{"id":"f8299b8a-c5a4-4c9f-bd89-4ea53a5bb62c","arxiv_id":"2608.09195","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A proto-hybrid star's early hot stages can block the cold maximum-mass configuration, for both local and global charge conservation.","lead":"Proto-neutron stars with quark matter cores are modeled through their trapped-neutrino, deleptonized, and cold stages. The models predict that the maximum mass of a cold hybrid star may be unreachable along the actual cooling path, because an intermediate hot stage becomes unstable first.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Sec. VII 'no astrophysical path' claim is overbroad: the paper's own cited slow-conversion and out-of-equilibrium stability mechanisms, as well as post-cooling accretion, can provide routes to the cold maximum mass, so the conclusion needs scoping.","rationale":"The paper's numerical work is internally consistent: the Sommerfeld expansion cross-checks (Fig. 1) and the Clausius-Clapeyron verification (Table I) support the EOS construction, and the constant-rest-mass argument is coherent under its stated assumptions. The load-bearing weakness is that the headline conclusion is stated without the assumptions it actually requires. The turning-point criterion used in Sec. VI is not the only stability condition relevant for proto-hybrid stars; the same section cites works [89, 90, 91, 92, 93, 94, 95, 96] showing that out-of-equilibrium effects and slow phase conversion can allow stable configurations beyond the turning point. Since the paper's own GCN discussion admits the cold maximum mass could, in principle, become viable under out-of-equilibrium effects, the Sec. VII sentence 'there is no astrophysical path' is stronger than the evidence. Moreover, the fixed-rest-mass evolution picture in Eq. (47) omits accretion, which is a standard route to increasing a cold star's mass; this alone invalidates the unrestricted reading of 'astrophysical path.' These concerns are not internal inconsistencies in the numerics, but they change the scope of what is claimed. A conditional acceptance that requires the authors to explicitly scope the conclusion to isolated, non-accreting, beta-equilibrated stars with fast phase conversion remains appropriate; hence the reader's CONDITIONAL verdict is preserved and no verdict shift is proposed.","tokens_in":23261,"tokens_out":11687,"duration_ms":126868,"concrete_test":"Recompute the maximum stable rest mass of the Sb=2 LCN hybrid sequences (SkI4+vMIT(a) and Ska+vMIT(a)) using a radial-oscillation stability analysis that includes slow phase-conversion junction conditions (e.g., the formalism of Pereira et al. 2018, Ref. [91]) and, if needed, out-of-equilibrium perturbations from Refs. [89, 90]. If the maximum rest mass reaches or exceeds the cold maximum rest mass, the Sec. VII no-path conclusion is falsified even for isolated stars; if it does not, the conclusion survives only for the non-accreting case and still requires an explicit accretion caveat.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central conclusion in Sec. VII states 'for all the models constructed in this study, there is no astrophysical path leading to the maximum-mass configurations predicted by the cold EOSs.' This follows from constant-rest-mass sequences in Fig. 6 with stability determined solely by the turning-point criterion. However, Sec. VI itself notes that for proto-compact stars out of weak equilibrium the range of gravitational stability can be extended beyond the maximum-mass configuration [89, 90], and that under a slow phase transition the dynamical stability region can also be widened [91, 92, 93, 94, 95, 96]. The authors even state for GCN that out-of-equilibrium effects could, in principle, extend the range of stability making the maximum mass configuration for the cold case a viable one. These statements directly undercut the categorical no-path claim: a star with the cold-maximum rest mass might pass through the intermediate stage if its stability window is extended by the mechanisms the paper itself cites. Additionally, the constant-rest-mass assumption in Eq. (47) excludes post-formation accretion, a standard astrophysical mass-growth channel; a lower-mass cold star can accrete to the maximum mass after cooling, providing a path not excluded by the paper's argument. Therefore, as stated, the conclusion is not established; it holds only for isolated, non-accreting stars with fast phase conversion and beta equilibrium.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs hot hybrid equations of state (EOSs) describing hadron-quark phase transitions during proto-neutron-star evolution. It considers three stages: neutrino-trapped matter with entropy per baryon S_b=1 and lepton fraction Y_l=0.4, deleptonized hot matter with S_b=2, and the cold T=0 endpoint. Hadronic matter is modeled with two Skyrme interactions (SkI4, Ska) and quark matter with two vector-MIT-bag parametrizations (vMIT(a), vMIT(b)), under both local (LCN) and global (GCN) electric-charge conservation. The authors verify their numerical thermodynamics against Sommerfeld expansions and the Clausius-Clapeyron relation, solve the Tolman-Oppenheimer-Volkoff equations, and study structural evolution through constant-rest-mass sequences. The central claim is that, for all models constructed, no astrophysical path leads to the maximum-mass configurations predicted by the cold EOSs, so earlier evolutionary stages can set an effective upper mass limit on cold hybrid stars.","tokens_in":23571,"tokens_out":4161,"duration_ms":41391,"significance":"The topic is timely and the paper contains several strengths: internal thermodynamic consistency checks via Sommerfeld expansions (Fig. 1, Fig. 3) and the Clausius-Clapeyron relation (Table I), a clear treatment of the entropy-per-baryon discontinuity in isentropic LCN constructions, and a physically motivated use of rest-mass sequences to discuss evolutionary viability. If the main conclusion were established, it would be an interesting and potentially important caveat for interpreting massive compact stars as hybrid stars: the cold EOS may allow a high maximum mass, but the intermediate protoneutron-star stage could prevent the star from ever reaching it. However, as discussed below, the conclusion as stated is broader than what the presented analysis and the paper's own caveats support.","major_comments":[{"comment":"The categorical statement in Sec. VII that \"for all the models constructed in this study, there is no astrophysical path leading to the maximum-mass configurations predicted by the cold EOSs\" is directly undercut by the authors' own qualifications in Sec. VI. There they state that for proto-compact stars out of weak equilibrium the range of gravitational stability can be extended beyond the maximum-mass configuration [89,90], that a slow phase transition can widen the dynamical stability region [91-96], and, for GCN, that out-of-equilibrium effects \"could, in principle, extend the range of stability making the maximum mass configuration for the cold case a viable one.\" In addition, the constant-rest-mass sequences built from Eq. (47) exclude post-formation accretion, which is a standard mass-growth channel: a star could pass through the intermediate stage at a lower rest mass and later accrete up to the cold maximum mass. The conclusion therefore holds only for isolated, non-accreting stars with fast phase conversion and beta equilibrium; it is not established as a general no-path statement. The conclusion should be reworded to state precisely these conditions, or the analysis should be extended to show that these mechanisms do not open a path in the models considered.","section":"Sec. VII and Sec. VI (last paragraph)"},{"comment":"The main conclusion rests on only two hand-picked quark-matter parametrizations, vMIT(a) and vMIT(b), which differ in both Gv and B (Gv=0.17 fm^-2, B^(1/4)=160 MeV vs Gv=0.3 fm^-2, B^(1/4)=165 MeV) and were chosen so that the cold LCN and GCN phase transitions occur at similar pressure. No sensitivity analysis is presented, and the wording \"for all the models constructed in this study\" covers only these two cases. The relative ordering of the maximum rest masses across the three stages, which is the basis of the no-path claim, could plausibly change with the stiffness of the quark phase and the transition pressure. A scan over Gv and B (or at least a discussion of how the gap between the stage-2 maximum rest mass and the cold maximum rest mass varies) is needed to determine whether the conclusion is a property of the construction scheme or an artifact of the particular parametrization pair.","section":"Sec. VI (parameter choice)"},{"comment":"The stability analysis relies entirely on the turning-point criterion dM/depsilon_c=0 applied to each EOS. As the authors themselves note, this criterion is not the final word for matter out of weak equilibrium or for slow phase conversion, where the stability region can be extended [89-96]. Since the central claim is about the absence of an astrophysical path, the paper should either incorporate these effects into the stability analysis or explicitly restrict the claim to the fast-conversion, beta-equilibrium limit. As written, the conclusion is a statement about the chosen stability criterion rather than about astrophysical paths in general.","section":"Sec. VI (stability criterion)"}],"minor_comments":[{"comment":"The caption says panels (c) and (d) denote results \"in the GCN scenario (local conservation of electric charge)\"; this should read \"global conservation of electric charge.\"","section":"Fig. 4 caption"},{"comment":"The caption states \"Panels (b) and (c) Ska was used\" in the description of the lower panels; the correct panels for Ska are (b) and (d).","section":"Fig. 5 caption"},{"comment":"There are several typos and misspellings: \"Claussius-Clapeyron\" should be \"Clausius-Clapeyron,\" \"Sommerefeld\" should be \"Sommerfeld,\" \"Specically\" should be \"Specifically,\" and \"aslow\" should be \"a slow.\"","section":"Throughout"},{"comment":"Reference [94] is incomplete: it reads \"P. B. Rau and A. Sedrakian, , Phys. Rev. D107, 103042 (2023)\" with no article title.","section":"Reference [94]"},{"comment":"The abstract uses the appropriately cautious phrasing that earlier stages \"may play a crucial role,\" but Sec. VII states a categorical no-path result. The language should be made consistent, with the conclusion reflecting the conditional nature of the analysis.","section":"Abstract vs Sec. VII"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid EOS-construction and TOV study with useful internal checks, but the headline conclusion in Sec. VII overstates what the model set and stability analysis can support. The authors already contain the necessary caveats in Sec. VI, so a revision that scopes the conclusion and adds a sensitivity study should be feasible. I would not recommend rejection, but the categorical phrasing is likely to be quoted by others and should be fixed before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Solid, careful work on hot hybrid EOSs for proto-neutron stars. The genuinely new piece is the LCN isentropic construction: instead of forcing equal entropy per baryon in both phases, which would break thermal equilibrium, they let the quark phase carry a different entropy, found from the phase diagram, and verify the result against the Clausius-Clapeyron relation. The Sommerfeld checks on both hadronic and quark sides are also done properly, and the agreement is clean. The paper is honest that the central conclusion, that early stages can block the cold maximum-mass configuration, was already reported in Refs. [55,61]; what it adds is a systematic LCN-versus-GCN comparison, including thermal twin solutions.\n\nThe main soft spot is the Sec. VII conclusion: \"for all the models constructed in this study, there is no astrophysical path leading to the maximum-mass configurations predicted by the cold EOSs.\" That is stronger than what the analysis shows. The rest-mass sequences use the turning-point criterion on fixed-entropy, beta-equilibrium EOSs, with constant rest mass and no accretion. The authors themselves note in Sec. VI that out-of-equilibrium proto-compact stars can have a wider stability region, that slow phase conversion widens the dynamical stability window for LCN, and that a GCN star could in principle be stabilized beyond the mass peak. If any of those mechanisms operates, or if the star accretes after cooling, the cold maximum mass may be reachable. So the claim should be scoped to \"within our sequence of equilibrium models, no path exists.\" As stated, it is not established.\n\nTwo more modest issues. The vMIT parameters are hand-picked, with Gv and B chosen separately for LCN and GCN so that the transition pressure roughly matches, and no sensitivity analysis is shown. A reader cannot tell how robust the no-path result is to those choices. And the comparison to Refs. [55,61] is qualitative; a quantitative baseline with the same hadronic EOS and quark model but a different construction would clarify what is actually new.\n\nThe citation pattern looks fine. Who is this for? Practitioners constructing hybrid EOSs for proto-neutron-star or merger-remnant applications. It deserves a serious referee; the construction framework is useful and the verification is real. The referee should push for a scoped conclusion and ideally a sensitivity test on the vMIT parameters.","headline":"Careful EOS construction with a well-verified LCN isentropic scheme, but the 'no astrophysical path' headline overreaches the paper's own assumptions.","tokens_in":24106,"tokens_out":1923,"would_cite":true,"duration_ms":20004,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["97.60.Jd","26.60.-c","21.65.-f"],"model":"deepseek-v4-flash","headline":"In every model studied, hybrid neutron stars fall short of the maximum mass allowed by their cold equations of state.","keywords":["proto-neutron star","hybrid star","quark-hadron phase transition","hot equation of state","neutrino trapping","Gibbs construction","Maxwell construction","maximum mass"],"falsifier":"A numerical evolution that carries a star with the cold maximum-mass rest mass through the $S_b=2$ stage without dynamical instability would falsify the claim.","tokens_in":23061,"feed_emoji":"🌟","tokens_out":15329,"duration_ms":133988,"temperature":0.7,"pith_summary":"This paper asks whether the hottest moments of a neutron star's life can limit how massive it can ever become once it cools. The authors compute hot hybrid equations of state — matter with both hadrons and deconfined quarks — at three proto-neutron-star stages: trapped neutrinos with entropy per baryon $S_b=1$ and lepton fraction $Y_l=0.4$; hotter, neutrino-free matter with $S_b=2$; and the cold $T=0$ endpoint. They then trace constant-rest-mass sequences through these stages and apply the turning-point stability criterion. The central claim is that, for all their models, no astrophysical path leads to the maximum-mass configurations predicted by the cold equations of state, regardless of whether electric charge is conserved locally or globally. If true, the earlier evolutionary stages set an effective upper mass limit on cold hybrid stars.","feed_headline":"No path reaches cold hybrid stars' max mass","feed_subtitle":"Even if a cold hybrid EOS allows massive stars, earlier hot stages forbid them.","key_machinery":"The engine of the paper is the construction of hot hybrid equations of state: two hadronic parametrizations (SkI4 and Ska) are matched to a vector-bag quark model through phase-equilibrium conditions. In the sharp-interface case (local charge neutrality) the authors use a Maxwell construction but let the hadronic and quark phases carry unequal entropies per baryon, fixing each EOS by requiring equal temperatures at coexistence and validating the result with the Clausius-Clapeyron relation. In the global-charge-conservation case the Gibbs construction with a mixed phase is used instead, and the trapped-neutrino stage always uses a mixed phase because the lepton fraction is only conserved globally. Structural evolution is then followed along constant-rest-mass sequences — each star keeps a fixed baryon number while its equation of state changes from stage to stage — and the turning-point criterion identifies which configurations are stable. This constant-rest-mass map is the object that exposes the missing path to the cold maximum mass.","core_discovery":"The paper's central discovery is that a proto-hybrid star's evolutionary history controls the maximum possible gravitational mass at its cold final state. Tracing constant-rest-mass sequences through the three stages, the authors find that in the local-charge-conservation case the middle, neutrino-free isentropic stage has a lower maximum rest mass than either the trapped-neutrino stage or the cold stage, so a star born heavier than that limit becomes dynamically unstable before it can cool into a cold maximum-mass configuration. In the global-charge-conservation case the cold maximum rests on a maximum rest mass that is itself unstable already at the first stage, so again no path reaches it. The finding holds for two hadronic parametrizations and two quark-model parametrizations, and it does not depend on whether electric charge is conserved locally or globally.","pith_inferences":["If this bottleneck is generic across equations of state, the highest observed neutron-star mass may constrain the proto-neutron-star stage as much as the cold matter model, changing how mass measurements are used in dense-matter inference.","The same constant-rest-mass reasoning could lower maximum predicted masses for purely hadronic or hyperonic proto-stars, since the instability mechanism depends on the hot stages rather than on quark matter specifically.","Rotation, accretion, and slow phase conversion are listed by the authors as open effects; a simulation that includes them would directly test whether the bottleneck survives.","The order-unity entropy difference between phases in the LCN case suggests that simpler isentropic hybrid models forcing equal entropy per baryon in both phases may misestimate transition pressures and stability windows."],"forward_implications":["The cold maximum mass is not reachable by standard cooling; any hybrid star observed near that mass would require a formation path that avoids the unstable stage, for example delayed phase conversion or rotation.","In local-charge-conservation models the $S_b=2$ stage is the bottleneck: it has the lowest maximum rest mass, so it sets an upper bound on the final mass.","In global-charge-conservation models the bottleneck appears already at the trapped-neutrino stage, whose maximum rest mass lies below that of the cold maximum.","Thermal twin star solutions (same mass, different radii) appear in the middle stage for local charge conservation, marking the phase-transition instability.","The derived hot hybrid EOSs are built to satisfy thermal equilibrium (unequal phase entropies in the LCN case) and pass the Clausius-Clapeyron test, making them usable inputs for further proto-neutron-star studies."],"supporting_citations":[{"why":"Defines the three proto-neutron-star stages (trapped neutrinos with $S_b=1$, $Y_l=0.4$; neutrino-free $S_b=2$; cold $T=0$) used throughout the evolution sequences.","marker":"[27]"},{"why":"Supplies the phase-equilibrium conditions for mixed hadron-quark matter with trapped neutrinos and globally conserved lepton fraction, used for stage-1 EOSs.","marker":"[51]"},{"why":"Identifies the temperature discontinuity problem in isentropic LCN hybrid EOSs, which the paper addresses by allowing different entropies per baryon in the two phases.","marker":"[52]"},{"why":"Gives an earlier finding that proto-neutron-star evolution erases the cold maximum-mass configurations for hybrid stars with a mixed phase, providing the comparison the present rest-mass analysis extends.","marker":"[55]"},{"why":"Introduces the Gibbs construction for more than one conserved charge, the basis of the global-charge-conservation mixed-phase EOS.","marker":"[67]"},{"why":"Establishes the constant-rest-mass sequence method used to trace the evolution of maximum mass along proto-neutron-star cooling.","marker":"[84]"},{"why":"Provides the turning-point criterion that fixes the unstable branches on the mass-rest-mass diagrams, on which the no-path conclusion relies.","marker":"[88]"}],"fun_headline_variants":["Hot past kills cold max mass for hybrid stars","Hybrid star's early life caps its final mass","Evolution bars hybrid stars from max mass","Proto-stage limits hybrid star's final weight","Born too hot, hybrid stars miss max mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on real proto-hybrid stars evolving at fixed rest mass through the three prescribed states ($S_b=1$ with trapped neutrinos, $S_b=2$ without neutrinos, then $T=0$), with stability judged by the standard turning-point criterion; rotation, accretion, mass loss, or slow phase conversion could break this.","fun_headline_variants_meta":{"raw":{"variants":["Hot past kills cold max mass for hybrid stars","Hybrid star's early life caps its final mass","Evolution bars hybrid stars from max mass","Proto-stage limits hybrid star's final weight","Born too hot, hybrid stars miss max mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000189,"raw_usage":{"total_tokens":1333,"prompt_tokens":937,"completion_tokens":396,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":327}},"tokens_in":553,"tokens_out":396,"duration_ms":4457,"temperature":1.0,"reasoning_tokens":327,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:39:25.876584+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical evolution that carries a star with the cold maximum-mass rest mass through the $S_b=2$ stage without dynamical instability would falsify the claim.","supporting_citations":[{"cited_title":"Laskos-Patkos, P","cited_arxiv_id":null,"evidence_quote":"Defines the three proto-neutron-star stages (trapped neutrinos with $S_b=1$, $Y_l=0.4$; neutrino-free $S_b=2$; cold $T=0$) used throughout the evolution sequences."},{"cited_title":"Sedrakian and A","cited_arxiv_id":null,"evidence_quote":"Supplies the phase-equilibrium conditions for mixed hadron-quark matter with trapped neutrinos and globally conserved lepton fraction, used for stage-1 EOSs."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Identifies the temperature discontinuity problem in isentropic LCN hybrid EOSs, which the paper addresses by allowing different entropies per baryon in the two phases."},{"cited_title":"Pagliara, M","cited_arxiv_id":null,"evidence_quote":"Gives an earlier finding that proto-neutron-star evolution erases the cold maximum-mass configurations for hybrid stars with a mixed phase, providing the comparison the present rest-mass analysis extends."},{"cited_title":"Hempel, G","cited_arxiv_id":null,"evidence_quote":"Introduces the Gibbs construction for more than one conserved charge, the basis of the global-charge-conservation mixed-phase EOS."},{"cited_title":"Constantinou, S","cited_arxiv_id":null,"evidence_quote":"Establishes the constant-rest-mass sequence method used to trace the evolution of maximum mass along proto-neutron-star cooling."},{"cited_title":"Bombaci, The maximum mass of a neutron star., Astron","cited_arxiv_id":null,"evidence_quote":"Provides the turning-point criterion that fixes the unstable branches on the mass-rest-mass diagrams, on which the no-path conclusion relies."}],"review_version":1}