{"id":"b83baf83-cdcf-4c7a-a22e-86e80b5786f0","arxiv_id":"2607.18117","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"New DFT calculations give MgHCu3 a superconducting temperature of 10–31 K, not the previously reported 42 K.","lead":"This paper re-runs computer simulations of the proposed superconductor MgHCu3 and finds the predicted critical temperature depends heavily on calculation settings, coming out at roughly 10–31 K instead of the earlier 42 K. It argues that many predicted high-temperature hydride superconductors need more rigorous numerical and experimental checking.","discovery_kind":"replication","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Uncontrolled phonon convergence and unreported μ* leave the 'never above 40 K' claim unproven; the paper's own admission that Migdal–Eliashberg fails at λ=2.95 means TC is genuinely unknown.","rationale":"The reader's weakest assumption identifies the same load-bearing issue: the computed TC range (10–31 K) can only support the headline 'below 40 K' if the spread across k-meshes/functionals is physical rather than a numerical artifact. The paper itself shows non-monotonic phonon behavior, including imaginary modes at intermediate meshes and stability at the densest mesh, and offers only a speculative interpretation ('vicinity of a phonon-driven phase transition') without a convergence study. The missing μ* value compounds the problem because TC depends exponentially on it, and the admitted breakdown of Migdal–Eliashberg at λ=2.95 means the highest-λ result cannot be used as a reliable upper limit. These are internal consistency concerns, not disagreements with external consensus. The paper does provide creditable evidence that electronic structure and lattice constants are robust, and it transparently reports the raw spread, which is why the verdict remains conditional rather than rejected. The concrete test—systematic q-grid/cutoff/μ* convergence—would settle whether the 'below 40 K' conclusion is a physical property of MgHCu3 or a numerical artifact of the chosen settings.","tokens_in":8835,"tokens_out":3499,"duration_ms":37566,"concrete_test":"Run an independent DFPT/EPW calculation for MgHCu3 using the same PBEsol and PBE pseudopotentials, systematically converging the phonon q-grid (e.g., 4×4×4, 6×6×6, 8×8×8) at a fixed dense k-mesh, with plane-wave cutoff varied by ±20%, and report McMillan–Allen–Dynes TC for μ* = 0.0, 0.1, and 0.15. If every converged combination gives TC < 40 K, the claim is robust; if any entry exceeds 40 K, the 'classical limit' assertion fails. Also check whether the re-entrant instability persists when the q-grid is refined.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim—that the computed TC values 'do not exceed the classical limit'—depends on treating the spread in Table 1 as a fair representation of method uncertainty. That assumption is not supported. Section 2.2 shows phonon spectra varying wildly with k-mesh and functional: PBE becomes dynamically unstable at 15×15×15 and 18×18×18, then stable again at 24×24×24 ('re-entrant stability'). The paper provides no convergence criterion, no variation of the phonon q-grid, no plane-wave cutoff or smearing tests, and only a fixed Gaussian broadening of 0.03 Ry. If the intermediate instabilities are numerical artifacts, the 24×24×24 'stable' results may be equally unreliable. Moreover, the McMillan–Allen–Dynes formula requires the Coulomb pseudopotential μ*, which is never stated in the text or SI. TC is exponentially sensitive to μ*: for the PBE 24×24×24 row (λ=2.95, ωlog=158 K), changing μ* from 0.1 to 0.0 raises TC from ~28 K to ~33 K, and the sensitivity grows with λ. The authors themselves concede that for λ>1.5 'Migdal-Eliashberg equations do not work well, so the precise TC value in fact remains unknown.' A calculation with undocumented convergence parameters cannot establish a rigorous upper bound of 40 K.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper re-examines the hypothetical perovskite hydride MgHCu3, which was previously predicted to superconduct at TC = 42 K, just above the often-quoted 40 K 'classical limit' for phonon-mediated superconductivity. Using first-principles DFT with PBEsol and PBE functionals and k-point meshes from 12×12×12 to 24×24×24, the authors find that the crystal structure and electronic density of states are robust, but phonon dispersions, the electron–phonon coupling constant λ, and the resulting McMillan–Allen–Dynes TC are highly sensitive to the computational settings. Their computed TC values range from 9.5 K to 31.3 K, all below 40 K, and they conclude that the earlier 42 K prediction is not reproduced and that high-TC hydride predictions need more careful numerical scrutiny and experimental benchmarking.","tokens_in":9222,"tokens_out":4045,"duration_ms":45753,"significance":"If fully supported, the paper would be a useful cautionary counterexample to a published ambient-pressure hydride superconductivity prediction, showing that numerical sensitivity alone can place TC far below the claimed value. The work has clear strengths: it is an independent re-computation, it compares two functionals and several k-meshes, it makes the underlying data available in the table and SI, and it openly states the limitation of Migdal–Eliashberg theory at large λ. It does not fit parameters to force a desired TC, so the negative result is not circular. However, the central claim that 'TC does not exceed the classical limit' currently rests on an unreported Coulomb pseudopotential μ*, on unverified phonon convergence, and on at least one TC value obtained outside the stated validity regime of the method. These issues are load-bearing and must be addressed before the conclusion can be considered established.","major_comments":[{"comment":"The McMillan–Allen–Dynes formula used to compute TC depends on the Coulomb pseudopotential μ*, but μ* is never stated in the text, in Table 1, or in the SI. Since TC is exponentially sensitive to μ*, particularly at λ = 2.95 (PBE, 24×24×24), the reported TC values such as 28.3 K are not reproducible and the conclusion that all values 'do not exceed the classical limit' is not fully supported. The authors should quote μ* for every row and show the TC(μ*) dependence over the standard 0.08–0.15 range.","section":"Methods / §2.3, Table 1"},{"comment":"The paper documents 're-entrant stability' — PBE is stable at 12×12×12, unstable at 15×15×15 and 18×18×18, and stable again at 24×24×24 — but provides no convergence criterion and no variation of the phonon q-grid, plane-wave cutoff, or smearing. If the intermediate imaginary modes are numerical artifacts, the 24×24×24 'stable' phonons and the TC derived from them may be equally unreliable. A q-grid convergence study, or at least a clear convergence criterion, is necessary before the spread in Table 1 can be interpreted as a faithful representation of method uncertainty.","section":"§2.2"},{"comment":"The authors state that for λ > 1.5 the Migdal–Eliashberg equations 'do not work well, so the precise TC value in fact remains unknown.' The PBE 24×24×24 row has λ = 2.95, yet its TC = 28.3 K is used as one of the main results. A value obtained outside the claimed validity range cannot support the upper-bound conclusion that the computed TC values do not exceed 40 K. Either an alternative treatment (e.g., full Eliashberg or a stated extrapolation) should be provided, or this row should be excluded from the central claim.","section":"§2.3"},{"comment":"The abstract states that TC values for 'different Gaussian broadenings' vary from ca. 10 to 31 K, but the range in Table 1 is obtained at a fixed Gaussian broadening of 0.03 Ry while varying k-point mesh and functional. This wording conflates two different numerical sensitivities. The broadening dependence is only reported in the SI and never quantified in the main text. The authors should rephrase the abstract and report the broadening-sensitivity range explicitly so that the source of the TC spread is clear.","section":"Abstract / §2"}],"minor_comments":[{"comment":"Typo: 'k-point mash' should be 'k-point mesh'. The footnote 'PPa)' is also unclear; please spell out the abbreviations.","section":"Table 1 caption"},{"comment":"The symbol L is used for the electron–phonon coupling constant; the standard notation λ would improve readability and avoid confusion with angular momentum or lattice parameters.","section":"Throughout"},{"comment":"The reference to 'S1 in SI' should be more precise (e.g., Fig. S1), and the SI figure numbering should be tied explicitly to the statements in the main text.","section":"§2.1"},{"comment":"The phrase 'increasing counterclockwise' in the figure caption is ambiguous. Label each panel with the k-point mesh used.","section":"§2.2 / Figure 2"},{"comment":"The Gaussian broadening value is given as 0.03 Ry with a citation to previous work, but the choice is not justified here and no convergence test in the broadening is shown in the main text. At minimum, state the range of broadenings explored and the resulting TC spread.","section":"Methods"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely question and the negative result is potentially valuable, but the current manuscript does not yet support its central upper-bound claim. The missing μ* and the unverified phonon convergence are the two decisive gaps; both are fixable within the scope of a revision. The manuscript fits the journal's scope and I would be willing to review a revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a legitimate critical follow-up that does its job — it shows the original 42 K prediction for MgHCu3 is not reproduced under routine methodological variation. The paper is worth reading for anyone treating that 42 K number as a benchmark for ambient-pressure hydride superconductivity.\n\nWhat's actually new: a concrete re-computation for the same compound with PBEsol (same as the original) and PBE across four k-meshes, with a clear table showing TC varies from 9.5 to 31.3 K. The original 42 K sits above every value they get. That is a real, useful negative result. They also flag that phonon stability is non-monotonic in k-mesh (\"re-entrant stability\"), a warning sign for the original calculation and for the field's usual convergence checks.\n\nCredit where earned: the work is straightforward, the table is transparent, and the authors are honest about the limits of the Eliashberg framework at λ=2.95. They don't overstate in the conclusion; they call for experimental benchmarking and further theory.\n\nSoft spots, in proportion. The main overreach is the abstract's \"they do not exceed the classical limit.\" That is presented as a firm bound, but they never state the Coulomb pseudopotential μ* used in the McMillan–Allen–Dynes formula. TC is exponentially sensitive to μ*, especially at large λ. The PBE 24×24×24 row (λ=2.95, ωlog=158 K) gives roughly 28–33 K for μ*=0.1–0.0 — still below 42 K, but the spread matters for a rigorous statement. More importantly, they don't test the phonon q-grid, plane-wave cutoff, or smearing, and they provide no convergence criterion. The \"re-entrant stability\" may be physical, but it could also be an artifact of an unconverged phonon calculation. So the exact TC bounds are not solid, but the qualitative conclusion — the 42 K value is fragile — holds up. Even if you give the original calculation every benefit of the doubt, this paper shows it's not reproducible in a straightforward rerun.\n\nOne minor point: the abstract says \"for different Gaussian broadenings\" while the text reports a single broadening (0.03 Ry) and defers the dependence to the SI. Sloppy.\n\nBottom line: this deserves a serious referee. It's a critical result for a specific predicted superconductor and raises a legitimate methodological flag for the hydride-TC field. It needs revision to state μ*, add some phonon-q-grid/cutoff checks, and soften the \"do not exceed 40 K\" claim to \"we find no evidence for TC above 40 K in our calculations.\" Then it's publishable. I'd bring it to reading group and would cite it if I were working on hydride superconductivity.","headline":"A useful, honest critical check: MgHCu3's 42 K claim doesn't survive routine k-mesh/functional variation, though the paper's own 40 K upper bound is overconfident because μ* and phonon convergence are unstated.","tokens_in":9694,"tokens_out":3238,"would_cite":true,"duration_ms":31532,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.20.Pq","71.15.Mb"],"model":"deepseek-v4-flash","headline":"A reexamination of the predicted perovskite hydride superconductor MgHCu3 finds that its previously reported 42 K critical temperature is not reproduced; with the same theoretical approach, computed values fall between about 10 and 31 K, al","keywords":["MgHCu3","hydride superconductor","phonon-mediated superconductivity","electron-phonon coupling","perovskite","density functional theory","critical temperature","BCS theory"],"falsifier":"A controlled convergence study that varies the phonon q-grid, energy cutoff, and electronic smearing for MgHCu3 — something the authors did not perform — would settle the issue: if a single, robust Tc above 40 K emerges under such a stress test, the paper's central conclusion is wrong. Alternatively, synthesizing MgHCu3 and measuring its resistivity or magnetic susceptibility would provide a direct experimental test of whether superconductivity occurs at 42 K, in the 10–31 K window, or not at all.","tokens_in":8735,"feed_emoji":"🧊","tokens_out":8879,"duration_ms":75601,"temperature":0.7,"pith_summary":"The paper revisits a published claim that the hypothetical ambient-pressure hydride MgHCu3 superconducts at 42 K, just above the long-standing '40 K limit' for phonon-mediated pairing. The authors show that while the crystal and electronic structure of this cubic perovskite are stable across the PBEsol and PBE functionals and over k-point meshes from 12×12×12 to 24×24×24, the phonon spectrum and all derived quantities change dramatically with those settings. Using the standard McMillan–Allen–Dynes formula, they obtain critical temperatures between roughly 9.5 K and 31.3 K (about 10–31 K) for the same 0.03 Ry Gaussian broadening, never approaching 42 K. The authors argue that MgHCu3 and many other claimed high-Tc hydrides need systematic multi-functional, multi-grid scrutiny and experimental benchmarking before their superconducting temperatures can be trusted.","feed_headline":"Recheck sees MgHCu3's Tc at 10–31 K, not 42 K","feed_subtitle":"Recomputed phonons with two functionals and four k-meshes keep Tc below the classical 40 K ceiling.","key_machinery":"The key object is the hypothetical cubic perovskite MgHCu3, studied with the standard DFT-based pipeline for phonon-mediated superconductivity: the PBEsol and PBE functionals, k-point meshes of 12×12×12 through 24×24×24, and the McMillan–Allen–Dynes formula applied to the Eliashberg function. The decisive physical quantity is the phonon dispersion, since the derived spectral function α²F(ω) determines both the electron-phonon coupling constant λ and the logarithmic average frequency ω_log, which together set Tc. The paper's central observation is that this phonon-derived quantity is highly unstable with respect to numerical settings, even though the underlying crystal and electronic structur","core_discovery":"The central claim is a negative replication of the 42 K superconducting critical temperature predicted for MgHCu3 under ambient pressure. The lattice constant and Fermi-level density of states computed here are nearly identical to the earlier report, but the phonon dispersions are extremely sensitive to the choice of functional and k-point grid: some intermediate grids give imaginary (unstable) phonon modes, the densest grid restores stability, and the PBEsol and PBE functionals produce qualitatively different phonon spectra. As a result, the logarithmic average phonon frequency varies from 158 K to 423 K and the electron-phonon coupling constant λ from 0.75 to 2.95, which translates into Tc","pith_inferences":["If the phonon sensitivity seen in MgHCu3 is common, other published ambient-pressure hydride Tc predictions may carry error bars far larger than their reported precision, and headline 'record' values could shift below or above the classical limit under the same stress tests.","The 're-entrant stability' pattern suggests a nearby structural phase transition; anharmonic phonon calculations could reveal whether the soft modes actually drive MgHCu3 into a lower-symmetry phase with a different — possibly zero — Tc.","A direct experimental attempt to synthesize MgHCu3 — even as a metastable film — and measure its resistivity or magnetization would be the decisive benchmark: observing or excluding superconductivity near the predicted temperatures would settle which of the computed values, if any, is physically relevant.","The paper's methodology (scanning k-meshes and functionals) could be adopted as a routine 'stress test' for any proposed hydride superconductor, catching numerically fragile predictions before they enter the literature."],"forward_implications":["If the spread of computed values reflects genuine methodological uncertainty, MgHCu3's ambient-pressure phonon-mediated Tc lies at 10–31 K, not near 42 K.","The phonons show 're-entrant stability' — imaginary modes at intermediate k-grids but stable at coarse and dense grids — indicating MgHCu3 is close to a phonon-driven instability, which could affect whether the material superconducts at all.","For MgHCu3, the k-point mesh and functional choice are at least as important as the underlying physics in determining predicted Tc; this caution extends to other computed hydride superconductors.","When λ exceeds about 1.5 (PBE, 24×24×24), the Migdal–Eliashberg approximation becomes unreliable, so the actual Tc in that regime is not well determined by this method.","The authors' recommendation is that theoretical high-Tc hydride predictions be cross-checked with multiple functionals and benchmarked against experiment before being cited as evidence for surpassing the classical limit."],"fun_headline_variants":["MgHCu3 Tc drops to 10–31 K in rigorous recheck","Superconductivity in MgHCu3: Tc depends on grid, runs 10–31 K","Computational detail slashes MgHCu3's Tc below 40 K","Grid/functional choice swings MgHCu3 Tc from 10 to 31 K","Phonon sensitivity: MgHCu3 Tc ranges 10–31 K, not 42 K"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire conclusion depends on the assumption that the rapid, non-monotonic variation of the computed phonons across k-meshes is a genuine physical response of MgHCu3 rather than an uncontrolled artifact of the numerical settings, since the paper does not vary the phonon q-grid, plane-wave cutoff, or smearing and gives no convergence criterion for the phonon results.","fun_headline_variants_meta":{"raw":{"variants":["MgHCu3 Tc drops to 10–31 K in rigorous recheck","Superconductivity in MgHCu3: Tc depends on grid, runs 10–31 K","Computational detail slashes MgHCu3's Tc below 40 K","Grid/functional choice swings MgHCu3 Tc from 10 to 31 K","Phonon sensitivity: MgHCu3 Tc ranges 10–31 K, not 42 K"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000816,"raw_usage":{"total_tokens":3403,"prompt_tokens":730,"completion_tokens":2673,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":474,"completion_tokens_details":{"reasoning_tokens":2558}},"tokens_in":474,"tokens_out":2673,"duration_ms":18102,"temperature":1.0,"reasoning_tokens":2558,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T15:56:29.764795+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A controlled convergence study that varies the phonon q-grid, energy cutoff, and electronic smearing for MgHCu3 — something the authors did not perform — would settle the issue: if a single, robust Tc above 40 K emerges under such a stress test, the paper's central conclusion is wrong. Alternatively, synthesizing MgHCu3 and measuring its resistivity or magnetic susceptibility would provide a direct experimental test of whether superconductivity occurs at 42 K, in the 10–31 K window, or not at all.","supporting_citations":[],"review_version":1}