{"id":"f536b0d2-089c-47c1-bb7a-0c93bfad8174","arxiv_id":"2412.05291","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Hirsch and Marsiglio rebut claims that their Bean-model analysis of trapped flux misrepresents the Meissner state, arguing the Comment plotted their equations outside their valid field range.","lead":"This paper is a reply to a formal Comment that accused the authors of hiding data and using a flawed model in their earlier analysis of magnetic flux trapping experiments on hydrides under high pressure. The reply defends the model, argues the Comment misused the equations, and rechallenges the evidence for superconductivity in these materials.","discovery_kind":"unclear","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Reply's refutation of the 'hiding/deleting' charge depends on a boundary condition that was never stated in the original paper; as published, Eqs. (4)-(5) do yield nonzero moments for H_M < H_p, so the Comment's reading is not 'blatantly false.'","rationale":"The reader identified the Bean-model applicability and Hp transferability as the weakest assumption. I think the more immediately load-bearing weakness is the Reply's reliance on a boundary condition that was never stated in the original paper. The Reply's strongest rhetorical claim—'all ten accusations are unfounded'—fails on claims 6 and 7 even if the Bean model is correct, because the Comment's use of the published equations below H_p is a faithful reading of the text. The Reply's subsequent letter cannot retroactively establish knowledge at the time of writing. This supports the CONDITIONAL verdict rather than a full acceptance of the Reply's refutation, so I leave the reader's verdict unchanged.","tokens_in":9459,"tokens_out":11748,"duration_ms":127339,"concrete_test":"Run the Fortran 77 code as posted in the Comment (arXiv:2312.04495) with H_M = 0 and the parameters used in Ref. [3], and record the printed m_trap. If the code returns a positive value, the Comment's statement that 'the code predicts a positive moment in the Meissner regime' is literally true; the only remaining question is whether the original paper's context made the H_M < H_p restriction explicit, which the Reply admits it did not. This single check settles whether the 'hiding/deleting' accusation is a misreading or a faithful reading of the model as published.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Reply's claim that all ten Comment accusations are unfounded rests on asserting that Eqs. (4)-(5) of Ref. [3] were understood to apply only for H_M >= H_p, with m_trap = 0 below H_p. But the Reply itself concedes in Sec. III.A that the original paper did not state this restriction. As printed, Eqs. (4)-(5) evaluated at H_M = 0 give r1, r2 > d/2 and a positive moment; the Fortran code shared with the Comment authors printed those numbers. The Comment's figures plot that output and call it the model's prediction. The Reply's defense is a retrospective boundary condition: 'it was completely obvious from the context.' Whether or not that is good physics, it does not make the Comment's reading 'blatantly false' as a matter of the published text. Moreover, the Appendix letter is dated December 8, 2023, one day after the Comment was posted, so it cannot show that the Comment authors knew the supposed restriction when they wrote. Therefore claims 6 and 7 are not fully refuted; the Reply has not established that all ten accusations are unfounded.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript is a formal Reply by Hirsch and Marsiglio to a Comment by Talantsev, Minkov, Ksenofontov, Bud'ko, and Eremets, which accused the authors of the original paper (J. Supercond. Nov. Mag. 35, 3141 (2022)) of using a wrong model, hiding/deleting parts of simulated datasets that disagree with the Meissner regime, restricting access to their computer code, and other methodological misconduct. The Reply argues that all ten accusations in the Comment are unfounded. Its central defense is that the Hirsch-Marsiglio model, based on the Bean critical-state model, predicts zero trapped magnetic moment for applied fields below the penetration threshold Hp, and that the Comment's accusation rests on applying Eqs. (4)--(5) of Ref. [3] outside their intended domain H_M >= Hp. The Reply also asserts that the model was subsequently validated against flux-trapping measurements on known superconductors (Bud'ko et al.) in Refs. [11,14], that the hydride ZFC data show a linear rather than quadratic field dependence and are therefore inconsistent with superconducting behavior, and that the Comment's authors were informed of the boundary-condition issue by a letter reproduced in the Appendix. The Reply includes a history of the code-sharing exchange and an acknowledgment that one of their own figures contained a sign error, which it deems irrelevant to the main issue.","tokens_in":9722,"tokens_out":5233,"duration_ms":49233,"significance":"If the Reply's arguments are correct, they would clear the authors of the data-hiding and misconduct charges and reinforce their earlier challenge to the interpretation of trapped-flux experiments on hydrides as evidence for high-temperature superconductivity. The Reply usefully clarifies the Bean-model prediction of quadratic ZFC trapped-moment field dependence and honestly acknowledges a sign error in a previous figure. However, the Reply's central historical defense is weakened by its own concession (Sec. III.A) that the original paper never explicitly stated the domain restriction H_M >= Hp for Eqs. (4)--(5). As a result, the Reply's strong claim that the Comment's reading is 'utterly and blatantly false' is overstated. The Reply also relies on a transferability assumption between separate screening and trapping experiments that is not defended. The paper makes a plausible technical case but does not fully establish that all ten accusations are unfounded.","major_comments":[{"comment":"The Reply concedes that it 'did not state explicitly that Eqs. (5) did not apply to the region HM < Hp,' yet in Section VI it calls the Comment's statements about nonzero moments in the Meissner regime 'utterly and blatantly false.' As printed, Eqs. (4)--(5) of Ref. [3] evaluated at HM = 0 yield r1, r2 > d/2 and a positive moment, so the Comment's reading is a plausible interpretation of the published text even if it is physically wrong. The Reply should acknowledge the ambiguity in the original paper and argue why the physical context makes the boundary condition m = 0 for HM <= Hp obvious, rather than accusing the Comment authors of knowingly making false statements.","section":"III.A"},{"comment":"The Reply's blanket claim that 'all of them are unfounded' (Section I) is not supported even by its own arguments. For claims 6 and 7, the Reply's own concession of the unstated domain restriction shows that the Comment's reading was not baseless, even if the Comment's inference of deliberate hiding is unwarranted. For claims 2 and 9, the Reply merely explains (Section III.B) why it did not consider the post-pressure-release reference measurements relevant, which is a scientific disagreement rather than a demonstration that the claim is unfounded. The Reply should be revised to claim that the accusations are 'not supported' or 'incorrect in our reading,' rather than 'unfounded' in every case.","section":"I, III.A, VI"},{"comment":"The Reply argues that it is difficult to understand how a sample that excludes magnetic fields smaller than about 95--108 mT (Refs. [17,19]) could trap flux between 42 mT and 108 mT. This argument assumes that the penetration field Hp measured in separate magnetic screening experiments applies quantitatively to the same samples and experimental conditions as the flux-trapping measurements. The Reply does not justify this transferability, and the Comment's position is that the trapping data themselves imply a lower threshold (about 42 mT) in those runs. Without direct evidence that the Hp values from different experimental setups are comparable, this argument does not by itself refute the Comment's claims.","section":"V"},{"comment":"The Reply uses the December 8, 2023 letter reproduced in the Appendix as evidence that the Comment authors knew the boundary condition and nonetheless repeated their claims. However, the Comment was posted on December 7, 2023 (Ref. [8]), one day before the letter was sent. The letter therefore cannot establish that the Comment authors knew of the boundary-condition restriction at the time they wrote their Comment. It can only show that they were informed afterward and did not retract. The Reply's rhetorical claim that the Comment authors 'must know' is not supported by the evidence presented.","section":"Appendix and Section VI"}],"minor_comments":[{"comment":"The phrase 'the authors of this Comment' in item 3 should read 'the authors of the Comment' to avoid confusion with the authors of the Reply.","section":"II, item 3"},{"comment":"There is a typo in the third paragraph: 'misuderstanding' should be 'misunderstanding.'","section":"IV"},{"comment":"The sentence 'Why do the authors of Ref. [1] choose to knowingly write such falsehoods and submit them for publication in a scientific journal?' is accusatory and would be more appropriately replaced by a factual statement that the Comment's interpretation is inconsistent with the Bean model and the intended domain of Eqs. (4)--(5).","section":"VI"},{"comment":"In the discussion of Ref. [19], the phrase 'Revaluation of the lower critical field' should be 'Re-evaluation of the lower critical field' to match standard English usage.","section":"V"},{"comment":"The Reply says 'in all the examples we showed (Figs. 3, 4, and 5 of Ref. [3]) we showed calculated ZFC values as dashed lines in red, and in all the figures the dashed red lines were plotted only for HM ≥ Hp.' It would be helpful to explicitly note in the Reply that the original paper did not state this restriction, to avoid the appearance of an after-the-fact justification.","section":"III.A"}],"recommendation":"major_revision","confidential_remarks":"The Reply is part of an ongoing and heated exchange. The technical core—the Bean-model quadratic ZFC dependence and the logical necessity of m=0 below Hp—appears sound, and the authors deserve credit for acknowledging a sign error in an earlier figure. However, the Reply's historical claims are too strong: the original paper's silence on the domain of Eqs. (4)--(5) makes the Comment's reading defensible as a textual matter, and the Reply's 'utterly and blatantly false' language is disproportionate. The cross-experiment comparison of Hp values in Section V also needs tightening. I believe these issues can be fixed by rewording the Reply's claims and adding an explicit acknowledgment of the original ambiguity, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here is my honest take on the Hirsch–Marsiglio Reply. The physics is on their side, but the paper overreaches in its accusation.\n\nWhat is right: The Bean critical-state model gives zero trapped moment for applied fields below the penetration threshold Hp, and the Comment's figures plotted the model equations in a regime where r1 and r2 exceed the sample radius—physically meaningless. The Reply clearly explains the quadratic ZFC prediction and contrasts it with the linear fit the Comment authors' own preprint used for the hydride data. That fit vanished in later versions, a checkable fact. The Reply also concedes the sign error in its Fig. 2, and makes a strong empirical point: if screening data imply Hp between 95 and 108 mT, trapping at 42 mT is hard to understand.\n\nThe soft spot is the Reply's central claim that all ten Comment accusations are 'utterly and blatantly false.' That is too strong. As the Reply itself admits in Sec. III.A, the original paper did not state that Eqs. (4)–(5) apply only for H ≥ Hp. The boundary condition was implicit in the physics, but it was not in the published text. The Comment authors' reading—evaluate the equations as written—is uncharitable but not fabricated. Calling it 'blatantly false' converts a legitimate ambiguity in the original paper into an accusation of dishonesty. The Appendix letter, dated December 8, 2023, cannot show the Comment authors knew the restriction before they wrote, because the Comment was posted the day before. So claims 6 and 7 are not fully refuted; the Reply has shown the Comment was wrong physically, but not that the Comment was knowingly dishonest.\n\nThe Reply also relies heavily on Refs. [11] and [14] for validation against known superconductors. Those papers do analyze external Bud'ko data, so it is not pure self-citation, but it is not independent confirmation. And the Reply dismisses Prozorov's point that other critical-state models can give non-quadratic ZFC behavior without addressing it much beyond 'the data are quadratic in known superconductors.' That is an empirical argument, not a proof.\n\nWho should read it: anyone following the hydride superconductivity controversy. It clarifies what the Hirsch–Marsiglio model does and exposes a real weakness in the Comment's use of the equations. But it does not settle the debate. A referee should insist the Reply be toned down: drop or soften the misconduct accusations and acknowledge that the original paper's failure to state the domain of validity contributed to the misunderstanding. With that change, the Reply makes a legitimate scientific point.\n\nYes, it deserves peer review—a serious referee should engage with it, but expect heavy revision.","headline":"The Reply's physics is right but its 'blatantly false' charge overreaches; the original paper never stated the H<Hp restriction, so claims 6 and 7 are not fully refuted.","tokens_in":10247,"tokens_out":3673,"would_cite":false,"duration_ms":34590,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The Reply argues that the Comment's charge of hidden data comes from evaluating the model below the penetration field, where no trapped moment exists.","keywords":["flux trapping","hydride superconductivity","Bean critical-state model","zero-field-cooled protocol","penetration field","Meissner state","trapped magnetic moment","quadratic field dependence"],"falsifier":"Perform a combined measurement on one hydride sample in a diamond anvil cell, without background subtraction, that records both the onset of magnetic screening (the penetration field $H_p$) and the lowest applied field at which a remnant moment appears after field removal; if a trapped moment appears below $H_p$ or if a known superconductor under identical conditions shows a linear rather than quadratic onset, the Reply's central claim is falsified.","tokens_in":9263,"feed_emoji":"🧲","tokens_out":8588,"duration_ms":92565,"temperature":0.7,"pith_summary":"This paper is a Reply to a Comment that accused the authors of hiding simulated data points and of failing to describe the Meissner state. The Reply argues that the accusation comes from applying the model's equations in the field region below the penetration threshold $H_p$, where the model predicts zero trapped moment and where no valid curve exists. Read correctly, the Reply claims, the Bean critical-state model predicts that zero-field-cooled (ZFC) trapped flux grows quadratically with $H - H_p$, not linearly. It then asserts that hydrides under pressure show linear ZFC trapping, while known superconductors show quadratic trapping, so the linear signal is evidence against superconductivity in the hydrides.","feed_headline":"Reply: hidden-data claim misreads model below penetration field","feed_subtitle":"The Reply says ZFC trapped flux in a superconductor must rise quadratically, not linearly.","key_machinery":"The machinery is the Bean critical-state model for a disk under the ZFC protocol. When a field is applied and removed, currents occupy an annulus between $r_2$ and $d/2$ and a disk inside $r_1$, yielding $m = m_s[1 - 2(r_1/(d/2))^3 + (r_2/(d/2))^3]$. As $H$ approaches $H_p$ from above, both $r_1$ and $r_2$ approach $d/2$, so the trapped moment goes to zero quadratically in $H - H_p$. The Reply's central move is to insist that the alternative linear formula, Eqs. (2)-(3), describes a field-cooled protocol, not a ZFC one, and that any use of the equations below $H_p$ produces radii outside the sample and is therefore unphysical.","core_discovery":"The core claim is that the Comment's \"hide/delete\" charge rests on a misreading of Eqs. (4) and (5) of the original paper, which give the inner and outer current-front radii $r_1$ and $r_2$; these radii must lie inside the sample, and using the equations for $H < H_p$ pushes them outside, which the model never asserts. The model's actual ZFC prediction is $m = m_s[1 - 2(r_1/(d/2))^3 + (r_2/(d/2))^3]$, which vanishes for $H \\le H_p$ and rises as $(H - H_p)^2$ just above threshold. From this, the Reply defends the original conclusion: the hydride data's reported linear dependence is inconsistent with the Bean model applied to a superconductor, and the reported trapping threshold of 42 mT conflicts with the independently measured penetration field of roughly 95 to 108 mT.","pith_inferences":["If this quadratic-onset criterion is adopted as a diagnostic, any future flux-trapping claim for hydrides must exhibit $m \\propto (H - H_p)^2$; a linear onset would point instead to ferromagnetic impurities or magnetomechanical artifacts.","The dispute could be settled empirically without new theory: measure trapping and screening on the same sample in the same cell, which would make $H_p$ and the trapping threshold directly comparable.","The Reply's logic suggests a cheap reanalysis of existing ZFC datasets on other candidate high-pressure superconductors: classify them by the power of the field onset, which may serve as a screening test independent of resistance measurements.","A strong test of the Reply's premise would be a trapped-flux measurement on a known type-II superconductor inside a diamond anvil cell; if it shows linear ZFC onset under pressure, the quadratic criterion would need to be relaxed."],"forward_implications":["The Comment's curves extending below $H_p$ are not predictions of the model; the model gives zero trapped moment for $H \\le H_p$.","Zero-field-cooled trapped flux in known superconductors rises quadratically in $H - H_p$, so the hydrides' linear rise is anomalous.","A sample that excludes fields below roughly 95 to 108 mT cannot trap flux at 42 mT; therefore the trapped moment in the hydrides is not superconducting in origin.","The omission of red curves for $H < H_p$ in the original figures was not data-hiding but a direct consequence of the model's boundary condition $m = 0$ for $H \\le H_p$.","Control measurements after pressure release are irrelevant because cracked diamonds and reduced pressure change both sample and environment."],"supporting_citations":[{"why":"The paper whose Eqs. (4)-(5) and figures are accused of hiding data; the Reply defends its ZFC quadratic prediction.","marker":"[3]"},{"why":"The Nature Physics report of hydride trapped flux that the Reply reanalyzes, citing its 42 mT trapping threshold.","marker":"[4]"},{"why":"The original arXiv v1 containing the linear fit, Eq. (1), that the Reply says was later silently removed.","marker":"[6]"},{"why":"Bean's 1962 letter introducing the critical-state model that underlies the Reply's equations.","marker":"[15]"},{"why":"Bean's 1964 review providing the slab field/current profile that justifies the disk-geometry radii r1 and r2.","marker":"[16]"},{"why":"Magnetic screening measurements giving Hp ~ 95 mT, used to show trapping at 42 mT is inconsistent.","marker":"[17]"},{"why":"Revaluation of the lower critical field, giving an even higher Hp ~ 108 mT, strengthening the inconsistency.","marker":"[19]"},{"why":"The Reply's own later analysis showing ZFC trapping in known superconductors is quadratic.","marker":"[11]"},{"why":"Cited as agreeing that the Bean model predicts quadratic ZFC field dependence, contrary to the Comment's claim.","marker":"[21]"},{"why":"Independent comment disproving the flux-creep signature, further undermining the hydride superconductivity claim.","marker":"[23]"}],"fun_headline_variants":["Quadratic, not linear: reply defends hydride flux model","Reply: comment misreads equations, flux rise is quadratic","Misreading key: reply says flux trap rises quadratically","Hydride reply: threshold vs penetration field conflict","Reply: hidden-data claim rests on equation misread"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the Bean critical-state model with a single uniform penetration field $H_p$ - and the particular value of $H_p$ measured in separate screening experiments on the same materials - applies to the trapped-flux measurements, so that a superconductor cannot trap flux below $H_p$.","fun_headline_variants_meta":{"raw":{"variants":["Quadratic, not linear: reply defends hydride flux model","Reply: comment misreads equations, flux rise is quadratic","Misreading key: reply says flux trap rises quadratically","Hydride reply: threshold vs penetration field conflict","Reply: hidden-data claim rests on equation misread"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000529,"raw_usage":{"total_tokens":2511,"prompt_tokens":868,"completion_tokens":1643,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":484,"completion_tokens_details":{"reasoning_tokens":1563}},"tokens_in":484,"tokens_out":1643,"duration_ms":11072,"temperature":1.0,"reasoning_tokens":1563,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:55:47.142460+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform a combined measurement on one hydride sample in a diamond anvil cell, without background subtraction, that records both the onset of magnetic screening (the penetration field $H_p$) and the lowest applied field at which a remnant moment appears after field removal; if a trapped moment appears below $H_p$ or if a known superconductor under identical conditions shows a linear rather than quadratic onset, the Reply's central claim is falsified.","supporting_citations":[{"cited_title":"the authors have restricted the publication of their simulation code, which we view as a breach of sci- entific integrity and open science principles","cited_arxiv_id":null,"evidence_quote":"The paper whose Eqs. (4)-(5) and figures are accused of hiding data; the Reply defends its ZFC quadratic prediction."},{"cited_title":"the authors 1 did not verify their model using any ZFC or FC data measured in well-studied supercon- ductors","cited_arxiv_id":null,"evidence_quote":"The Nature Physics report of hydride trapped flux that the Reply reanalyzes, citing its 42 mT trapping threshold."},{"cited_title":"This feature of the proposed model was not discussed by the authors1 and obviously contradicts the physics for the trapped magnetic flux in superconductors.”","cited_arxiv_id":null,"evidence_quote":"The original arXiv v1 containing the linear fit, Eq. (1), that the Reply says was later silently removed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Bean's 1962 letter introducing the critical-state model that underlies the Reply's equations."},{"cited_title":"Hirsch-Marsiglio model","cited_arxiv_id":null,"evidence_quote":"Bean's 1964 review providing the slab field/current profile that justifies the disk-geometry radii r1 and r2."},{"cited_title":"Hirsch-Marsiglio model","cited_arxiv_id":null,"evidence_quote":"Magnetic screening measurements giving Hp ~ 95 mT, used to show trapping at 42 mT is inconsistent."},{"cited_title":"predictions","cited_arxiv_id":null,"evidence_quote":"Revaluation of the lower critical field, giving an even higher Hp ~ 108 mT, strengthening the inconsistency."},{"cited_title":"Such a low estimate for Hp is inconsistent with what the authors of Ref","cited_arxiv_id":null,"evidence_quote":"Cited as agreeing that the Bean model predicts quadratic ZFC field dependence, contrary to the Comment's claim."},{"cited_title":"the demon- stration of a diamagnetic response is imperative","cited_arxiv_id":null,"evidence_quote":"Independent comment disproving the flux-creep signature, further undermining the hydride superconductivity claim."}],"review_version":1}