{"id":"a3aaed54-b23c-4316-b643-83a001b54e5b","arxiv_id":"2505.13301","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A gamma-function growth model using parameters fixed by the cosmic star formation history reproduces the observed galaxy stellar mass function from z=0 to z=8 for low and intermediate mass galaxies, but not for massive galaxies at high redshift.","lead":"This paper applies a simple two-parameter mathematical growth curve, the gamma function, to evolve the present-day galaxy mass function backwards in time to z=8. The authors find the curve matches observed galaxy counts at intermediate and low masses for most of cosmic history, but fails at the most massive galaxies before z~2.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Universal-growth assumption is untested for individual galaxies; GAME0's low/intermediate-mass success is a rigid log-shift of the z=0 GSMF and does not by itself establish the claimed gamma growth law.","rationale":"The reader's weakest_assumption identifies the same load-bearing point: universal mass-history factor and number conservation. My concern sharpens it: GAME0 is not a flexible physical model of growth but a rigid translation of the z=0 GSMF in log-mass, so the low/intermediate-mass agreement is exactly the regime where the input low-mass slope and a single normalization can dominate the comparison. The paper itself flags the universal-growth simplification in Section 3.1 and reports the large high-mass RMSDs in Appendix B, but the central abstract claim that the scheme 'describes successfully the evolution of the GSMF over 13.5 Gyrs' is still justified mainly by excluding the high-mass end. The concrete merger-tree test would settle whether the mechanism is real at the level of individual galaxies. If the median histories are mass-dependent, the aggregate match must be regarded as an empirical coincidence or a consequence of the chosen z=0 reference, not evidence for the proposed physical gamma growth pattern. This does not invalidate the paper's useful empirical result, but it does mean the paper should remain conditional on providing this direct mechanistic check, separating GAME0's predictive claim from GAME1's tuned extension, and reporting total-RMSD metrics that include the high-mass failures.","tokens_in":54860,"tokens_out":9841,"duration_ms":109538,"concrete_test":"Download the public EAGLE or IllustrisTNG merger trees; select z=0 galaxies in the same mass bins used in Fig. 1 and compute the median and 16-84% scatter of M*(T)/M*(z0) for each bin. Check whether these histories are mass-independent and equal to gamma(3,0.5T)/Gamma(3) using the same T = Age - 0.17 Gyr convention. If the median histories vary systematically with final stellar mass, or if the low/intermediate-mass bins show large scatter around the universal curve, then the number-conserving universal-growth mechanism behind Eq. (4) is not what produces the apparent GAME0 agreement with the observed low/intermediate-mass GSMFs.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of GAME0 is that Eq. (4) with fixed alpha=3, beta=0.5 predicts the z=0 to z=8 GSMF because every mass bin grows by the same factor. But since M(T) = M0 * g(T) with g(T)=gamma(3,0.5T)/Gamma(3), the predicted high-z GSMF is a rigid log-shift of the z=0 GSMF: shape and slope are unchanged, and number density in each bin is exactly conserved. This is not a derived consequence of galaxy growth; it is a no-crossing, number-conserving assumption about individual growth histories. The assumption is known to fail for massive galaxies, and the paper's own Appendix B shows it: total RMSD including the high-mass end reaches 1.20 dex at z=3, 1.26 dex at z=5, and 1.74 dex at z=7. The claimed success for low and intermediate masses is an aggregate curve comparison; the paper provides no direct check that galaxies in those bins actually follow the same median M(T)/M(z0) curve, nor that the result is robust to the hand-drawn 'average' z=0 GSMF as opposed to, for example, the steeper Wang et al. (2024b) low-mass slope. Without such a check, the empirical match could be a consequence of the steep low-mass slope of the input GSMF and the chosen normalization, rather than of the proposed universal gamma growth physics.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents GAME0 and GAME1, analytical models for the evolution of the galaxy stellar mass function (GSMF) from z=0 to z=8. GAME0 assumes that every present-day stellar mass bin grows according to the same incomplete-gamma function previously used to fit the cosmic star formation rate density (CSFRD), Eq. (4), with α=3.0, β=0.5 Gyr^-1, and no further tuning to high-redshift mass functions. The predicted GSMFs are compared with a large compilation of observed GSMFs, with cosmological simulations (EAGLE, IllustrisTNG, Simba, ELUCID+L-Galaxies), and with empirical models such as UniverseMachine and Leja et al. (2020). The authors report good agreement for low- and intermediate-mass galaxies, with an average RMSD of 0.17 dex up to M*, and propose GAME1, which introduces a mild mass-dependent adjustment of β at z>2, to improve the high- and low-mass ends. They conclude that the evolution of the GSMF is set by simple and physically motivated growth with few parameters.","tokens_in":55079,"tokens_out":7957,"duration_ms":75444,"significance":"If the central claim holds, the result is valuable: a two-parameter, no-re-tune description of the low- and intermediate-mass GSMF over 13.5 Gyr, with parameters tied to accretion and gas-consumption physics. The paper's strengths include the breadth of the observational comparison, the quantitative RMSD and AIC tables, the inclusion of recent JWST data, and the explicit acknowledgement of modeling assumptions in Section 3.1. However, because Eq. (4) is a rigid log-shift of the z=0 GSMF with exactly conserved number densities, the empirical agreement at low and intermediate masses may largely reflect the shape of the adopted z=0 GSMF rather than a validated universal growth law for individual galaxies. The total-mass part of the prediction is also inherited from the earlier CSFRD fit, so the genuinely new content is the shape evolution of the mass function, which is exactly where the model shows its largest failures.","major_comments":[{"comment":"The mapping M(T)=M0*g(T) with a mass-independent g(T) is a rigid log-shift of the z=0 GSMF: the shape and low-mass slope are unchanged and the number of galaxies in every bin is conserved. The paper's own Section 3.1 (second bullet) concedes that massive z=0 galaxies have lower-mass progenitors, i.e., the number-conserving assumption is violated; Table B3 shows the expected consequence, with GAME0 total RMSD reaching 1.20 dex at z=3 and 1.74 dex at z=7. The authors do not quantify progenitor bias for intermediate-mass bins, so the low/intermediate-mass success cannot be claimed as direct evidence for universal gamma growth. A test using median M(T|M0) growth tracks in EAGLE, IllustrisTNG, or Simba, or a continuity-model comparison with mass-dependent growth, is needed.","section":"Section 3.1, Eq. (4)"},{"comment":"The input z=0 GSMF is a hand-drawn 'average' of several measurements, and GAME0 inherits its low-mass slope and normalization exactly. Because the high-z low-mass slope is the same as the z=0 low-mass slope under the rigid-shift mapping, the claimed agreement at low and intermediate masses is sensitive to this choice; adopting the steeper Wang et al. (2024b) or Xu et al. (2022) low-mass slopes could change the high-z predictions by more than the quoted RMSD. The gray uncertainty region in Figs. 2-4 is not propagated into the GAME0 curves, and no sensitivity test is presented. This is load-bearing for the central claim and should be addressed.","section":"Section 2, Fig. 1"},{"comment":"The statement that deviations appear 'solely' at z>1.5 and 'specifically for very small and exceedingly massive objects' is not supported by the paper's own tables. Table B3 shows that the total RMSD including the high-mass end is already 0.60 dex at z=1.5 and 0.61 dex at z=2.0, while the up-to-M* RMSD is about 0.18 dex at both redshifts, so massive galaxies dominate the deviation well within the claimed regime. At z=4, the total RMSD is 0.79 dex versus 0.177 dex up to M*, again a high-mass effect. No table or figure isolates a systematic failure at the very low-mass end; the 'up to M*' statistics include low masses and show RMSD values of 0.2-0.3 dex at z=5-8. The claim should be qualified to the high-mass end, or a separate low-mass RMSD should be presented.","section":"Abstract and Section 3.2 vs. Appendix B"},{"comment":"The parameters α and β are inherited from fits to the CSFRD in earlier work (Katsianis et al. 2021b, 2023). Since the CSFRD is the time derivative of the total stellar mass density, and GAME0's total stellar mass density is g(T) times the z=0 value by construction, the total-mass-growth part of the 'prediction' is not independent: it is forced once α and β reproduce the CSFRD. The genuinely predictive content is the shape evolution of the GSMF, i.e., mass-dependent growth and number conservation, which is precisely where GAME0 fails at high masses. The '0 parameters re-tuned' claim should be reframed to acknowledge this inheritance, so that readers can correctly identify the novel and the constrained parts of the model.","section":"Sections 3-4"}],"minor_comments":[{"comment":"The expression for τ⋆ in Eq. (12) is written ambiguously with what appears to be a missing multiplication sign; the simplified form τ⋆ = 0.5 + 1.5 exp(-0.5 (log10 M - 10.85)^2) stated in the text is much clearer and should be used in the displayed equation.","section":"Section 5, Eqs. (12)-(13)"},{"comment":"The role of f0 is not made concrete: the example sets the z=0 mass equal to the final mass, yet with βT = 6.775 the factor γ(3, βT)/Γ(3) is about 0.965, not 1. The authors should specify f0 explicitly and use it consistently in the worked example.","section":"Section 3.1, Eq. (5)"},{"comment":"There are numerous typographical errors: 'sold green line' should be 'solid green line'; Fig. 9 z=0.9 panel legend says 'GAME1, z=2.0'; 'Marchensini' should be 'Marchesini'; 'EALGE' should be 'EAGLE'; 'tunned' should be 'tuned'; and 'consenus' should be 'consensus'. A careful proofreading pass is needed.","section":"Figures 8-10 and general text"},{"comment":"The RMSD values are reported with inconsistent precision (e.g., 0.2075 in Table B2 versus 0.21 in the text and 0.17 in Table B1 summaries). Uniform significant figures should be used throughout the tables and text.","section":"Appendix B tables"},{"comment":"The meaning of the 'x' symbols and open circles in the top panels is not defined in the caption; the caption should state explicitly which mass bins are classified as not well captured by GAME0.","section":"Fig. 7 caption"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of MNRAS and addresses a timely question. The main concern is framing: the 'prediction' language overstates the novelty because the total stellar-mass assembly is inherited from the earlier CSFRD fit, and the low/intermediate-mass match is a rigid-shift test of the z=0 GSMF shape. The paper also overstates where deviations occur relative to its own RMSD tables. These issues are fixable with additional robustness tests and a reframed presentation. The extensive self-citations to the authors' previous CSFRD work are appropriate, but the '0 parameters re-tuned' claim should be softened. I support publication after major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a serious look, but the headline claim is overstated. What is actually new: the authors take a two-parameter gamma growth curve (alpha=3, beta=0.5 Gyr^-1) previously fit to the cosmic star formation rate density and apply it, with no re-tuning for GAME0, to evolve the full z=0 stellar mass function to higher redshifts. They compare against a broad set of observed GSMFs and state-of-the-art simulations, including recent JWST data, and quantify performance with RMSD and AIC. For low and intermediate masses, GAME0 matches observations surprisingly well at z<1.5, with RMSDs around 0.1-0.2 dex, and even at z=4-8 the agreement at the low-mass end is decent. GAME1 adds one log-normal mass-dependent correction to beta, anchored to the z=8 GSMF, and improves the high-mass end. As a compact recipe for generating quick mock mass functions, this is genuinely useful.\n\nThe soft spots are significant but not fatal. The load-bearing assumption is that all galaxies, in every mass bin, grow by the same factor, so M(T) = M0 * gamma(alpha,betaT)/Gamma(alpha). That makes the predicted high-z GSMF a rigid log-shift of the z=0 GSMF, conserving shape and number density in each bin. Mechanisms that change abundance matching, like mergers or mass-dependent growth, are acknowledged in Section 3.1 but never actually tested. The paper provides no direct check that individual galaxies follow the same median growth curve, and without that, the low/intermediate-mass success could largely reflect the steep low-mass slope of the adopted average z=0 GSMF. The physical derivation in Section 4 is really a post-hoc consistency argument: the fitted alpha and beta are shown to match literature scalings, not derived from first principles. And the abstract's claim that deviations occur 'solely' at very high redshifts and for very small/massive objects is contradicted by the paper's own RMSD tables, where including the high-mass end gives total RMSDs of 1.2 dex at z=3, 1.26 dex at z=5, and 1.74 dex at z=7.\n\nAll that said, the paper is honest about many of these issues in the body, clearly separates GAME0 (predictive) from GAME1 (tuned), and provides a transparent, reproducible comparison framework. The central empirical claim for low/intermediate masses holds up well enough to be useful. The right referee report would ask for a cleaner presentation of total RMSD, a softening of the 'first-principles' language, and preferably a test of the universal-growth assumption against individual galaxy SFHs in simulations. This deserves peer review, not desk rejection.","headline":"A compact gamma-growth model that usefully maps the low/intermediate-mass galaxy stellar mass function from z=0 to z=8, but the high-mass failures are larger than the abstract admits and the 'prediction' rests on an untested universal-growth assumption.","tokens_in":55780,"tokens_out":2262,"would_cite":true,"duration_ms":24449,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that a single gamma growth curve, with parameters already fixed by the cosmic star formation rate density, reproduces the observed galaxy stellar mass function from z=0 to z=8 without re-tuning to high-redshift data.","keywords":["galaxy stellar mass function","gamma growth model","cosmic star formation rate density","galaxy evolution","high-redshift galaxies","JWST observations","stellar mass assembly","star formation timescale"],"falsifier":"Follow the same galaxies across epochs, using merger trees from simulations or stellar-mass measurements of individual galaxies at two redshifts in deep JWST fields, and test whether fractional mass growth $M_{*}(T)/M_{*,0}$ is truly identical across mass bins; the paper's own comparison shows the universal curve overshoots the observed high-mass end by up to about 1 dex at z>1.5, so a decisive check is whether deeper high-redshift surveys of massive galaxies widen that gap beyond observational error.","tokens_in":54576,"feed_emoji":"🌌","tokens_out":19905,"duration_ms":161207,"temperature":0.7,"pith_summary":"The paper tries to establish that the evolution of the galaxy stellar mass function over 13.5 billion years is governed by the same few-parameter gamma growth pattern that already describes the cosmic star formation rate density. Starting from the present-day (z=0) mass function and the mass-history formula $M_{*}(T) = M_{*,0}\\,\\gamma(3.0, 0.5\\,T)/\\Gamma(3.0)$, with $\\alpha = 3.0$ and $\\beta = 0.5\\,\\mathrm{Gyr}^{-1}$ taken unchanged from cosmic star formation, the authors evolve each local mass bin backward in time and compare with observed mass functions from z=0 to z=8. They report agreement with low- and intermediate-mass galaxies across the full range, with typical scatter around 0.17 dex, while deviations appear only for the rarest, most massive galaxies at z>1.5. A sympathetic reader would care because, if correct, the result means the backbone of galaxy assembly, number counts in mass bins, needs no mass-dependent tuning or exotic feedback machinery, only accretion physics encoded in two parameters, plus one extra parameter to recover the high-mass end at early times.","feed_headline":"One growth curve predicts the galaxy mass function to z=8","feed_subtitle":"With just two fixed parameters, the curve behind cosmic star formation reproduces 13.5 billion years of galaxy growth.","key_machinery":"The load-bearing object is the gamma growth motif, in the specific form of the incomplete-gamma ratio $\\gamma(\\alpha,\\beta T)/\\Gamma(\\alpha)$: the fraction of a galaxy's final (present-day) stellar mass that has been assembled after time $T$ since the first stars formed. The two parameters carry the physics: $\\alpha = 3.0$ sets the early power-law rise $T^{\\alpha-1} = T^{2}$, tied through $\\alpha = 2Y/(3-Y)$ to the radial density profile of the accreting matter, while $\\beta = 0.5\\,\\mathrm{Gyr}^{-1}$ sets the exponential decline, tied to the depletion timescale equated with the z=0 halo dynamical time $\\tau_{\\mathrm{dyn}} \\approx 2\\,\\mathrm{Gyr}$. The scheme's working mechanism is a one-to-one mapping: every present-day mass bin is evolved backward along this universal curve, so galaxy numbers are conserved while bins shift to smaller masses; where the predicted and observed mass functions diverge, the divergence marks where the universal-growth assumption, rather than the gamma form itself, breaks down.","core_discovery":"The paper's central claim is that galaxy stellar mass grows, on average, along the same gamma growth curve as the cosmic star formation rate density: the growth rate $\\frac{dM}{dT} = M_{z,0}\\frac{\\beta^{\\alpha}}{\\Gamma(\\alpha)}T^{\\alpha-1}e^{-\\beta T}$ integrates to $M_{*}(T) = M_{*,0}\\,\\gamma(\\alpha,\\beta T)/\\Gamma(\\alpha)$, with $\\alpha = 3.0$ and $\\beta = 0.5\\,\\mathrm{Gyr}^{-1}$ left at the values already set by cosmic star formation rather than re-tuned. Applied bin-by-bin to the z=0 stellar mass function and evolved backward in time, this single curve reproduces the observed galaxy stellar mass function from z=0 to z=8 for galaxies up to the characteristic mass, with average scatter of roughly 0.17 dex, and the paper shows the same scheme agrees with recent JWST-based mass functions at z ≈ 4–8. Deviations appear only for very low-mass and exceedingly massive galaxies at z>1.5, which the paper traces to physical processes that shorten gas-consumption timescales at both extremes, chiefly mergers and low-angular-momentum collapse. A second version (GAME 1) lets $\\beta$ vary with present-day stellar mass through a log-normal form centered at $\\log_{10}(M_{*}/\\mathrm{M}_{\\odot}) \\approx 10.85$, restoring agreement across the full mass range with one additional parameter calibrated at z=8.","pith_inferences":["If the universal-curve mapping is right, it makes a strong statement about individual galaxies that the paper does not test: a galaxy's present-day stellar mass alone determines its entire assembly history. This is checkable with star-formation histories of local galaxies and is most likely to fail for the most massive systems, where merger-dominated assembly is expected, the same regime where GAM","The log-normal $\\beta$ correction is implicitly a claim about the mass dependence of star-formation efficiency: efficiency peaks near $\\log_{10}(M_{*}/\\mathrm{M}_{\\odot}) \\approx 10.85$ and falls symmetrically toward dwarf and giant extremes. Direct measurements of molecular-gas depletion timescales as a function of stellar mass at z ≈ 2–4 could test that claim against Eq. (13).","The same gamma machinery could be pointed at other galaxy statistics, such as the star formation rate function or quenched fractions; the paper's observation that the star formation rate function evolves nearly in parallel across bins at low redshift suggests a gamma-based prediction for the SFR function at higher redshifts would be a natural and independent check.","Because everything is anchored to the z=0 mass function, the scheme inherits the systematics of local measurements; the paper averages several discrepant local determinations, so a better-constrained low-mass slope at z=0, for example from wider-area spectroscopy, would directly sharpen or challenge the high-redshift predictions."],"forward_implications":["The low- and intermediate-mass end of the mass function at any redshift z ≤ 8 becomes a prediction from local data alone: the present-day mass function plus two fixed parameters fixes the number density of these galaxies at all earlier epochs.","Because GAME 0 works with no mass-dependent tuning for more than 9 billion years, the paper's reading is that feedback mechanisms acting selectively at the low- and high-mass ends are not needed to explain the observed shape evolution of the mass function at z < 1.5.","The breakdown at the high-mass end for z > 1.5 identifies where the universal-growth picture fails, and the GAME 1 fix says the required adjustment is faster gas consumption (shorter depletion timescales) at both mass extremes at early times, not a late-time suppression of star formation.","The formalism's two parameters are tied to gravitational-collapse scales (the density profile of accreting matter and the z=0 halo dynamical time), so if the scheme holds, the mass function's evolution carries direct information about collapse physics rather than about tuned subgrid feedback; the paper reports GAME matches the observed z=0–8 mass function with average scatter comparable to or bett","The authors conclude that both their scheme and current simulations are consistent with JWST-derived mass functions at z ≈ 4–8, which they read as evidence that the early massive galaxies seen by JWST do not force a departure from standard growth physics once stellar masses are measured with near-infrared (MIRI) constraints included."],"supporting_citations":[{"why":"Supplies the gamma growth pattern for the cosmic star formation rate density, with $\\alpha = 3.0$ and $\\beta = 0.5\\,\\mathrm{Gyr}^{-1}$, that GAME 0 reuses unchanged.","marker":"Katsianis et al. (2021b)"},{"why":"Links $\\beta$ to the z=0 dynamical timescale of dark-matter halos ($\\tau_{\\mathrm{dyn}} \\approx 2$ Gyr) and shows halo mass accretion histories follow the same pattern, grounding the parameters physically.","marker":"Katsianis et al. (2023)"},{"why":"The turbulent-collapse accretion model whose solution $\\dot{M} \\propto M^{1/2}$ integrates to a $t^{2}$ power law, motivating the early-time growth exponent that sets $\\alpha = 3.0$.","marker":"Murray & Chang (2015)"},{"why":"Provides the analytic relation between the density profile of accreting matter and the accretion power law that maps the profile index $Y$ to $\\alpha = 2Y/(3-Y)$.","marker":"Wang et al. (2018)"},{"why":"One of the main z=0 galaxy stellar mass functions that, averaged with other local measurements, is the observational anchor from which all earlier mass bins are evolved.","marker":"Baldry et al. (2012)"},{"why":"Observational measurement that gas-consumption timescales average about 2 Gyr at z=0, setting $\\beta = 0.5\\,\\mathrm{Gyr}^{-1}$ and motivating the redshift-dependent correction in GAME 1.","marker":"Tacconi et al. (2018)"},{"why":"High-redshift stellar mass functions at $z \\approx 4$–8 used as comparison data showing GAME 0 succeeds for low- and intermediate-mass galaxies beyond $z=1.5$.","marker":"Song et al. (2016)"},{"why":"JWST-based mass functions at $z \\approx 3.5$–8.5 used to show GAME 1 and current simulations both match recent early-galaxy counts.","marker":"Navarro-Carrera et al. (2024)"}],"fun_headline_variants":["One gamma curve sets galaxy masses from z=0 to z=8","Two parameters, 13.5 Gyr, one growth law for galaxies","Star formation's growth curve also predicts galaxy mass function","Simple gamma fit matches galaxy masses to redshift 8","Same growth pattern behind stars and galaxies to z=8"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that every galaxy in a given present-day mass bin grew along the same universal gamma curve, so a galaxy's mass today uniquely fixes its mass at any earlier time and galaxy numbers are conserved as bins are shifted backward, ignoring mass-dependent growth, mergers, and the fact that today's massive galaxies assembled from many smaller progenitors.","fun_headline_variants_meta":{"raw":{"variants":["One gamma curve sets galaxy masses from z=0 to z=8","Two parameters, 13.5 Gyr, one growth law for galaxies","Star formation's growth curve also predicts galaxy mass function","Simple gamma fit matches galaxy masses to redshift 8","Same growth pattern behind stars and galaxies to z=8"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000796,"raw_usage":{"total_tokens":3661,"prompt_tokens":1257,"completion_tokens":2404,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":873,"completion_tokens_details":{"reasoning_tokens":2328}},"tokens_in":873,"tokens_out":2404,"duration_ms":17679,"temperature":1.0,"reasoning_tokens":2328,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:16:11.848492+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Follow the same galaxies across epochs, using merger trees from simulations or stellar-mass measurements of individual galaxies at two redshifts in deep JWST fields, and test whether fractional mass growth $M_{*}(T)/M_{*,0}$ is truly identical across mass bins; the paper's own comparison shows the universal curve overshoots the observed high-mass end by up to about 1 dex at z>1.5, so a decisive check is whether deeper high-redshift surveys of massive galaxies widen that gap beyond observational error.","supporting_citations":[],"review_version":1}