{"id":"3e5977a9-0b64-4548-85a1-200a1461de58","arxiv_id":"2411.09248","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Using profile likelihood on GRB 160625B spectral lags, the authors report no global chi-square minimum below the Planck scale and set 95% lower limits of 2.55e16 GeV (linear) and 1.85e7 GeV (quadratic) on the LIV energy scale.","lead":"This paper reanalyzes gamma-ray burst data to test whether the speed of light depends on photon energy, a possible signature of quantum gravity. It applies profile likelihood, a particle-physics statistical tool, and obtains one-sided lower limits on the quantum gravity energy scale rather than the bounded intervals found by earlier Bayesian analyses.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 95% limits rest on an unvalidated Δχ²=4.0 calibration: the profile minimum lies at the Planck boundary, so the Wilks/Newman threshold is not self-evidently applicable, and the one-sided versus two-sided choice is not justified.","rationale":"The central claim has two parts: (a) the profile likelihood is monotone decreasing in EQG, so there is no interior minimum below Planck; and (b) the 95% lower limits are EQG≥2.55e16 GeV and EQG≥1.85e7 GeV. The first part is supported by the published figures and by the authors' cross-check with two independent minimizers, and I have no concrete objection to it. The second part is where the argument is least secure. The confidence statement relies on Δχ² following a chi-square distribution with one degree of freedom and a threshold of 4.0, but the profile's maximum is at the Planck boundary, which is a non-regular setting. The paper's own Section III notes that the Feldman-Cousins treatment is needed close to a boundary, yet it applies the Newman prescription because the intercept is far from the boundary; this conflates the position of the tested EQG value with the position of the reference maximum. A Monte Carlo coverage study can settle the matter directly. If the coverage is adequate, the limits stand; if not, the numbers need to be recalibrated. This is exactly the assumption flagged by the reader, so I agree with the reader's weakest-assumption diagnosis and see no reason to change the conditional verdict.","tokens_in":6162,"tokens_out":13384,"duration_ms":155100,"concrete_test":"Generate Monte Carlo pseudo-data from the best-fit model using the public code and data, for true EQG values spanning the quoted limits and the Planck boundary, with tau and alpha fixed to the profiled best-fit values but re-profiled in each fit. For each true EQG, compute the profile-likelihood Δχ² curve and record the empirical 95th percentile of the distribution of Δχ² at that EQG; also record the fraction of simulations in which the true EQG lies above the Δχ²=4.0 lower limit. If the coverage is below 95% or the empirical threshold differs substantially from 4.0, recompute the limits with the corrected threshold or with a Feldman-Cousins construction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline numbers are read off the profile-likelihood curve at Δχ²=4.0, labeled as 95% c.l. This calibration is the load-bearing step. First, Δχ²=4.0 is the 95.4% quantile of a chi-square distribution with one degree of freedom for a two-sided likelihood-ratio test, whereas a one-sided lower limit is more naturally associated with Δχ²=2.71. The paper does not explain why the two-sided threshold is appropriate for a one-sided claim. Second, and more importantly, chi-squared minimum is attained at the Planck-scale edge of the parameter grid, i.e., at the physical boundary. The authors note that the Δχ²=4 intercept is far from the boundary, but that does not address the fact that the reference maximum in the likelihood ratio sits on the boundary; the regularity conditions for Wilks' theorem are therefore not automatically satisfied. The paper explicitly mentions the Feldman-Cousins prescription for the boundary case but declines to use it. Without a coverage check, the quoted limits EQG≥2.55e16 GeV and EQG≥1.85e7 GeV are not established as 95% confidence limits; they are plausible profile-likelihood crossings.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"Desai and Ganguly reanalyze the GRB 160625B spectral-lag data of Wei et al. (2017) using profile likelihood. They profile over the intrinsic-lag parameters tau and alpha, scan E_QG on a logarithmic grid from 10^6 to 10^19 GeV, and find that Delta-chi^2 decreases monotonically with E_QG for both linear and quadratic LIV, with the minimum at the Planck-scale upper boundary. They therefore quote one-sided 95% lower limits E_QG >= 2.55e16 GeV (n=1) and E_QG >= 1.85e7 GeV (n=2), and argue that profile likelihood avoids the bounded Bayesian credible intervals obtained by marginalization.","tokens_in":6422,"tokens_out":7937,"duration_ms":96217,"significance":"If the statistical calibration is correct, this is a useful proof-of-principle: it demonstrates that the choice of marginalization versus profiling can change the qualitative form of the constraint, and it provides public code and a reproducible pipeline for GRB LIV analyses. The central qualitative result, namely the absence of an interior minimum in the profiled chi-square, is clearly presented and is robust to the minimization algorithm, since Nelder-Mead and Powell give the same result. The numeric 95% limits, however, are not yet established because the threshold and boundary treatment are not justified in the manuscript.","major_comments":[{"comment":"The limits are read from the Delta-chi^2 = 4.0 intercept, which the text labels '95.4% (95%, to shorten notation)'. For a one-sided 95% lower limit on one parameter, the standard likelihood-ratio threshold is Delta-chi^2 = 2.71 (the 90th percentile of chi-square with one degree of freedom), whereas Delta-chi^2 = 4.0 corresponds to a central two-sided 95.4% interval. Because the profile decreases with E_QG, the Delta-chi^2 = 4.0 intercept is larger than the Delta-chi^2 = 2.71 intercept, so the quoted limits are stronger than a conventional one-sided 95% limit. Please recompute the limits with the one-sided threshold and state explicitly which confidence convention is being used.","section":"Section IV, Figs. 1-2"},{"comment":"The justification for using the Neyman/Wilks calibration is that the Delta-chi^2 = 4 intercept is far from the Planck boundary, but the relevant regularity condition concerns the location of the global maximum used as the reference: here chi^2_min sits at the Planck-scale edge of the grid. The likelihood-ratio statistic is therefore not automatically asymptotically chi-square with one degree of freedom, and the Feldman-Cousins prescription or a Monte Carlo coverage check is required even when the intercept is far from the boundary. Please add a coverage check or use the Feldman-Cousins prescription before quoting the limits as 95% confidence limits.","section":"Section IV"}],"minor_comments":[{"comment":"The GRB name is misspelled as 'GRB 1606025B' in the section headings; it should be 'GRB 160625B'.","section":"Sections IV and V"},{"comment":"'Newman prescription' should read 'Neyman prescription'.","section":"Section IV"},{"comment":"The phrase '95.4% (95%, to shorten notation)' is inaccurate; 95.4% is not a shorthand for 95%. Please use the precise percentile corresponding to the chosen confidence convention.","section":"Section IV"},{"comment":"The comparison mixes 1-sigma Bayesian credible intervals from W17 with 95% frequentist lower limits; a sentence clarifying that these are not directly comparable confidence levels would avoid confusion.","section":"Sections I and V"},{"comment":"The cosmological parameters H0 and Omega_M are fixed to the values used by W17; the paper should state explicitly that no uncertainty from these parameters is propagated into the quoted limits.","section":"Section II, Eq. (3)"}],"recommendation":"major_revision","confidential_remarks":"The main issue is localized but load-bearing: the one-sided confidence calibration is not justified, and the direction of the error is non-conservative in the sense that Delta-chi^2 = 4.0 gives stronger lower limits than Delta-chi^2 = 2.71. A proper one-sided treatment, possibly with a Feldman-Cousins or Monte Carlo coverage check, should be straightforward and would likely preserve the qualitative conclusion about the absence of an interior minimum. No concerns about data provenance beyond the reliance on W17's published lag table."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid, useful paper. The genuinely new thing is the application of profile likelihood to a GRB spectral-lag LIV analysis, and it produces a result absent from the prior Bayesian literature: the Δχ² curve for EQG decreases monotonically to the Planck scale, so there is no interior minimum, and the previous bounded 1σ intervals from Wei et al. (2017) and Gunapati et al. (2022) look like consequences of marginalization. The authors ship code and data and cross-check the minimization with two independent algorithms. That earns credit.\n\nThe main soft spot is the confidence calibration. They quote 95% c.l. lower limits from the intercept at Δχ² = 4.0, which is the 95.4% quantile of a chi-square with one dof for a two-sided likelihood-ratio test, not the standard one-sided 95% threshold of Δχ² = 2.71. Second, the minimum sits at the Planck-scale boundary, so Wilks regularity conditions are not automatically satisfied. Their note that the Δχ² = 4 intercept is far from the boundary doesn't address the fact that the reference maximum is on the boundary. Cleaner to say the limits are plausible profile-likelihood crossings; without a coverage study or Feldman-Cousins treatment, the '95%' label is not established.\n\nThis is fixable, not load-bearing. The qualitative result — monotone profile, no bounded interval — is unaffected by the threshold choice; only the numerical limits shift. The paper is clearly written, honest about assumptions, and the citation pattern is fine; self-citations are to background and their own earlier work, not circular.\n\nI'd send this to a serious referee. The calibration point needs a careful check, but the core reanalysis is informative and the method transfer to GRB lags is new. For me it's a conditional accept with the confidence statement to be redone.","headline":"Useful profile-likelihood reanalysis that likely overturns the bounded Bayesian interval for GRB 160625B, but the quoted 95% limits rest on an unvalidated Δχ²=4.0 calibration.","tokens_in":6956,"tokens_out":2529,"would_cite":true,"duration_ms":23810,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A profile-likelihood reanalysis of the GRB 160625B spectral-lag data finds no interior minimum for the Lorentz-invariance-violation scale below the Planck scale, yielding one-sided lower limits of $2.55\\times10^{16}$ GeV and…","keywords":["Lorentz invariance violation","spectral lag","gamma-ray bursts","profile likelihood","quantum gravity energy scale","frequentist inference","GRB 160625B"],"falsifier":"Generate Monte Carlo realizations of the 37 spectral-lag measurements from the best-fit model with no LIV, fit each realization with the same profile-likelihood procedure, and check the coverage of the reported 95% one-sided intervals; if coverage is substantially below 95% (or if $\\Delta\\chi^2=4$ is not the right one-sided cutoff), the quoted limits would need revision. Equivalently, if a scan that extends the grid above the Planck scale finds an interior global minimum, the monotonicity claim would be falsified.","tokens_in":5950,"feed_emoji":"⏱️","tokens_out":5467,"duration_ms":52146,"temperature":0.7,"pith_summary":"This paper reanalyzes the spectral-lag data of gamma-ray burst GRB 160625B with a frequentist profile-likelihood method, revisiting earlier Bayesian work that reported bounded credible intervals for the Lorentz-invariance-violating energy scale $E_{QG}$. The authors find that, for both linear and quadratic models of energy-dependent photon speed, the profiled $\\chi^2$ decreases monotonically as $E_{QG}$ approaches the Planck scale, so no interior minimum exists below the Planck energy. Consequently they quote one-sided 95% lower limits, $E_{QG} \\geq 2.55 \\times 10^{16}$ GeV for linear and $E_{QG} \\geq 1.85 \\times 10^{7}$ GeV for quadratic LIV, instead of central intervals. The result matters because it shows how the choice between marginalizing and profiling over astrophysical nuisance parameters can change the form of the final constraint on a fundamental physics scale.","feed_headline":"Profile likelihood flips GRB lag constraint to one-sided limit","feed_subtitle":"Frequentist reanalysis replaces Bayesian intervals with 95% lower limits on the LIV energy scale.","key_machinery":"The central tool is the profile likelihood, defined by maximizing the full Gaussian likelihood over the nuisance parameters $(\\tau, \\alpha)$ for each fixed $E_{QG}$; in practice this is done by minimizing $\\chi^2$ over $(\\tau,\\alpha)$ on a logarithmic grid in $E_{QG}$ with a Nelder-Mead simplex and cross-checked with Powell minimization. The resulting $\\Delta\\chi^2$ curve is calibrated with the standard asymptotic result that $\\Delta\\chi^2$ follows a $\\chi^2$ distribution with one degree of freedom, and the 95% lower limit is read off where $\\Delta\\chi^2 = 4$, with the caveat that the boundary-corrected prescription applies near the physical boundary. The load-bearing feature is that the profile-likelihood curves are monotone decreasing, so the only extremum consistent with the data sits at the Planck-scale boundary.","core_discovery":"Using the same data, likelihood, and parametric model as the earlier analysis (ref. [5]), the authors profile over the two astrophysical lag parameters $\\tau$ and $\\alpha$ and scan $E_{QG}$ on a logarithmic grid from $10^{6}$ to $10^{19}$ GeV. For both $n=1$ and $n=2$ LIV, the resulting $\\Delta\\chi^2(E_{QG}) = \\chi^2(E_{QG}) - \\chi^2_{\\min}$ decreases monotonically with increasing $E_{QG}$, with the minimum attained at the upper edge of the grid, the Planck scale. Because no interior minimum exists below the Planck boundary, the paper argues that a one-sided lower limit is the correct statistical statement, and it derives 95% lower limits of $2.55 \\times 10^{16}$ GeV and $1.85 \\times 10^{7}$ GeV for linear and quadratic LIV, respectively, from the $\\Delta\\chi^2 = 4$ intercepts. This directly contrasts with the closed $1\\sigma$ intervals obtained by Bayesian marginalization in refs. [5] and [7].","pith_inferences":["A natural extension would be a Monte Carlo coverage check: simulate mock lag datasets under the null hypothesis of no LIV and see whether the $\\Delta\\chi^2 = 4$ cutoff really gives 95% coverage when the fitted minimum is at the boundary; if the correct one-sided threshold is instead $\\Delta\\chi^2 \\simeq 2.71$, the quoted limits would shift by a factor related to the shape of the curve.","The contrast with Bayesian intervals may owe to the volume effect in marginalization; a direct comparison of the profile likelihood with a profile posterior could isolate whether the prior choice or the marginalization itself produces the bounded intervals.","If applied to the larger sample of GRBs with spectral-lag data, the method could test whether the monotone trend is generic, which would strengthen the case that previously reported LIV constraints from spectral lags should be re-expressed as lower limits."],"forward_implications":["If the profiling result is correct, the previously reported bounded credible intervals for $E_{QG}$ are not reproduced; the data only support a lower limit, not a finite range.","The method provides a prior-free way to set one-sided limits on $E_{QG}$, avoiding the volume effects that can arise when marginalizing over nuisance parameters.","The same procedure can be applied to other gamma-ray burst spectral-lag datasets that have been analyzed only with Bayesian methods, potentially converting bounded intervals into lower limits or vice versa.","The monotone $\\Delta\\chi^2$ behavior implies the GRB 160625B spectral-lag data show no statistically significant LIV-induced turnover below the Planck scale in these models."],"supporting_citations":[{"why":"Supplies the spectral-lag data for GRB 160625B and the fiducial model for intrinsic and LIV-induced time lags used throughout.","marker":"[5]"},{"why":"Provides the previous variational-inference Bayesian analysis whose bounded 1-sigma intervals are the contrast for the one-sided limits.","marker":"[7]"},{"why":"Demonstrates the use of profile likelihood in a cosmology setting and motivates the method transfer to this problem.","marker":"[12]"},{"why":"Gives the asymptotic chi-squared distribution of Delta chi-squared used for the intercept calibration.","marker":"[21]"},{"why":"Provides the numerical recipes, including minimization and the Delta chi-squared threshold prescription, used to compute and interpret the profile.","marker":"[22]"},{"why":"Supplies the boundary-corrected confidence-interval prescription that the paper argues is unnecessary here because the intercepts are far from the boundary.","marker":"[23]"}],"fun_headline_variants":["Profile likelihood flips GRB lag LIV to one-sided bounds","No Planck-scale minimum: GRB lag sets LIV lower limits","Spectral lag reanalysis: profile likelihood trumps Bayesian","GRB 160625B: one-sided LIV limits from frequentist stats","LIV constraint from GRB lag becomes one-sided via profiling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quoted limits assume that the distribution of the profile-likelihood ratio $\\Delta\\chi^2$ is the asymptotic one-degree-of-freedom $\\chi^2$, with the 95% cutoff at $\\Delta\\chi^2 = 4$, even though the global minimum used to define $\\Delta\\chi^2$ sits at the Planck-scale boundary of the parameter space.","fun_headline_variants_meta":{"raw":{"variants":["Profile likelihood flips GRB lag LIV to one-sided bounds","No Planck-scale minimum: GRB lag sets LIV lower limits","Spectral lag reanalysis: profile likelihood trumps Bayesian","GRB 160625B: one-sided LIV limits from frequentist stats","LIV constraint from GRB lag becomes one-sided via profiling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000301,"raw_usage":{"total_tokens":1758,"prompt_tokens":992,"completion_tokens":766,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":678}},"tokens_in":608,"tokens_out":766,"duration_ms":8905,"temperature":1.0,"reasoning_tokens":678,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:50:55.630073+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate Monte Carlo realizations of the 37 spectral-lag measurements from the best-fit model with no LIV, fit each realization with the same profile-likelihood procedure, and check the coverage of the reported 95% one-sided intervals; if coverage is substantially below 95% (or if $\\Delta\\chi^2=4$ is not the right one-sided cutoff), the quoted limits would need revision. Equivalently, if a scan that extends the grid above the Planck scale finds an interior global minimum, the monotonicity claim would be falsified.","supporting_citations":[{"cited_title":"A New Test of Lorentz Invariance Violation: the Spectral Lag Transition of GRB 160625B","cited_arxiv_id":"1612.09425","evidence_quote":"Supplies the spectral-lag data for GRB 160625B and the fiducial model for intrinsic and LIV-induced time lags used throughout."},{"cited_title":"Variational Inference as an alternative to MCMC for parameter estimation and model selection","cited_arxiv_id":"1803.06473","evidence_quote":"Provides the previous variational-inference Bayesian analysis whose bounded 1-sigma intervals are the contrast for the one-sided limits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the asymptotic chi-squared distribution of Delta chi-squared used for the intercept calibration."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the numerical recipes, including minimization and the Delta chi-squared threshold prescription, used to compute and interpret the profile."}],"review_version":1}