from the publisher would not really be justified. Page 5, caption to Fig.1, we refer to all 3 subpanels, so change bottom panel --> bottom panels. Page 5, in and after Eq.(1), the use of D/Dt for the advective derivative is common in the field. It is indeed defined, so it should be ok. Page 6, change marginnote \entry{$m=0$ and $m=1$ magnetic fields}{vary with azimuth $\phi$ like $e^{\ii m\phi}$ and correspond to ASS and BSS fields} to \entry{$m=0$ and $m=1$ magnetic fields}{are defined as ASS and BSS fields and vary with azimuth $\phi$ like $e^{\ii m\phi}$.} Page 6, line 2, suggested change ok, i.e., change "and is able to predict" --> "and can predict" Page 6, bottom of paragraph 1, suggested change ok, i.e., change like -> such as Page 6, paragraph 2, suggested change ok, i.e., delete "it was shown that" Page 6, Sec. 2.2, paragraph 2, suggested change ok, i.e., change called the -> termed the Page 6, Sec. 2.2, paragraph 2, change "for a definition of" --> "for the definition of" Page 7, the marginnote for "Dynamo" has been moved to page 3, and that on Dynamos with Euler potentials should be removed. Page 7, as noted before, the D/Dt is a derivative, but it is commonly written like this and cannot be replaced by d/dt. Page 8, Sec. 2.3, change ok. Page 8, Sec. 2.4, the page number for the direct quote is 47. Page 8, Sec. 2.4, end of paragraph 1, suggested change ok, i.e., change "This" --> "His speculation" % EN I think these are the missing ones: Page 9, "The alpha effect: example of a mean-field dynamo": --"higher derivatives terms" should become "higher-derivative terms" --Ok with rephrasing --Ok with adding z subscript as k_z(?) --"later in this review" meaning Sections 2.4 and 4.1 (?) %%% Page 9, Sec. 2.4, end of paragraph 1, suggested change ok, i.e., move marginnote on "Large-scale dynamos" from page 11 to here, i.e., put \entry{Large-scale dynamos}{create coherent structures on large spatial and temporal scales} before the paragraph starting with "The first rigorous examples .." Page 9, Sec. 2.4, OK to remove margin note "The evolution of B" Page 9, Sec. 2.4, end of paragraph 4 (ending with "from earlier times"), and before paragraph 5 (starting with "These classifications...") add a margin note explaining the pumping velocity: \entry{Pumping velocity $\bm{\gamma}$}{is a contribution to the mean electromotive force given by the off-diagonal terms of the $\alpha$ tensor through $\gamma_i=-\frac{1}{2}\epsilon_{ijk}\alpha_{jk}$} Page 10, Sec. 2.4, end of paragraph 6, OK to rephrase. Page 10, Sec. 2.4, Keep "rank three tensor" throughout. Page 11, Sec. 2.5, end of paragraph 1, suggested change ok, i.e., change "mean" --> "mean fields" Page 11, Sec. 2.5 OK to change to "also depends" Page 11, Remove margin note "Magnetic Reynolds number" Page 11, Move the margin note "Large-scale dynamo" to page 8, as already stated above. Page 11, Remove margin note "Type of averaging" Page 11, Sec. 2.6. OK to change "was found to be" to "is" Page 11, Sec. 2.6, OK with removed italics Page 12, Table 2, OK to change checkmarks with "Yes" and the dashes with "No" Page 12, Sec. 2.6.1. Ok to change to "Roberts flow I" to match term in margin Page 12, Sec. 2.6.2 "they" can be replaced by "the two components”" Page 12, Sec. 2.6.2 OK with the rephrase Page 13, Sec. 2.6.3. The reference to R{\"a}dler is Radler 1969: @ARTICLE{1969MDAWB..11..194R, author = {{R{\"a}dler}, K.~H.}, title = "{On the Electrodynamics of Turbulent Fields under the Influence of Corilois Forces}", journal = {Monats. Dt. Akad. Wiss}, keywords = {MAGNETIC FIELDS, TURBULENCE, ROTATION, THEORY}, year = 1969, month = jan, volume = {11}, pages = {194-201}, adsurl = {https://ui.adsabs.harvard.edu/abs/1969MDAWB..11..194R}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } Page 13, Sec. 2.6.3, "as will be discussed below" can be replaced with "as will be discussed in the following section" or "Section 2.6.4" Page 13, Sec. 2.6.4, OK to change to “Another important class of large-scale dynamos” Page 13, Sec. 2.6.4, OK to delete "it was found" Page 13, Change margin note "Incoherent alpha effect" to: \entry{An incoherent $\alpha$ effect}{is an $\alpha$ effect with frequent sign changes} Page 13, Sec. 2.6.4. OK to delete "what is known as" Page 13, just under "2.7. Small-Scale Dynamos", move the first paragraph from 2.7.1 to here: "Under fully isotropic conditions and without helicity, dynamo action is still possible---both for large and small values of the magnetic Prandtl number $\Pm$ \citep{Kaz68}; see the detailed discussion by \cite{Scheko+04}. The existence of small-scale dynamos under isotropic conditions implies that the concept of nonmagnetic Kolmogorov turbulence hardly exists in astrophysics, where the medium is usually always highly conducting." Page 14, Remove margin note "Nonmagnetic Kolmogorov turbulence" Page 14, Sec. 2.7.1, OK with rephrase page 14, Sec.3.1, paragraph 2, line 5, regarding your query, replace "one" by "energy density" page 14, line -4 (from the bottom), after "in three dimensions", add ", which is routinely seen during laboratory plasma relaxation \citep{Ji+95}" with reference: @ARTICLE{Ji+95, author = {{Ji}, H. and {Prager}, S.~C. and {Sarff}, J.~S.}, title = "{Conservation of Magnetic Helicity during Plasma Relaxation}", journal = {\prl}, year = 1995, month = apr, volume = {74}, number = {15}, pages = {2945-2948}, doi = {10.1103/PhysRevLett.74.2945}, adsurl = {https://ui.adsabs.harvard.edu/abs/1995PhRvL..74.2945J}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } Page 15, The margin note "Catastrophic quenching" is to be removed from here, content merged with the one on Page 3 (see earlier note). Page 15, Remove marginnote "In a closed domain" Page 15, Section 3.1, OK with rephrase Page 15, Sec. 3.2. OK with rephrase Page 15, Sec. 3.3, replace "what they called a ``vacuum cleaner experiment''" --> "the preferential removal of small scale magnetic fields" Page 15., Sec. 3.3. OK to change "it" --> "this experiment". Page 17, Sec. 3.3 OK with rephrase. Page 17, Sec. 3.3 OK to remove "found to be". Page 17, in the caption to Figure 5, suggested change not ok; instead, remove "the small-scale magnetic helicity", so that it reads "right-hand side of Equation 8". Page 17, Rephrase margin note \begin{marginnote}[] \entry{Convolution}{an operation that becomes a multiplication in Fourier space} \end{marginnote} Page 17, Sec. 4.1 Rephrase as "can be expressed nonlocally in terms of" Page 17, Sec 4.1, OK to rephrase as "but we refer the reader to" Page 17, Sec 4.1, OK with rephrase Page 18, Sec. 4.2 OK to change to "termed". Page 18., to avoid having two parentheses one after the other, change opening parenthesis to a colon, i.e., change "new effects emerge (turbulent ..." --> "new effects emerge: turbulent ..." and remove closing parenthesis again. Page 18, Sec. 4.3, OK to change to "termed" Page 18, Sec. 4.3, OK to change to "called" Page 19, Margin note on pumping to be moved to page 9 (instead of "The evolution of B") as per previous note. Page 19, Sec. 4.4 Subscripts not ok. In all four cases, it should read \sin kz or \cos kz. Page 19, Sec. 4.4, OK to change to "termed". Page 19, Sec. 4.4, OK to change to "increases". Page 19, Sec. 4.4, OK to delete "it was found that". Page 19, Sec. 4.4, better change "approximately like" --> "approximately proportional to". Page 19, Sec. 4.4, OK to change "is found to depend" --> "depends". Page 19, Sec. 4.4, OK to change "was found to vary" to "varies" Page 19, Sec. 4.4, OK to change "referred to" to "termed a". Page 19, Sec. 4.4, OK to change "can be" to "is". Page 19, Sec. 4.4, OK to change "field" to "fields". Page 20, textbox "Evolution equation for nonlocality in space and time", OK to change "right inside" --> “right-hand side”. Page 20, textbox "Dynamos from the memory effect" OK to change "it" --> "the memory effect". Page 21, Text to add after Section 5.1 "Possibilities for seed fields" The conditions in the early Universe provide several possibilities for seeding galactic dynamos. The seeds could be primordial, which generally means that they were generated during inflation or phase transitions, or they could originate from a cosmic battery. Other theories also involve later seeding from astrophysical processes. We examine these possibilities in the following sections. By mentioning "cosmic battery" here we can also keep the margin note, but move it to the end of the introductory paragraph of Sec.5.1. Page 21, Section 5.1, Keep capitalization for "Galaxy". Page 21, Textbox "Battery Mechanisms": Add the phrase: "\cite{Garaldi2021} performed cosmological simulations testing, among other scenarios, the efficiency of the Biermann and Durrive battery terms through cosmic time. They found that, although the two batteries behave similarly, the Durrive term produces systematically weaker magnetic fields by approximately three orders of magnitude." At the end of the textbox. Page 22, Sec. 5.1.2, first sentence, OK with suggested rephrase. Page 22, Sec. 5.1.2, replace "ones" with "seeds" (not "magnetic fields" as suggested because it would be too repetitive). Page 22, Sec. 5.1.3, OK to delete "Interestingly" Page 22, Sec. 5.1.3, OK to change "have been able to access" to "have accessed" Page 22, Sec. 5.1.4, suggested change *not* ok. Each of the forces should be referred to in singular form, so change to "of the weak force and the electromagnetic force or the" Page 22, Sec. 5.1.4, OK with rephrase Page 22, Sec. 5.1.4, Replace "In the following" --> "Hereafter". Page 23, Sec. 5.1.4, OK to change "It should be noted" to "Note". Page 23, Sec. 5.1.4, OK to delete "can" Page 23, Sec. 5.1.4, OK to move text to figure caption. The typo in the same caption: "permissible a few strength" should become "permissible field strength", as also mentioned in the figure comments to Glenda Mahoney. Page 23, Figure 7: - Abbreviations: CTA=Cerenkov Telescope Array EW=Electro-Weak LAT=Large Area Telescope QCD=Quantum Chromo Dynamics UHECR=Ultra High-Energy Cosmic Rays -References * Jedamzik & Saveliev is actually *2019* not 2014: @ARTICLE{2019PhRvL.123b1301J, author = {{Jedamzik}, Karsten and {Saveliev}, Andrey}, title = "{Stringent Limit on Primordial Magnetic Fields from the Cosmic Microwave Background Radiation}", journal = {\prl}, keywords = {Astrophysics - Cosmology and Nongalactic Astrophysics, 35Q20, 60J99, 65M06, 68W10, 76W05, 78M31, 83F05, 85A40, J.2}, year = 2019, month = jul, volume = {123}, number = {2}, eid = {021301}, pages = {021301}, doi = {10.1103/PhysRevLett.123.021301}, archivePrefix = {arXiv}, eprint = {1804.06115}, primaryClass = {astro-ph.CO}, adsurl = {https://ui.adsabs.harvard.edu/abs/2019PhRvL.123b1301J}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } * Fujita & Kamada 2016: @ARTICLE{2016PhRvD..93h3520F, author = {{Fujita}, Tomohiro and {Kamada}, Kohei}, title = "{Large-scale magnetic fields can explain the baryon asymmetry of the Universe}", journal = {\prd}, keywords = {High Energy Physics - Phenomenology, Astrophysics - Cosmology and Nongalactic Astrophysics, High Energy Physics - Theory}, year = 2016, month = apr, volume = {93}, number = {8}, eid = {083520}, pages = {083520}, doi = {10.1103/PhysRevD.93.083520}, archivePrefix = {arXiv}, eprint = {1602.02109}, primaryClass = {hep-ph}, adsurl = {https://ui.adsabs.harvard.edu/abs/2016PhRvD..93h3520F}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } * Natwariya & Bhatt 2020: @ARTICLE{2020MNRAS.497L..35N, author = {{Natwariya}, Pravin Kumar and {Bhatt}, Jitesh R.}, title = "{EDGES signal in the presence of magnetic fields}", journal = {\mnras}, keywords = {cosmology: observations, Dark matter, Reionization, first stars, dark ages, Magnetic fields, MHD, magnetic fields, reionization, dark matter, Astrophysics - Cosmology and Nongalactic Astrophysics}, year = 2020, month = sep, volume = {497}, number = {1}, pages = {L35-L39}, doi = {10.1093/mnrasl/slaa108}, archivePrefix = {arXiv}, eprint = {2001.00194}, primaryClass = {astro-ph.CO}, adsurl = {https://ui.adsabs.harvard.edu/abs/2020MNRAS.497L..35N}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } * Jedamzik & Pogosyan 2020: @ARTICLE{2020PhRvL.125r1302J, author = {{Jedamzik}, Karsten and {Pogosian}, Levon}, title = "{Relieving the Hubble Tension with Primordial Magnetic Fields}", journal = {\prl}, keywords = {Astrophysics - Cosmology and Nongalactic Astrophysics, High Energy Physics - Phenomenology}, year = 2020, month = oct, volume = {125}, number = {18}, eid = {181302}, pages = {181302}, doi = {10.1103/PhysRevLett.125.181302}, archivePrefix = {arXiv}, eprint = {2004.09487}, primaryClass = {astro-ph.CO}, adsurl = {https://ui.adsabs.harvard.edu/abs/2020PhRvL.125r1302J}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } * Fermi/LAT is Ackermann et al. 2018: @ARTICLE{2018ApJS..237...32A, author = {{Ackermann}, M. and {Ajello}, M. and {Baldini}, L. and {Ballet}, J. and {Barbiellini}, G. and {Bastieri}, D. and {Bellazzini}, R. and {Bissaldi}, E. and {Blandford}, R.~D. and {Bloom}, E.~D. and {Bonino}, R. and {Bottacini}, E. and {Brandt}, T.~J. and {Bregeon}, J. and {Bruel}, P. and {Buehler}, R. and {Cameron}, R.~A. and {Caputo}, R. and {Caraveo}, P.~A. and {Castro}, D. and {Cavazzuti}, E. and {Charles}, E. and {Cheung}, C.~C. and {Chiaro}, G. and {Ciprini}, S. and {Cohen-Tanugi}, J. and {Costantin}, D. and {Cutini}, S. and {D'Ammando}, F. and {de Palma}, F. and {Desai}, A. and {Di Lalla}, N. and {Di Mauro}, M. and {Di Venere}, L. and {Favuzzi}, C. and {Finke}, J. and {Franckowiak}, A. and {Fukazawa}, Y. and {Funk}, S. and {Fusco}, P. and {Gargano}, F. and {Gasparrini}, D. and {Giglietto}, N. and {Giordano}, F. and {Giroletti}, M. and {Green}, D. and {Grenier}, I.~A. and {Guillemot}, L. and {Guiriec}, S. and {Hays}, E. and {Hewitt}, J.~W. and {Horan}, D. and {J{\'o}hannesson}, G. and {Kensei}, S. and {Kuss}, M. and {Larsson}, S. and {Latronico}, L. and {Lemoine-Goumard}, M. and {Li}, J. and {Longo}, F. and {Loparco}, F. and {Lovellette}, M.~N. and {Lubrano}, P. and {Magill}, J.~D. and {Maldera}, S. and {Manfreda}, A. and {Mazziotta}, M.~N. and {McEnery}, J.~E. and {Meyer}, M. and {Mizuno}, T. and {Monzani}, M.~E. and {Morselli}, A. and {Moskalenko}, I.~V. and {Negro}, M. and {Nuss}, E. and {Omodei}, N. and {Orienti}, M. and {Orlando}, E. and {Ormes}, J.~F. and {Palatiello}, M. and {Paliya}, V.~S. and {Paneque}, D. and {Perkins}, J.~S. and {Persic}, M. and {Pesce-Rollins}, M. and {Piron}, F. and {Porter}, T.~A. and {Principe}, G. and {Rain{\`o}}, S. and {Rando}, R. and {Rani}, B. and {Razzaque}, S. and {Reimer}, A. and {Reimer}, O. and {Reposeur}, T. and {Sgr{\`o}}, C. and {Siskind}, E.~J. and {Spandre}, G. and {Spinelli}, P. and {Suson}, D.~J. and {Tajima}, H. and {Thayer}, J.~B. and {Tibaldo}, L. and {Torres}, D.~F. and {Tosti}, G. and {Valverde}, J. and {Venters}, T.~M. and {Vogel}, M. and {Wood}, K. and {Wood}, M. and {Zaharijas}, G. and {Fermi-LAT Collaboration} and {Biteau}, J.}, title = "{The Search for Spatial Extension in High-latitude Sources Detected by the Fermi Large Area Telescope}", journal = {\apjs}, keywords = {BL Lacertae objects: general, catalogs, gamma rays: general, ISM: H ii Regions, ISM: supernova remnants, Astrophysics - High Energy Astrophysical Phenomena}, year = 2018, month = aug, volume = {237}, number = {2}, eid = {32}, pages = {32}, doi = {10.3847/1538-4365/aacdf7}, archivePrefix = {arXiv}, eprint = {1804.08035}, primaryClass = {astro-ph.HE}, adsurl = {https://ui.adsabs.harvard.edu/abs/2018ApJS..237...32A}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } Page 23, second-last line, *not* ok to change from "galaxy" to Galaxy. Page 24, Section 5.1.5, OK to change highlighted text to "As mentioned in Section 2.1, Martin-Alvarez et al. (2021) traced the evolution of the primordial field and the field injected by stellar sources separately". Page 24, *not* OK to change "SN" to "Sn", but should add "Supernova" before using the acronym (SN). Otherwise ok with rephrase. Page 25, OK to delete "Interestingly". Page 25, Sec. 5.1.6 OK with rephrase. Page 25, Sec. 5.2, OK to change "A number of" to "Several". Page 25, Sec. 5.2, OK to delete "the question of" Page 26, Sec. 5.2.1, OK with rephrase. Page 26, Sec. 5.2.1, delete the duplicate "compression", so that is says: "...associated with 2-D compression, stretching, and bending..." Page 26, Sec. 5.2.1, OK to change "show a visualization of" to "visualize". Page 26, Sec. 5.2.1, OK to change "their" to "Brandenburg & Ntormousi (2022)", but also remove "simulation" afterwards. Page 26, Sec. 5.2.2, OK with addition of "also". Page 27, Text to be added under 6.1 "Global Magnetic Field Structure": One of the strongest existing tests for dynamo theories is the predicted structure of the large-scale magnetic field contrasted to observations. In the next sections we outline the predictions from different models. Page 27, Sec. 6.1.2, OK with rephrase. Page 27, Sec. 6.2, OK with all changes. Page 28, Sec. 6.2, change the beginning of the sentence to: "Yet another very different case is NGC 6946, whose field may consist of structures usually termed magnetic arms. Magnetic arms are often interlaced with the stellar arms, but can also be phase-shifted relative to them (for a more ...." Page 28, Sec. 6.3. OK with both changes. Page 28, Fig. 10, Yes, we should use the proper symbol for the magnetic Reynolds number. Page 29, Sec. 6.4, OK to change "the majority of" to "most" Page 29, Sec. 6.4, keep capitalization for "Galactic" Page 29, Sec. 6.4, OK to change "following section" to “Section 6.5” Page 29, Keep "Galactic" capitalized throughout this page because the discussion regards our Galaxy, not galaxies in general. Page 29, Fig. 11, ok to move ", where the range of RMs is saturated at |RM| = 250 rad m^{-2}" outside the parenteses. Page 30, Sec. 6.5, keep capital for "Galaxy" Page 30, Sec. 6.5, OK to change "who also compare with" to "who also make comparisons with". Page 31, right after Eq. 12, suggested change *not* ok. The asterisk means complex conjugation and is an extra operation, as explained. Page 31, Sec. 6.6, OK to delete "turned out that" Page 31, caption of Fig. 12, the expression in parentheses is to be read as “= 90 minus latitude” Page 31, Sec. 7.1, OK to change "referred to as" to "termed" Page 31, Sec. 7.1, MM stands for "molecular medium", so change "molecular" --> "molecular medium". Page 31, Sec. 7.1, OK with addition of "energy". Page 31, remove margin note "PrM>>1" Page 31, caption of Table 3, should be "molecular medium". Page 32, Sec. 7.1, "further below" refers to Sec. 7.3 Page 32, Sec. 7.2. The suggested rephrase: “However, no similar scheme, such as smoothed particle hydrodynamics (SPH), which rely on divergence cleaning algorithms, is applicable to Lagrangian codes” changes the meaning of the text. "no similar scheme" refers to Constrained Transport. Therefore, either not change the original text at all, or change in a way that maintains the meaning: "Constrained Transport cannot be used in Lagrangian codes, such as SPH". Page 32, Caption of Fig. 13, ok with the addition of the highlighted text. Page 32, Sec. 7.2, OK to change "rates" to “rate". Page 32, Sec. 7.2, OK with the addition of "finding". Pages 32/33, Sec. 7.2, ok to change highlighted text to: OK to change to “As we have stressed in Section 2.2, the addition of an almost negligibly small diffusivity to the evolution equations for the Euler potentials does not correspond to any physical magnetic diffusivity and leads to wrong results where no dynamo is possible—even for flows that are either fast or slow dynamos” Page 33, paragraph starting with "Table 4": OK with all suggested changes. Page 33, Ok with caption change to Table 4. Page 33, Sec. 7.3, OK to delete "what is known as" Page 34, Sec. 7.3, OK with rephrase, OK to delete "Interestingly". Page 34, Caption of Fig. 14, ok with rephrase. Page 34, Sec. 7.4, OK with changing "a number of" to "several". Page 35, Sec. 7.4, not ok to change "finally" to "In the final paper". We suggest to write: "\citet{Rieder_Teyssier_2017b} studied the magnetic field evolution in a cosmological context." Page 35, Sec. 7.4, OK to delete "an". Page 35, Sec. 7.4, not ok to replace "sets in" to "sets at", but remove "around" and add "at", so that the sentence reads "sets in at redshift z<3." Page 35, Sec. 7.4, last sentence on the page, ok with rephrase. Page 36, Beginning of Sec. 8: The sections we refer to are: 2.4, 3.3, 4.5, 5.1.5, 5.1.6, 6.1.2, 6.3. Since they are several, it is better to have a text like "it was suggested several times so far", or something similar. Page 36, Beginning of Sec. 8, ok to change "referred to as" to "termed". Page 36, Sec. 8.1, second paragraph, rephrase to avoid duplicate "predict" and use "include" on the second occurrence, so it reads: "These estimates are compatible with the predictions of cosmological magnetic field evolution models, which include detectable intergalactic magnetic fields from the evolution of primordial seeds" Page 37, Sec. 8.1, OK with the addition of "galaxies" Page 37, Sec. 8.1 OK to change "hydro" to "hydrodynamic" Page 37, Caption of Fig. 15, *not* OK to change "face-on" to "head-on", as explained above. Page 38, Sec. 8.3, OK to change "will have an impact on" to "affects". Page 38, Sec. 9, Ok to delete "First of all" Page 38, Sec. 9, ok to change "it" to "they" (indeed refers to cosmological seeds) Page 38, Sec. 9, OK with rephrases Page 38, Sec. 9., OK with suggested rephrase: "It remains important to continue to investigate this and to think about dynamos beyond just the immediate proximity of a galaxy”. Page 39: The disclosure statement can be published, no conflicts to disclose. Page 40, Beck R, Wielebinski R. 2013 reference, page span is 641-723.