{"id":"ce73bbf0-2429-4917-8586-af3ceb6da3b3","arxiv_id":"2412.16048","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A general parameterization of modified photon dispersion relations is introduced, and simulations show that the assumed lag-redshift model changes both the inferred quantum gravity scale and the ability to discriminate models.","lead":"The paper proposes a general way to write down modified dispersion relations, the equations that may make light travel at slightly different speeds depending on energy, and derives the resulting time delays. It then simulates gamma-ray bursts and flaring galaxies to show that the choice of model changes the constraints on the quantum gravity scale by up to an order of magnitude.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The simulation-based conclusions rest on a pipeline that the paper itself shows fails to reproduce the published Fermi-LAT GRB 090510 constraint; until that discrepancy is resolved, the model-dependent limits and detection claims may be artifacts.","rationale":"The reader's weakest assumption focused on the polynomial single-order-I ansatz behind Eq. (25) and on neglected systematics. I agree with the conditional verdict, but I do not see the polynomial assumption as the most load-bearing issue: any smooth modified dispersion relation has a polynomial leading-order Taylor term, so Eq. (25) may be reasonably general for the intended regime. The more concrete and unresolved threat to the paper's simulation-based conclusions is the GRB 090510 discrepancy reported by the authors themselves in Sec. IV A. If the pipeline cannot reproduce a published single-source likelihood constraint, then the order-of-magnitude differences in Λ limits, the claim that a real lag is detected under every wrong model, and the 4.3σ discrimination hint for DSR2 could be artifacts of the simplified simulation setup rather than robust phenomenological statements. The theoretical framework could still stand, but the numerical demonstration needs validation against real data or a clear statement that all quantitative results are only relative. This is why I keep the reader's CONDITIONAL verdict: the paper should either resolve the GRB 090510 discrepancy with a like-for-like reprocessing or explicitly restrict the simulation conclusions to relative comparisons only.","tokens_in":17508,"tokens_out":31327,"duration_ms":288145,"concrete_test":"Reprocess the actual Fermi-LAT GRB 090510 dataset with the updated analysis code used in this paper, using the JP model and the same event selection and energy range as Vasileiou et al. (2013), and compare the reconstructed 95% CL limit on Λ and its uncertainty with [26]. Then repeat the 1000-realization no-lag simulation for GRB 090510 including the Fermi-LAT instrument response (effective area and energy dispersion) to see whether the simulated λ distribution shifts up to the published value. If the discrepancy persists after faithful response modeling, the simulation pipeline is not validated and the model-comparison results should be treated as illustrative only; if it disappears, the central numerical conclusions are supported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central numerical claims — that the inferred Λ limit can vary by an order of magnitude across lag-redshift models, that a Planck-scale JP lag is detected under every model, and that DSR2 is excluded at 4.3σ — all depend on the simulation and likelihood pipeline producing faithful reconstructions of realistic gamma-ray data. The paper itself flags an unresolved validation failure in Sec. IV A: for GRB 090510, the 1000 no-lag simulations give EQG below the Planck scale for every model, whereas the Fermi-LAT likelihood analysis of the same source in [26] yields a much stronger constraint. The authors state that the discrepancy is too large to be a simple statistical effect and that only a new analysis with the same software can settle it. Because instrument response functions and systematic uncertainties are deliberately neglected (Sec. III B), there is no independent check that the injected lags, the reconstructed λ values, and the likelihood-ratio significances map correctly onto real detector data. The theoretical parameterization of Eq. (25) may well be correct; the load-bearing gap is that the quantitative demonstration of model dependence and discrimination is built on an unvalidated simulation pipeline.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a general polynomial parameterization of modified dispersion relations (MDRs) in FLRW spacetimes, expressing the first-order photon time delay as Eq. (25) with free redshift-dependent coefficient functions B_m(t(z)). From this parameterization it derives or recovers six I=1 benchmark lag-redshift models: Jacob & Piran (JP), a rescaled kappa-Poincare model (RekaP), curvature-induced DSR (CInd), a spatial-momentum modification (SpaM), and two DSR models (DSR1, DSR2). The authors simulate AGN and GRB datasets with and without injected lags, reconstruct the quantum-gravity scale Lambda with a likelihood fit, and report that the inferred limit varies by up to an order of magnitude across models, that an injected Planck-scale JP lag is detected under all models but with biased magnitude, and that a likelihood-ratio test excludes DSR2 at 4.3 sigma.","tokens_in":17744,"tokens_out":9768,"duration_ms":83315,"significance":"If validated, Eq. (25) is a genuinely useful unifying framework for gamma-ray LIV searches: it reduces the choice of MDR model to a choice of B_m coefficients and makes the redshift dependence of the time delay explicit in a form that can be implemented directly in analysis software. The paper is also transparent about its limitations: it explicitly states that instrument response functions and systematics are neglected and that the GRB 090510 simulation result disagrees with the published Fermi-LAT likelihood result. However, the central numerical claims rest on a simulation and likelihood pipeline that is not yet shown to reproduce real data, and the reported differences are presented without statistical uncertainties. The paper is therefore best assessed as a promising methodological proposal whose quantitative conclusions require further validation before they can be used to interpret real gamma-ray data.","major_comments":[{"comment":"The manuscript itself states that for GRB 090510 the 1000 no-lag simulations give a scale lower than the Planck scale for all models, while the published Fermi-LAT likelihood analysis [26] yields a much stronger constraint, and that the discrepancy is too large to be explained by a simple statistical effect. This is a load-bearing validation failure because the central quantitative claims of Secs. IV A and IV B - the order-of-magnitude model dependence of the limits, the detection of an injected lag under all models, and the 4.3 sigma exclusion of DSR2 - are produced by the same simulation and likelihood pipeline. Please either resolve the discrepancy (for example, by reproducing the [26] result on the real GRB 090510 dataset with the updated software) or demonstrate explicitly that the simplified simulations are nevertheless sufficient for the comparative statements made in the paper.","section":"Sec. IV A, GRB 090510 comparison"},{"comment":"The paper deliberately neglects instrument response functions and nuisance parameters in both simulations and analysis, citing [36] for a typical factor of about 2 weakening of IACT constraints and 10% for Fermi-LAT. These systematic effects are comparable to or larger than several of the reported differences between models (for example, JP versus SpaM or RekaP at low redshift), so the numerical limits in Fig. 2 and the significances in Fig. 4 cannot be assumed to carry over to real data. Please either include response functions in the simulations or explicitly mark all numerical limits and significances as illustrative and provide the model-dependent correction factors.","section":"Sec. III B, instrument response and systematics"},{"comment":"The text says that for GRB 090510 'the one thousand simulations give a scale lower than the Planck scale in all models,' which implies a distribution over realizations, but Fig. 2 shows only single point values with no error bars or spread. Without a measure of the dispersion of the Lambda limits across the 1000 realizations, the claimed factor-of-10 differences between models cannot be assessed for statistical significance. Please add error bars, quantiles, or a separate figure showing the distribution of reconstructed Lambda limits for each model and source.","section":"Fig. 2 and Sec. IV A, uncertainty on limits"},{"comment":"The test statistic used to claim exclusion of DSR2 at 4.3 sigma is described only as 'computing the square of the Lcomb(lambda_min) ratio obtained from the (JP) model and each tested model.' This is ambiguous and statistically nonstandard, particularly because the models are non-nested. Please define the test statistic explicitly (for example, 2 Delta ln L), state the null distribution used to convert the value into standard deviations, and justify its applicability to non-nested model comparison.","section":"Sec. IV B, likelihood-ratio test"}],"minor_comments":[{"comment":"The caption contains a duplicated label '(z)*kappa(z)*kappa' in the printed text; this should be corrected.","section":"Fig. 1 caption"},{"comment":"The model called 'RekaP' in the equation labels and text appears as 'kP' in Fig. 2; please unify the notation to avoid confusion with the kappa-Poincare bicrossproduct model, which at first order is degenerate with JP.","section":"Secs. II C and IV A, model notation"},{"comment":"The sentence 'our simulation results are compatible with the uncertainties given in [26] for the Pair View (PV) and Sharpness-Maximization Method (SMM), while reducing the important bias observed for GRB 090510 in the same paper' is unclear in light of the preceding sentence about a large discrepancy with the likelihood result of [26]; please clarify what is meant.","section":"Sec. IV A, GRB 090510 discussion"},{"comment":"In Eq. (24) the symbol p is used without an explicit statement of whether it is the physical or comoving spatial momentum; please define it consistently to avoid ambiguity in the conversion from the Hamiltonian parameterization to the energy expression.","section":"Eq. (24)"}],"recommendation":"major_revision","confidential_remarks":"The theoretical parameterization is solid and the paper addresses an important need in the gamma-ray LIV community. My reservation is that the simulation-based claims are presented with more confidence than the validation supports, particularly given the acknowledged GRB 090510 discrepancy and the lack of uncertainties on the limits. I believe the paper can be brought to a publishable state by addressing the validation issue, adding uncertainties, and clarifying the statistical test, so major revision rather than rejection is appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's real contribution is Eq. (25): a polynomial parameterization of modified dispersion relations that yields a single, code-friendly time-delay formula, with specific models recovered by choosing the coefficients B_m. That is genuinely useful and new, and the derivations are clean. The paper also does a honest job of comparing six lag-redshift models on simulated data, and the message that model choice can shift derived limits by an order of magnitude is worth taking seriously, even if the absolute numbers are illustrative.\n\nWhat it does well: the theory section is careful, the degeneracy between JP and kappa-Poincare at first order is noted, and the new SpaM and RekaP models are clearly placed relative to existing literature. The code update is a practical step forward, and the simulations cover a reasonable mix of source types and redshifts.\n\nWhere it is soft: the most important concern is the unresolved discrepancy with the Fermi-LAT GRB 090510 analysis in [26]. The paper admits the difference is too large for statistics and that only a reanalysis with the same software can settle it. That is an honest statement, but it means the simulation pipeline is not validated against a real published constraint. Combined with the deliberate neglect of instrument response and systematics, the numerical limits in Fig. 2 and the 4.3 sigma exclusion claim should be read as relative comparisons within the simulation, not as reliable predictions for real data. The paper mostly says this, but the abstract and some phrasing in Sec. IV B overreach when it says a real lag will \"always\" be detected; that is based on one injected scenario and does not account for source-intrinsic lags or systematics. A minor issue: the limits in Fig. 2 have no error bars, which would have helped calibrate the spread across models.\n\nThe central parameterization stands on its own. The simulation study is a proof of principle, not a final answer. A serious referee should ask for clarification of the 090510 discrepancy, for explicit error bars or at least a statement that the limits are only relative, and for softening the general detection claim.\n\nWho this is for: anyone working on quantum-gravity time-delay phenomenology or on LIV constraints from gamma-ray bursts. It deserves a serious referee; the theoretical framework justifies the time, even if the numerical results need revision.","headline":"A useful unifying parameterization of MDR time delays, but the simulation-based quantitative claims need a caveat until the GRB 090510 validation gap is resolved.","tokens_in":18293,"tokens_out":1402,"would_cite":true,"duration_ms":14312,"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 single parameterized time-delay formula reproduces all polynomial modified dispersion relations used in gamma-ray quantum-gravity searches, and simulations show the inferred Planck-scale limit can vary by an order of magnitude depending…","keywords":["modified dispersion relations","time delays","gamma-ray bursts","active galactic nuclei","quantum gravity phenomenology","Lorentz invariance violation","parameterized lag-redshift relation","simulated observations"],"falsifier":"Measure the lag-redshift relation $\\kappa(z)$ from two or more flaring sources at very different redshifts with an order-of-magnitude gain in sensitivity: if the inferred $\\kappa(z)$ cannot be fitted by any finite set of polynomial coefficients $B_m$, the polynomial parameterization is falsified. A sharper test for the model family: the (DSR2) model predicts a negative time lag for sources at $z<0.95$ for a positive $\\Lambda$, so observing a positive lag from a low-redshift AGN while a high-redshift GRB shows a negative lag would rule out that model's sign structure.","tokens_in":17334,"feed_emoji":"⏱","tokens_out":6211,"duration_ms":53343,"temperature":0.7,"pith_summary":"This paper argues that gamma-ray time-delay searches for quantum-gravity effects have been tied to a single lag-redshift model, and that this is too narrow. It presents a general parameterization of polynomial modified dispersion relations in a cosmological spacetime, whose associated time-delay formula reduces to a single compact expression, Eq. (25), encompassing existing and new models through the choice of parameter functions $B_m$. Simulations of realistic flaring AGN and gamma-ray burst data show that the lower limit on the energy scale $\\Lambda$ can shift by up to an order of magnitude depending on the assumed lag-redshift model, with the standard (JP) model giving the most stringent bound. An injected Planck-scale lag is detected under all models considered, but the inferred magnitude is model-dependent, and one model (DSR2) even flips the sign of the lag, which would mislead about subluminal versus superluminal propagation. The paper concludes that model choice should be treated as a systematic uncertainty and that a source sample evenly spread in redshift is needed to discriminate between models.","feed_headline":"Six lag models, one formula: quantum-gravity limits shift tenfold","feed_subtitle":"All proposed dispersion relations collapse into one time-delay formula; the inferred energy scale depends on the model.","key_machinery":"The central object is the parameterized time-delay formula Eq. (25), constructed from the polynomial MDR Hamiltonian $h(t,p_t,w)=p_t^2 \\Lambda^{-I} \\sum_m B_m(t(z))\\, p_t^m w^{I-m}$ (Eq. 18). The functions $B_m$ carry all model information; each choice of $B_m$ turns Eq. (25) into a different lag-redshift relation $\\kappa(z)=\\int_0^z \\frac{\\sum_m B_m(z')\\,(1+z')^m}{H(z')}\\,dz'$. For a fixed leading order $I$, the formula separates the energy dependence $E_{01}^I - E_{02}^I$ from the redshift geometry $\\kappa(z)$, so that a single likelihood code can test any polynomial model by swapping $B_m$. This converts the analysis from a single-model search into a model-comparison framework, and it also reveals degeneracies: different dispersion relations can produce the same time delay at first order.","core_discovery":"The central claim is that every polynomial modified dispersion relation of the form $h(t,p_t,w)=p_t^2 \\Lambda^{-I} \\sum_m B_m(t(z))\\, p_t^m w^{I-m}$, evaluated to leading order in $1/\\Lambda$, yields a time delay $\\Delta t = \\frac{I+1}{2}\\,\\frac{E_{01}^I - E_{02}^I}{\\Lambda^I} \\int_0^z \\frac{\\sum_m B_m(z')\\,(1+z')^m}{H(z')}\\,dz'$. This single formula, Eq. (25), covers the well-known (JP) model, $\\kappa$-Poincar\\'e-type models, curvature-induced models, and two DSR-inspired models, plus new ones, simply by choosing $B_m$. The paper demonstrates that this choice changes the lag-redshift relation enough that, in lag-free simulated data, the inferred lower limit on $\\Lambda$ varies by about an order of magnitude between models; when a Planck-scale lag is injected assuming the standard (JP) model, all other models still detect a lag but assign it a different magnitude, and the (DSR2) model even inverts its sign.","pith_inferences":["If the framework is right, the historical single-model limits on $\\Lambda$ may carry a systematic bias; re-analyzing archival gamma-ray burst and AGN data with the full family of $B_m$ could convert existing non-detections into a band of model-dependent limits and possibly reveal weak model preferences.","Because Eq. (25) is linear in $B_m$, a sufficiently loud lag detection across multiple redshifts would let one reconstruct the shape of $\\kappa(z)$ almost non-parametrically, yielding a direct measurement of the redshift dependence of the dispersion-relation correction rather than just a single scale.","A natural next step, not taken in the paper, is to inject lags from the other models and check whether the standard (JP) recovery is also biased; the paper only injects the (JP) lag, so the reverse model-robustness is untested.","The formalism implicitly assumes Finsler-type Hamiltonian dynamics; if quantum gravity instead predicts non-polynomial dispersion relations (for example exponential or logarithmic), the parameterization would need extension before the same data-comparison machinery applies."],"forward_implications":["If a time lag is detected, its measured magnitude and the derived energy scale depend on the assumed modified dispersion relation, so limits quoted with the standard model are not directly comparable with limits from other models.","A Planck-scale lag injected in the standard (JP) model is detected under all six lag-redshift models considered, but with a biased magnitude; one model (DSR2) would even report a negative lag, inverting the subluminal/superluminal interpretation.","Choosing the wrong model can change the lower limit on the quantum-gravity scale by roughly an order of magnitude, so future experimental searches should report limits under multiple models rather than only the standard one.","A source sample evenly distributed in redshift is important for discrimination: some models are best separated at low redshift, others at high redshift, so combining AGNs and gamma-ray bursts widens the model-testing power.","The parameterization opens the way to fit the coefficients $B_m(t)$ directly to observations, turning a future detection into a model-selection test rather than a single-scale measurement."],"supporting_citations":[{"why":"Supplies the standard (JP) model that the parameterization must reproduce and against which all limits are compared.","marker":"[11]"},{"why":"Derives the general first-order time-delay formula that the polynomial parameterization particularizes.","marker":"[14]"},{"why":"Gives the $\\kappa$-Poincar\\'e modified dispersion relation on FLRW spacetime, one of the models recovered by choosing $B_m$.","marker":"[13]"},{"why":"Provides the curvature-induced DSR model (CInd) that the paper includes in its comparison.","marker":"[15]"},{"why":"Supplies the two DSR-FLRW models (DSR1 and DSR2) tested in the simulations.","marker":"[16]"},{"why":"Provides the likelihood analysis and simulation methodology used to generate and fit the mock data.","marker":"[36]"},{"why":"Gives the published Fermi-LAT limit on the (JP) model that the simulations reassess and compare against.","marker":"[26]"}],"fun_headline_variants":["One formula, many lags: quantum-gravity scale varies by model","Unified time-delay formula tests quantum-spacetime models","Model choice skews quantum-gravity energy limits tenfold","One formula discriminates photon-lag models in gamma-ray data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes the quantum-gravity modification of the photon dispersion relation is a polynomial in energy and momentum at a single leading order in $1/\\Lambda$, with all redshift dependence carried by the coefficients $B_m(t(z))$; if the true modification is non-polynomial or mixes orders in $\\Lambda$, the parameterized time-delay formula and the model comparisons built on it do not apply.","fun_headline_variants_meta":{"raw":{"variants":["One formula, many lags: quantum-gravity scale varies by model","Unified time-delay formula tests quantum-spacetime models","Model choice skews quantum-gravity energy limits tenfold","One formula discriminates photon-lag models in gamma-ray data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000542,"raw_usage":{"total_tokens":2681,"prompt_tokens":1111,"completion_tokens":1570,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":727,"completion_tokens_details":{"reasoning_tokens":1498}},"tokens_in":727,"tokens_out":1570,"duration_ms":8927,"temperature":1.0,"reasoning_tokens":1498,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:50:49.936347+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the lag-redshift relation $\\kappa(z)$ from two or more flaring sources at very different redshifts with an order-of-magnitude gain in sensitivity: if the inferred $\\kappa(z)$ cannot be fitted by any finite set of polynomial coefficients $B_m$, the polynomial parameterization is falsified. A sharper test for the model family: the (DSR2) model predicts a negative time lag for sources at $z<0.95$ for a positive $\\Lambda$, so observing a positive lag from a low-redshift AGN while a high-redshift GRB shows a negative lag would rule out that model's sign structure.","supporting_citations":[{"cited_title":"Redshift and lateshift from homogeneous and isotropic modified dispersion relations","cited_arxiv_id":"1802.00058","evidence_quote":"Derives the general first-order time-delay formula that the polynomial parameterization particularizes."},{"cited_title":"Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes","cited_arxiv_id":"1612.01390","evidence_quote":"Gives the $\\kappa$-Poincar\\'e modified dispersion relation on FLRW spacetime, one of the models recovered by choosing $B_m$."},{"cited_title":"First Combined Study on LIV from Observations of Energy-dependent Time Delays from Multiple-type Gamma-ray Sources -- Part I. Motivation, Method Description and Validation through Simulations of H.E.S.S., MAGIC and VERITAS Datasets","cited_arxiv_id":"2201.02087","evidence_quote":"Provides the likelihood analysis and simulation methodology used to generate and fit the mock data."}],"review_version":1}