{"id":"67f48507-a00a-4ad2-a130-e3e4ffbc322a","arxiv_id":"2609.30112","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Folding direct Urca cooling into a Bayesian EoS inference leaves radius and maximum mass nearly unchanged but pushes the central proton fraction of a 1.4 solar-mass neutron star to about 0.15.","lead":"A Bayesian study of neutron star interiors now adds direct Urca cooling data, which carry information about the star's internal composition, on top of mass, radius and tidal measurements. The cooling constraint barely changes the inferred radius or mass, but it shifts the proton fraction of a typical neutron star toward a higher value.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"The headline composition constraint (Y_p≈0.15 at 1.4 M_sun) rests on the premise that sources classified as rapidly cooling cool via nucleonic dUrca; for Cassiopeia A the paper's own references offer a competing superfluid-triggered mechanism.","rationale":"The reader's conditional verdict is sound, and its identified circularity (cooling-derived masses feeding a cooling-interpretation likelihood, b126) is genuine and honestly conceded by the authors. I agree the cooling-source input is the fragile link in the chain. However, I locate the sharper load-bearing point one step earlier: Eq. (2) presupposes that each classified 'rapid cooling' object actually cools via nucleonic dUrca, so that M_DU ≤ M_source. The paper concedes non-uniqueness (b16), and for its flagship anchor, Cassiopeia A, the paper's own Refs. [33, 34] advance superfluid-triggered cooling that need not require crossing Y_DU. If that interpretation is right, the composition posterior is inflated regardless of any independent mass determination, because the failure is in the classification premise rather than the mass input. This strengthens the reader's conditional rather than overturning it: the same remedy direction applies (better cooling-source characterization), but the concrete test differs — drop or deweight Cas A under the superfluid hypothesis. I recommend UNCHANGED because the verdict CONDITIONAL already correctly captures that the central claim is not settled. I give credit where due: results are consistent across four EoS constructions, the limitation is stated rather than hidden, SAX J1808 provides at least one independent-mass anchor, and the paper flags the HESS J1731 mass debate (b61). Absence of shipped code or data artifacts does constrain independent verification, but is not itself an argument-level defect. The disagreement with the reader is one of emphasis within an otherwise aligned assessment: the mass circularity is downstream of the classification premise, and a single-source classification test would settle which is the binding fragility.","tokens_in":16676,"tokens_out":4550,"duration_ms":35739,"concrete_test":"Re-run the full Astro + chiEFT + dUrca inference (all four EoS constructions: metamodel and extended-Skyrme, each with random and causal n_break) with Eq. (2) modified so that Cassiopeia A is removed from the product over rapidly cooling sources — i.e., its mass is treated as non-informative for dUrca activity, consistent with the superfluid-triggered cooling interpretations in Refs. [33, 34] that the paper cites. Compare the central Y_p(1.4 M_sun) and its 95% credible interval against the fiducial ≈0.15 peak. If the peak drops toward ≈0.12 or below, or if the dUrca posterior no longer dominates the chiEFT+Astro composition posterior in Fig. 5, then the headline composition constraint is not robust to the classification of a single anchor source. If Y_p remains ≈0.15, the rapid-cooling ⇒ dUrca classification concern is mitigated for the composition result.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's flagged circularity — that the rapid-cooling source masses anchoring Eq. (2) derive from thermal modeling the dUrca constraint is meant to interpret (conceded in b126) — is real and is partially mitigated only for SAX J1808, whose mass is independently measured (b58). But the sharper, still-unresolved load-bearing assumption sits one step earlier: the likelihood equates 'rapid cooling' with 'nucleonic dUrca active, so M_DU ≤ M_source.' The paper itself concedes this identification is not unique (b16): superfluidity can accelerate cooling, and hyperon/quark channels can mimic dUrca. Critically, for Cassiopeia A, a primary anchor in the product over rapidly cooling sources in Eq. (2), the two most prominent published interpretations — Refs. [33] and [34], cited by the authors — attribute the observed cooling decline to the onset of neutron-superfluid-triggered enhanced neutrino emission, not to crossing the proton-fraction threshold Y_DU. If Cas A cools via such a non-dUrca channel, including it as an unconditional dUrca-active anchor near 1.5 M_sun forces M_DU below that mass and inflates the inferred proton fraction at canonical mass — exactly the quantity the paper claims the dUrca constraint dominates (Y_p≈0.15, Fig. 5, b4). Fixing the mass circularity would not repair this: even with perfectly independent masses, misclassification would bias Y_p upward. Thus the single most load-bearing condition is the rapid-cooling ⇒ dUrca classification, with Cas A as the concrete test case, not merely the mass estimates feeding Eq. (2). The dUrca-only blue bands in Figs. 1 and 5 show this is a prior-backed expectation (higher Y_p), which makes the classification premise the thing that converts prior into posterior.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"This paper extends the JESTER Bayesian inference framework to compute the β-equilibrated, charge-neutral composition of neutron-star matter — including muons — and the associated direct Urca (dUrca) threshold, and introduces a cooling likelihood (Eqs. 2–4) into the multimessenger constraint set. Rapidly cooling sources (Cassiopeia A, Vela, PSR B2334+61, SAX J1808.4−3658) are treated as anchors forcing the dUrca onset mass M_DU below their masses, while the slow-cooling source HESS J1731−347 sets the lower side. Across four EoS constructions (metamodel and extended-Skyrme, each with random or causal breakdown density n_break), the authors find that the dUrca constraint has only minor impact on macroscopic properties (R_1.4 ≈ 11.89–11.91 km, M_TOV ≈ 2.18–2.27 M_sun), but dominates the composition posterior, concentrating the central proton fraction of a 1.4 M_sun star at Y_p ≈ 0.15 (Fig. 5, b4). This contrasts with the recent result of Ref. [38], in which nuclear data disfavor dUrca onset below 1.4 M_sun.","tokens_in":17117,"tokens_out":7230,"duration_ms":45009,"significance":"If the constraints hold, the sharp composition posterior (Y_p ≈ 0.15) sets up a testable tension with laboratory-based determinations (Ref. [38]), and the paper correctly notes that rapid cooling near 1.4 M_sun would then require larger source masses or a non-nucleonic channel. The self-consistent β-equilibrium treatment with muons and the explicit inclusion of a composition-sensitive likelihood is a genuine methodological step, and the authors deserve credit for implementing the dUrca threshold (Eq. (1)) cleanly and for openly flagging the limitation of their anchor masses (b126) and the debated HESS J1731 values (b61). The value of the work nonetheless hinges on the validity of the rapid-cooling ⇒ dUrca identification for the specific source set, which is the principal correctness risk; the requested robustness tests would determine whether the headline composition claim is supported.","major_comments":[{"comment":"The likelihood in Eq. (2) equates 'rapid cooling' with 'nucleonic dUrca active' and applies this identification unconditionally to Cassiopeia A. However, the two published interpretations of Cas A's cooling decline that the paper itself cites — Refs. [33] (Page et al.) and [34] (Shternin et al.) — attribute the rapid cooling to neutron-superfluid-triggered enhanced neutrino emission rather than to crossing the proton-fraction threshold Y_DU. Because Cas A is one of the principal anchors in the product over rapidly cooling sources in Eq. (2), treating it as a dUrca-active object forces M_DU below roughly 1.5 M_sun, which is precisely the condition that drives the headline Y_p ≈ 0.15 result in Fig. 5. The non-uniqueness is acknowledged in b16, but the likelihood implements the dUrca-only identification and no robustness test is presented. The inference should be rerun with Cas A excluded (or with the superfluid-triggered onset implemented as an alternative), and the resulting shift in the Y_p(1.4 M_sun) posterior reported; without such a test the central composition claim is not yet supported.","section":"Sec. III, Eq. (2); Figs. 3–5","authors_acknowledge":"However, superfluidity it- self could also accelerate cooling, which makes the identi- fication of a rapidly cooling source with nucleonic dUrca is not unique [33, 34].","authors_acknowledge_p":0.83},{"comment":"The masses anchoring Eq. (2) for Cas A, Vela, and PSR B2334+61 are themselves derived from the thermal-cooling modeling that the dUrca constraint is meant to interpret, a circularity the authors concede in b126. What remains unresolved is the quantitative impact: since Eq. (2) compares these mass estimates directly to M_DU, a bias in any anchor mass transfers into a bias of the inferred threshold mass and hence of Y_p. The authors should report a sensitivity analysis, e.g., rerunning the inference with SAX J1808.4−3658 (whose mass is independently measured, per the discussion in Sec. III) as the only rapid-cooling anchor, and comparing the resulting Y_p and R_1.4 posteriors against the full-source results. The conclusions suggest such an exercise is meaningful (b127), and it is within the scope of the present analysis.","section":"Sec. III and Sec. V (b126)","authors_acknowledge":"The constraint of Eq. (2) enters entirely through the comparison between the measured mass of a cooling ob- ject and the threshold massM DU, yet for most rapidly cooling sources the mass is itself derived from the ther- mal modeling we wish to interpret.","authors_acknowledge_p":0.95},{"comment":"The slow-cooling lower anchor HESS J1731−347 carries a mass estimate that the authors themselves describe as 'strongly under debate' (b61), with newer distance and observational data shifting the values upward. Because this source is the only lower-side anchor in Eq. (2), a shift toward larger masses would relax the upper bound on M_DU and could move the composition posterior away from the high-Y_p peak. The authors frame the inclusion as 'proof of principle' (b61), which is acceptable for a methodology paper, but the headline Fig. 5 claim should be accompanied by a demonstration that the Y_p result is robust to excluding this source or to using the updated mass value.","section":"Sec. III (b61)","authors_acknowledge":"We emphasize that the mass and radius of HESS J1731-347 measured in [57] is strongly under debate, as using more recent observational data or distance measurements no- ticeably shifts the mass and radius towards larger values.","authors_acknowledge_p":0.88}],"minor_comments":[{"comment":"The sentence 'which makes the identification of a rapidly cooling source with nucleonic dUrca is not unique' contains a stray 'is' and should read '...is not unique' without it.","section":"Sec. I (b16)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The numeric annotations in the captions are garbled ('13:70+1:40 ¡2:04 km' and similar), with the plus/minus symbols and super/subscripts corrupted; these need to be regenerated cleanly before publication.","section":"Figs. 3 and 4 captions","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The prior on the randomly sampled breakdown density n_break is not fully specified; state explicitly whether it is uniform on [1n_sat, 4n_sat] and whether the random and causal n_break treatments receive equal prior weight.","section":"Sec. II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The uniform prior on n_DU in density is not uniform in threshold mass M(n_DU), because the mass-density relation from the TOV equations is nonlinear; a sentence justifying this weighting, or switching to a mass-uniform prior, would improve clarity.","section":"Eq. (4)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The contrast with Ref. [38] (Y_p ≈ 0.07–0.09) is stated in a single sentence; a short discussion of whether the discrepancy is attributable to the cooling likelihood entering the fit versus being evaluated a posteriori, and of which observation would resolve the tension, would strengthen the paper.","section":"Sec. IV","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The paper is honest about its limitations, which is appreciated. My main concern for the editor is the gap between the abstract's framing — that dUrca 'provides a constraint... favoring a higher proton fraction' — and the dependence of that result on the contested classification of Cas A as a dUrca-active source. The robustness tests I request (Cas A removal, SAX-only anchors, HESS removal) are inexpensive to run given the framework already exists, and they would convert a conditional claim into a supported one. If the authors decline to run them, the abstract should explicitly flag the conditional nature of the composition constraint."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"Two things to know before you read it. The genuinely new move is that the dUrca constraint enters the Bayesian likelihood itself rather than being evaluated a posteriori, which forces a self-consistent beta-equilibrium proton fraction, and they build that into jester properly. The headline result is that this barely moves the macroscopic posteriors — R_1.4 stays near 11.9 km, M_TOV near 2.2 — but it pins the central proton fraction of a 1.4 M_sun star to roughly 0.15 and dominates the composition posterior.\n\nThe derivation is clean. Eq. (1) for Y_DU from beta-equilibrium, charge neutrality, and momentum conservation is standard, Eqs. (2)–(4) spell out the likelihood explicitly, and the results are consistent across all four EoS constructions (metamodel and Skyrme, each with random and causal n_break). That consistency matters because Y_p is only defined where the nucleonic description holds, and Skyrme retains that to higher density than the metamodel. The paper is also honest in the conclusions: b126 concedes the mass circularity, b16 concedes the rapid-cooling-to-dUrca identification is not unique.\n\nThe soft spot is the stress-test's point, and I think it is sharper than the mass circularity. Even with perfectly independent masses, the likelihood treats every rapid-cooling source as an unconditional dUrca anchor, M_DU ≤ M_source. For Cas A specifically, the two most prominent published interpretations — refs [33] and [34], which they cite — explain the observed cooling decline with superfluid-triggered enhanced neutrino emission, not with crossing the proton-fraction threshold. If Cas A is cooling through that channel, including it as an anchor near 1.5 M_sun forces M_DU below that mass and inflates the inferred Y_p — exactly the quantity the paper claims the dUrca constraint dominates. Fixing the mass estimates would not repair this, since misclassification biases Y_p upward on its own. The HESS J1731 slow-cooling anchor is also under open debate, which they acknowledge (b61). On top of that, no code or data artifacts ship, so the posterior is not independently reproducible as-is.\n\nThis is a conditional result, not a broken one. The framework extension is legitimate, the likelihood is explicit, and the sensitivity of the composition posterior to a single source classification is a physical question, not a statistical artifact. I would send it to a serious referee with two requested changes: re-run with Cas A deweighted or assigned a prior probability of being dUrca-cooled versus superfluid-triggered, and drop or robustly deweight the HESS J1731 anchor. The science is careful; it just leans on anchors it cannot yet verify.","headline":"A legitimate framework extension whose headline composition constraint rests on a load-bearing classification — rapid cooling equals dUrca — that the paper's own best Cas A references contradict.","tokens_in":18530,"tokens_out":738,"would_cite":true,"duration_ms":23338,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"Adding direct Urca cooling to Bayesian multimessenger inference leaves neutron star radii and maximum masses nearly unchanged, but it sharply narrows the inferred central proton fraction of canonical stars to about 0.15, showing that…","keywords":["direct Urca","neutron star cooling","equation of state","Bayesian inference","proton fraction","symmetry energy","multimessenger","chiral effective field theory"],"falsifier":"Take an independent mass measurement of one of the rapid-cooling anchors, such as Cassiopeia A or Vela, obtained without any thermal cooling modeling: if that mass lies below the dUrca threshold region, the central proton-fraction posterior near 0.15 should collapse toward the lower values that laboratory symmetry-energy data alone imply. A definitive resolution of the HESS J1731$-$347 mass debate would likewise move the slow-cooling anchor and re-test the constraint from the other end.","tokens_in":18178,"feed_emoji":"⚛️","tokens_out":6552,"duration_ms":42997,"temperature":0.7,"pith_summary":"This paper adds a new kind of information to Bayesian multimessenger inference of the neutron star equation of state: direct Urca (dUrca) cooling, which can turn on only when the core proton fraction crosses a threshold set by the symmetry energy. The central result is that this composition-sensitive constraint makes almost no difference to macroscopic properties such as the canonical radius ($R_{1.4} \\approx 11.89$–$11.91$ km), the maximum mass ($M_{\\rm TOV} \\approx 2.18$–$2.27\\,M_\\odot$ with the metamodel), or the tidal deformability. In contrast, the dUrca constraint dominates the composition posterior, pushing the central proton fraction of a $1.4\\,M_\\odot$ star to about $0.15$. The authors argue that rapid-cooling observations therefore carry genuinely complementary information about matter composition that macroscopic observables cannot reach.","feed_headline":"Neutron star cooling data pin core proton fraction near 15%","feed_subtitle":"Direct-Urca cooling barely moves neutron star radii but sharply narrows the inferred composition of 1.4-solar-mass stars.","key_machinery":"The load-bearing object is the direct Urca threshold, the minimum proton fraction $Y_{\\rm DU} = \\left(1 + \\left(1 + (Y_e/Y_p)^{1/3}\\right)^3\\right)^{-1}$ at which momentum conservation allows the reactions $n \\to p + e^- + \\bar\\nu_e$ and its inverse to run; the threshold is about $11.1\\%$ in npe matter and rises to about $14.8\\%$ when muons are present. The authors implement $\\beta$-equilibrium and charge neutrality self-consistently in the jester framework to compute the proton fraction and the onset density $n_{\\rm DU}$, then build a likelihood (their Eq. 2) that compares the threshold mass $M_{\\rm DU}$ with the measured masses of rapidly cooling sources (SAX J1808.4$-$3658, Cassiopeia A, PSR B2334+61, Vela) and the slowly cooling source HESS J1731$-$347 through cumulative distribution functions. Where the nucleonic model terminates before $n_{\\rm DU}$, the likelihood is marginalized over the agnostic sound-speed-extension branch, since no microscopic composition can be defined there.","core_discovery":"Across four equation-of-state constructions (a metamodel and an extended-Skyrme functional, each evaluated with either a randomly chosen or a causality-limited nucleonic breakdown density), the authors find that folding the direct Urca likelihood into the joint posterior leaves macroscopic neutron star properties essentially unchanged: for the metamodel the canonical radius stays near $R_{1.4} \\approx 11.89$–$11.91$ km and the maximum mass near $M_{\\rm TOV} \\approx 2.18$–$2.27\\,M_\\odot$, with the Skyrme construction giving $R_{1.4} \\approx 12.2$ km and $M_{\\rm TOV} \\approx 2.16\\,M_\\odot$. The dUrca constraint instead reshapes the composition: the posterior for the central proton fraction of a $1.4\\,M_\\odot$ star concentrates around $Y_p \\approx 0.15$, well above the $Y_p \\approx 0.07$–$0.09$ that laboratory symmetry-energy data alone would suggest. The authors interpret this as evidence that rapid-cooling observations carry composition information complementary to both nuclear theory and macroscopic astrophysical measurements, and they note that if both results stand, rapid cooling near $1.4\\,M_\\odot$ requires either larger source masses or a non-nucleonic fast-cooling channel.","pith_inferences":["The cleanest test of whether the $Y_p \\approx 0.15$ result survives is to break the circularity the authors themselves flag: re-run the analysis with mass priors for the rapid-cooling sources that exclude any information from thermal cooling models, since most of those masses are currently derived from the paradigm being tested.","The framework treats the dUrca threshold as a sharp on/off switch set purely by the central proton fraction; realistic treatments of nucleon superfluidity, which can both suppress and accelerate cooling, could blur that threshold and materially change the inferred composition, so the switch assumption is itself testable.","The systematic gap between the random- and causality-limited $n_{\\rm break}$ constructions shows that composition claims are only well defined where the nucleonic model holds; future work should report, per mass, the fraction of the posterior within which a nucleonic composition exists.","If independent mass measurements of sources like Cassiopeia A or Vela come in below the dUrca region, the proton-fraction posterior should collapse toward low values, making source-mass determination a direct discriminator between the two competing pictures."],"forward_implications":["Including direct Urca cooling in the Bayesian likelihood barely changes macroscopic neutron star properties such as radius, tidal deformability, and maximum mass, which remain set by chiral EFT and astrophysical measurements.","The dUrca constraint becomes the dominant driver of the inferred central proton fraction of canonical-mass stars, favoring values near 0.15 instead of the 0.07–0.09 obtained from laboratory symmetry-energy data alone.","Cooling observations provide composition information that macroscopic observables do not, so full multimessenger inference should include them even when their effect on radii is negligible.","If both this result and the laboratory-derived low proton fraction hold, then rapid cooling near $1.4\\,M_\\odot$ requires either larger masses for the cooling sources or a non-nucleonic fast-cooling channel."],"supporting_citations":[{"why":"Defines the direct Urca process and supplies the threshold condition behind Eq. (1).","marker":"[58]"},{"why":"Supplies the numerical threshold values, about 11.1% in npe matter and 14.8% with muons, that anchor the onset calculation.","marker":"[28]"},{"why":"The jester framework that the authors extend to compute proton fraction and dUrca threshold self-consistently.","marker":"[40]"},{"why":"Provides the metamodel construction used for the nucleonic part of the equation of state.","marker":"[41]"},{"why":"The contrasting laboratory-based result ($Y_p \\approx 0.07$–$0.09$) that the dUrca constraint must be reconciled with.","marker":"[38]"},{"why":"Defines the minimal cooling paradigm used to classify which sources are rapidly cooling.","marker":"[59]"},{"why":"Supplies the HESS J1731$-$347 mass and radius used as the slow-cooling anchor, whose debated value is acknowledged.","marker":"[57]"},{"why":"Provides the independently measured cooling profile and mass for SAX J1808.4$-$3658, the one rapid-cooling anchor not derived from cooling models.","marker":"[47]"}],"fun_headline_variants":["Direct Urca cooling pins neutron star proton fraction near 15%","Cooling data sharpen neutron star proton fraction, leave radii unchanged","Direct Urca cooling reshapes inferred core composition, not size","Cooling observations favor higher proton fraction in neutron stars"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The masses of most rapidly cooling sources that anchor the direct Urca likelihood (Cassiopeia A, Vela, PSR B2334+61) are themselves derived from the very thermal cooling models the constraint is meant to interpret, so part of the proton-fraction constraint reduces to input from the same paradigm, and the slowly cooling anchor HESS J1731$-$347 has a mass that is itself under active debate.","fun_headline_variants_meta":{"raw":{"variants":["Direct Urca cooling pins neutron star proton fraction near 15%","Cooling data sharpen neutron star proton fraction, leave radii unchanged","Direct Urca cooling reshapes inferred core composition, not size","Cooling observations favor higher proton fraction in neutron stars"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000622,"raw_usage":{"cost":0.000621768,"is_byok":false,"cost_details":{"upstream_inference_cost":0.000621768,"upstream_inference_prompt_cost":0.000127848,"upstream_inference_completions_cost":0.00049392},"total_tokens":2882,"prompt_tokens":1118,"completion_tokens":1764,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":256,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":1693}},"tokens_in":1118,"tokens_out":1764,"cost_source":"openrouter_usage","duration_ms":9849,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":1693,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-09-25T03:29:39.516437+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Take an independent mass measurement of one of the rapid-cooling anchors, such as Cassiopeia A or Vela, obtained without any thermal cooling modeling: if that mass lies below the dUrca threshold region, the central proton-fraction posterior near 0.15 should collapse toward the lower values that laboratory symmetry-energy data alone imply. A definitive resolution of the HESS J1731$-$347 mass debate would likewise move the slow-cooling anchor and re-test the constraint from the other end.","supporting_citations":[{"cited_title":"Direct URCA process in neutron stars, Phys. Rev. Lett.66, 2701","cited_arxiv_id":null,"evidence_quote":"Defines the direct Urca process and supplies the threshold condition behind Eq. (1)."},{"cited_title":"Kl¨ ahn, D","cited_arxiv_id":null,"evidence_quote":"Supplies the numerical threshold values, about 11.1% in npe matter and 14.8% with muons, that anchor the onset calculation."},{"cited_title":"Wouters, P","cited_arxiv_id":null,"evidence_quote":"The jester framework that the authors extend to compute proton fraction and dUrca threshold self-consistently."},{"cited_title":"The equation of state for dense nucleonic matter from a metamodeling. I. Foundational aspects","cited_arxiv_id":"1708.06894","evidence_quote":"Provides the metamodel construction used for the nucleonic part of the equation of state."},{"cited_title":"Ruling out nucleonic direct Urca cooling in low-mass neutron stars using nuclear data","cited_arxiv_id":"2609.24940","evidence_quote":"The contrasting laboratory-based result ($Y_p \\approx 0.07$–$0.09$) that the dUrca constraint must be reconciled with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the minimal cooling paradigm used to classify which sources are rapidly cooling."},{"cited_title":"G. P¨ uhlhofer, and A. Santangelo, A strangely light neutron star within a supernova remnant, Nature Astron.6, 1444","cited_arxiv_id":null,"evidence_quote":"Supplies the HESS J1731$-$347 mass and radius used as the slow-cooling anchor, whose debated value is acknowledged."},{"cited_title":"Constraints on Thermal X-ray Radiation from SAX J1808.4-3658 and Implications for Neutron Star Neutrino Emission","cited_arxiv_id":"astro-ph/0612232","evidence_quote":"Provides the independently measured cooling profile and mass for SAX J1808.4$-$3658, the one rapid-cooling anchor not derived from cooling models."}],"review_version":1}