{"id":"48550786-bc0c-4db3-95a7-7c4a49ae8ca6","arxiv_id":"2504.14295","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Adding three extreme GRB photons preserves the fitted Lorentz-violation scale E_LV ~ 3e17 GeV, but only when an energy-dependent intrinsic delay term, itself a fitting construct, absorbs the new TeV photons.","lead":"Three record-energy gamma-ray burst photons, from Fermi, MAGIC, and LHAASO, are added to a 14-photon sample and re-fit with a model where the intrinsic emission time grows linearly with photon energy. The fitted Lorentz-violation scale stays near 3e17 GeV across data combinations, but the evidence for this model over a simpler one is weak.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The linear intrinsic-delay model (Eq. 5) has negligible AIC support and fails a generalization test: fitting the original 14 photons alone predicts the 12.2 TeV LHAASO delay as roughly 900 s versus the observed 340 s, so the claimed consistency is post-hoc.","rationale":"The reader's weakest_assumption correctly identifies the linear intrinsic-emission-time model (Eq. 5) as the load-bearing premise. I agree with that identification but sharpen it: the linear form is not merely lacking independent justification; it actively enables a near-perfect cancellation for the TeV photons, and the model's parameters fit the new photons only when those photons are included in the fit. The out-of-sample prediction test is the cleanest way to demonstrate that the consistency is post-hoc. The AIC evidence is negligible (Delta_AIC ~ 0.59 for Case b), so the model-selection argument does not rescue the claim. My proposed test is computational and directly settles whether the central claim of a consistent framework is meaningful. I therefore keep the reader's CONDITIONAL verdict unchanged: the paper needs a physical or independent motivation for Eq. (5) and an out-of-sample demonstration before the claimed E_LV can be accepted.","tokens_in":13039,"tokens_out":20425,"duration_ms":169174,"concrete_test":"Leave out all three new photons and fit Model C to the original 14 FGST photons only (the Case a setup). From the posterior predictive distribution of (aLV, alpha, mu, sigma), compute the predicted Delta_tobs/(1+z) and its 95% credible interval for the MAGIC 1.07 TeV photon (GRB 190114C, z=0.4245) and the LHAASO 12.2 TeV photon (GRB 221009A, z=0.151), using the authors' Eq. (8) divided by (1+z). If the observed values (48.86 s and 340.19 s) fall outside the 95% intervals, the model does not generalize, and the claim that it provides a consistent framework for the three photons is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that Model C consistently explains all three new photons with E_LV ~ 3e17 GeV rests on the linear energy-dependent intrinsic delay Delta_tin = Delta_tin,c + alpha*Es (Eq. 5). For the LHAASO 12.2 TeV photon, the fitted Model C parameters (e.g., Case b: aLV=3.34e-18 GeV^-1, alpha=-0.20 s/GeV, mu=-1.07 s) produce an LV delay of roughly 2,900 s in the observer frame, which must be almost exactly cancelled by the intrinsic term alpha*Es ~ -2,440 s plus a small mu, leaving the observed 340 s. This delicate cancellation is entirely a consequence of the assumed linear-in-energy form. The AIC comparison gives Delta_AIC = 0.59 between Model C and the simpler Model A for the full 17-photon dataset (Case b), i.e., adding alpha improves the fit by less than 1 AIC unit. More importantly, the model fails a natural out-of-sample check: using the Case a posterior (14 old FGST photons only, alpha=-0.15, mu=-4.49, aLV=3.28e-18), the predicted Delta_tobs/(1+z) for the LHAASO photon is of order 890 s (observed 340.19 +/- 4.35 s), a residual several hundred seconds or ~50-100 sigma. Thus the apparent consistency across the five cases is achieved only by refitting the model to include the very photons it was supposed to explain; the linear intrinsic-delay term is an ad hoc degree of freedom that absorbs the TeV outliers. With negligible AIC preference and no predictive power for the new photons, the inferred E_LV ~ 3e17 GeV is not a robust inference.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript applies three phenomenological models (A, B, C) for the intrinsic time delay of high-energy GRB photons to a dataset consisting of the 14 multi-GeV Fermi photons studied previously plus three 'remarkable' photons: the 99.3 GeV Fermi photon from GRB 221009A, the 1.07 TeV MAGIC photon from GRB 190114C, and the 12.2 TeV LHAASO photon from GRB 221009A. Using Bayesian fits with the bilby package, the authors conclude that Model C, which combines a linear-in-energy intrinsic delay (Eq. 5) with a Lorentz-violating arrival-time delay, yields consistent parameters across five data combinations (Cases a–e), with E_LV ~ 3×10^17 GeV, α ~ −0.2 s/GeV, and μ ~ 0 s. They further claim that AIC selects Model C as the best model.","tokens_in":13434,"tokens_out":20427,"duration_ms":168750,"significance":"If the central claim were correct, the paper would provide a unified, energy-dependent intrinsic-delay framework that reconciles GeV and TeV GRB photon arrival times with a consistent Lorentz-violation scale near 3×10^17 GeV, a result of substantial interest for quantum-gravity phenomenology. The paper is transparent in reporting posterior tables and AIC values, and it uses a reproducible Bayesian pipeline with publicly available data. However, the significance is undercut by the following issues: the AIC preference for Model C is statistically negligible in the base cases; the claimed cross-case consistency is an in-sample property with no predictive validation; and the key energy-dependent intrinsic-delay term is an ad hoc linear ansatz that strongly degenerates with the LV term. These points, detailed in the major comments, mean that the evidence for the central claim is not compelling as presented.","major_comments":[{"comment":"The claim that 'Model C exhibits the best performance' is not supported by the reported AIC values. In Case a (the original 14 photons) and Case b (all 17 photons), the AIC difference between Model C and the simpler Model A is only Δ = 0.54 and 0.59, respectively, which is well below the conventional threshold of Δ < 2 for models to be considered indistinguishable. Adding the parameter α therefore does not provide significant evidence for Model C over Model A in the datasets that define the paper's main inference. The paper should either temper this claim or provide a statistical test (e.g., AIC weights or Bootstrap) that quantifies the evidence.","section":"Tables 5 and 6, Eq. (9)–(10)"},{"comment":"The consistency of the Model C parameters across Cases a–e is entirely in-sample. The parameters for Cases d and e are obtained by fitting the very photons whose consistency is asserted, so no predictive test is performed. A direct posterior-predictive check is missing. To illustrate: using the Case a posterior (Table 4: aLV = 3.28×10⁻¹⁸ GeV⁻¹, α = −0.15 s/GeV, μ = −4.49 s) and Eqs. (3)–(5), the predicted Δt_obs/(1+z) for the 12.2 TeV LHAASO photon is of order 800 s, far above the observed 340.19 ± 4.35 s from Table 1. Even allowing for the large posterior uncertainties, the absence of any out-of-sample validation means the claimed 'consistent framework' is not distinguished from a re-fitting that absorbs the TeV outliers. The authors should present a leave-one-out or posterior-predictive analysis, or explicitly restrict their claim to the in-sample behavior.","section":"Section 3, Tables 4–5"},{"comment":"The low-energy reference times for the two newly included GRBs, 2.59 ± 5.00 s for GRB 190114C and 251.33 ± 5.00 s for GRB 221009A, are manual selections with no supporting light-curve analysis. Since every Δt_obs is defined relative to these peaks, a shift of a few seconds directly changes the fitted time delays, and the stated ±5 s uncertainty is comparable to the reported uncertainties on the GeV-photon delays (e.g., ±4.35 s). The paper does not test the sensitivity of the results to the choice of reference time. The authors should either justify these peaks quantitatively from the GBM light curves or demonstrate that the posteriors are robust under variations of the reference time within a plausible range.","section":"Table 1 and accompanying text"},{"comment":"The linear energy dependence of the intrinsic emission time, Δt_in = Δt_in,c + α E_s, is an ad hoc assumption imported from ref. [7] and is not physically derived. Because both the LV term (Eq. 3) and the intrinsic term are linear in photon energy for n=1, the fit suffers from a strong degeneracy between aLV and α. For example, the observed delay of the 12.2 TeV LHAASO photon arises from the near-cancellation of a large positive LV delay (~2.8×10³ s) and a large negative intrinsic delay (~−2.1×10³ s), both of which scale linearly with energy. The paper should demonstrate that the inferred E_LV is not an artifact of this assumed functional form, for example by testing an alternative power-law index or by constraining α through independent spectral-lag observations. Without such a test, the physical interpretation of E_LV ~ 3×10¹⁷ GeV is not robust.","section":"Eq. (5) and Section 2"}],"minor_comments":[{"comment":"The phrase 'the newly proposed model' is vague; the abstract should explicitly name Model C and define α and E_LV.","section":"Abstract and Introduction"},{"comment":"The header 'α (s· GeV−11)' contains a typo; it should read 'α (s·GeV⁻¹)'.","section":"Table 4 column header"},{"comment":"The sentence stating that Model C is 'derived purely through data fitting without arbitrary preconceptions' is inaccurate, since Eq. (5) itself is a specific, arbitrary functional choice; this sentence should be revised.","section":"Discussion near Model B/C"},{"comment":"The AIC discussion should explicitly acknowledge that Δ < 2 is conventionally interpreted as no meaningful difference; the current wording 'It is evident' overstates the statistical support.","section":"Section 3, Tables 5–6"},{"comment":"The paragraph acknowledging the small sample size is welcome, but it is placed at the end without quantitative discussion; the authors could add a sentence on how selection effects might bias the time-delay measurements.","section":"Section on limitations"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a follow-up to the authors' earlier work (ref. [7]) and carries forward the key linear intrinsic-delay ansatz without independent justification. I am concerned that the central claim is not backed by a predictive test and that the AIC evidence is weak in the base cases. If the authors can add a posterior-predictive check and a sensitivity analysis for the reference times, the paper might become publishable; as it stands, the in-sample consistency does not establish the claimed Lorentz-violation scale. The paper has already appeared in Physics of the Dark Universe, which may explain the somewhat polished but unvalidated presentation; nevertheless, the technical issues remain."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe headline: this is a routine extension of the authors' own program, and the central claim—Model C giving a consistent Lorentz-violation framework—doesn't survive contact with the evidence. The AIC difference over Model A is 0.54 in the base case, which is a tie, and the linear intrinsic-delay term is doing all the work.\n\nWhat is new: they add three extreme photons (99.3 GeV from Fermi, 1.07 TeV from MAGIC, 12.2 TeV from LHAASO) to the 14-photon sample they already analyzed, and refit the three models from ref. [7]. The Bayesian pipeline is standard and the parameter tables are complete. They also show that Model A cannot reconcile GeV and TeV photons, which is a useful negative result.\n\nThe problems: the central claim of Model C's consistency is built on an ad hoc linear energy-dependent intrinsic delay, Eq. (5), with a free coefficient α. That term cancels the LV delay for the TeV photons. The AIC comparison shows Model C is essentially indistinguishable from Model A, so the extra parameter isn't justified. More seriously, the model fails an out-of-sample check: fitting only the original 14 photons (Case a of Model C) predicts a delay of roughly 900 s for the 12.2 TeV LHAASO photon, whereas the observed value is about 340 s. The apparent consistency across the five cases comes from including the new photons in the fit before claiming they are consistent—a circularity. The reference-time choices for the two new bursts are also manual inputs with crude uncertainties.\n\nThe paper does acknowledge the small sample, which is honest, but that doesn't address the logical issue.\n\nWho should read it? Anyone interested in the ongoing debate about LV from GRB time delays, and it's a good case study in how flexibly parameterized models can produce post-hoc consistency. I would not cite it as evidence for LV, but I'd consider citing it as a methodological caution.\n\nFor peer review: send it to referees, because the claim is important and the analysis is transparent enough to evaluate. The referee should demand a pre-specified analysis protocol (including reference-peak selection) and an out-of-sample prediction. Without that, the paper is a weak constraint rather than a detection.","headline":"The paper's Model C is an ad hoc parameterization that absorbs TeV outliers, the AIC shows no preference over the simpler model, and an out-of-sample check fails—so the claimed LV scale is not robust.","tokens_in":14014,"tokens_out":2474,"would_cite":false,"duration_ms":22632,"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 Lorentz-violation scale of about 3×10^17 GeV, combined with an intrinsic delay that grows linearly with photon energy, explains the arrival times of the 99.3 GeV, 1.07 TeV, and 12.2 TeV photons from GRB 221009A and GRB 190114C.","keywords":["Lorentz invariance violation","gamma-ray bursts","light-speed variation","intrinsic emission time","GRB 221009A","GRB 190114C","high-energy photons","time-delay analysis"],"falsifier":"Take a GRB with two or more high-energy photons spanning a wide energy range and an unambiguous low-energy peak, then measure the delay versus energy; if the delays do not fall on a single straight line with the same $\\alpha\\sim -0.2$ s GeV$^{-1}$ and the same $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV used here, Model C is ruled out.","tokens_in":12763,"feed_emoji":"🔭","tokens_out":8227,"duration_ms":71104,"temperature":0.7,"pith_summary":"The paper tries to establish that the arrival times of the three highest-energy photons ever seen from gamma-ray bursts can all be explained by one Lorentz-violating dispersion relation with scale $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV, provided the GRB source emits high-energy photons with an intrinsic delay that grows linearly with photon energy. This matters because it would turn three iconic single-photon events, observed by three different telescopes across GeV and TeV energies, into a single consistent probe of light-speed variation. The authors show that treating the intrinsic delay as a constant fails: adding the 1.07 TeV or 12.2 TeV photon shifts the fitted scale to $\\sim 2\\text{--}3\\times 10^{18}$ GeV. With a linear intrinsic delay (their Model C), all five data combinations converge on the same $E_{\\rm LV}$, $\\alpha\\sim -0.2$ s GeV$^{-1}$, and $\\mu\\sim 0$ s, implying that high-energy photons are emitted earlier than low-energy ones at the source.","feed_headline":"Three record GRB photons fit one Lorentz-violation scale","feed_subtitle":"An energy-dependent intrinsic delay reconciles the 99.3 GeV, 1.07 TeV, and 12.2 TeV photons at one scale.","key_machinery":"The load-bearing mechanism is the modified photon dispersion relation (Eq. 1), $E^2=p^2c^2[1-s_n(pc/E_{\\rm LV})^n]$, whose $n=1$ linear term produces the velocity shift and arrival-delay integral in Eqs. (2)--(3). The paper's key addition is Eq. (5), $\\Delta t_{\\rm in}=\\Delta t_{\\rm in,c}+\\alpha E_s$, an energy-dependent intrinsic emission delay, and Model C combines both: $\\Delta t_{\\rm obs}=\\Delta t_{\\rm LV}+(1+z)(\\Delta t_{\\rm in,c}+\\alpha E_s)$. This linear intrinsic term is what absorbs the large observed delays of the 1.07 TeV and 12.2 TeV photons, allowing the Lorentz-violation scale to stay at $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV across all five data combinations. The Bayesian posteriors for $a_{\\rm LV}=1/E_{\\rm LV}$, $\\alpha$, $\\mu$, and $\\sigma$ are compared across Models A, B, and C using the Akaike information criterion.","core_discovery":"The paper's central claim is that the observed delays of three extraordinary GRB photons are all described by a single subluminal, linear-in-energy Lorentz-violating dispersion relation with $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV, once the intrinsic emission delay at the source is allowed to depend linearly on photon energy as $\\Delta t_{\\rm in} = \\Delta t_{\\rm in,c} + \\alpha E_s$ with $\\alpha\\sim -0.2$ s GeV$^{-1}$ and $\\mu\\sim 0$ s. Under this Model C, $\\Delta t_{\\rm obs} = \\Delta t_{\\rm LV} + (1+z)\\Delta t_{\\rm in}$, and Bayesian fits to five data combinations (the 14 multi-GeV Fermi photons alone, plus each new photon individually, plus all three together) return mutually consistent parameters $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV, $\\alpha\\sim -0.2$ s GeV$^{-1}$, and $\\mu\\sim 0$ s. The analysis also shows that Model A, which treats the intrinsic delay as a constant, cannot simultaneously accommodate the TeV photons and the GeV sample: including the 1.07 TeV or 12.2 TeV photon shifts the fitted $E_{\\rm LV}$ to $\\sim 2\\text{--}3\\times 10^{18}$ GeV. The paper interprets this as evidence that high-energy photons are emitted earlier at the GRB source, by an amount proportional to their energy.","pith_inferences":["Because the linear intrinsic-delay term adds one free parameter, its ability to reconcile the three photons does not by itself prove that the dispersion relation is modified; an independent, non-LV source model that produces the same $\\alpha$ would remove the need for $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV.","A testable extension is to apply Model C to the full Fermi-LAT spectral-lag sample, not just the highest-energy photon per burst; if $\\alpha$ is truly intrinsic to GRB emission, its value should be stable across many bursts and uncorrelated with redshift.","The claimed $\\alpha\\sim -0.2$ s GeV$^{-1}$ implies a measurable spectral-lag pattern inside single bursts: sub-GeV photons should lag GeV photons by hundreds of milliseconds to seconds, which can be checked with light-curve cross-correlations."],"forward_implications":["If Model C is right, the intrinsic GRB delay is not a nuisance constant but a physical, energy-dependent term: high-energy photons leave the source earlier than low-energy photons by roughly 0.2 s per GeV of source-frame energy.","The same Lorentz-violation scale, $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV, applies across three observatories and two energy decades, making the record single-photon events from GRB 221009A and GRB 190114C mutually consistent probes of light-speed variation.","Under Model A, adding either TeV photon forces $E_{\\rm LV}$ to $\\sim 2\\text{--}3\\times 10^{18}$ GeV, so ignoring energy-dependent intrinsic emission would bias the inferred LV scale upward when TeV photons are included.","Model C is preferred by the Akaike information criterion in all five data combinations, which is a direct corollary of the paper's fits and should be checked by external replication."],"supporting_citations":[{"why":"Supplies the 14 multi-GeV FGST photon events and the constant intrinsic-delay fit that Model A reproduces.","marker":"[5, 6]"},{"why":"Introduces the three models and the linear intrinsic-delay relation $\\Delta t_{\\rm in}=\\Delta t_{\\rm in,c}+\\alpha E_s$ that the analysis adopts.","marker":"[7]"},{"why":"Reports the 99.3 GeV Fermi photon from GRB 221009A and the GBM light curves used for the low-energy reference peak.","marker":"[8]"},{"why":"Reports the MAGIC detection of the 1.07 TeV photon from GRB 190114C and prior Lorentz-violation bounds from that event.","marker":"[9, 10]"},{"why":"Reports the LHAASO detection of the 12.2 TeV photon from GRB 221009A analyzed here.","marker":"[11]"},{"why":"Provides the modified dispersion relation and the cosmological time-delay integral used in Eqs. (1)--(3).","marker":"[12]"}],"fun_headline_variants":["One Lorentz scale explains three extraordinary GRB photons","Energy-dependent intrinsic delay unifies three GRB photons","A single LV scale ties together three remarkable photons","Three exceptional photons, one Lorentz-violation scale","Consistent LV scale from three extreme GRB photons"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's conclusions rest on the assumption that the GRB source emits high-energy photons with an intrinsic delay that grows linearly with photon energy; if that linear form (or the manually chosen low-energy reference peak) is wrong, the fitted $E_{\\rm LV}$ is an artifact of the assumed formula.","fun_headline_variants_meta":{"raw":{"variants":["One Lorentz scale explains three extraordinary GRB photons","Energy-dependent intrinsic delay unifies three GRB photons","A single LV scale ties together three remarkable photons","Three exceptional photons, one Lorentz-violation scale","Consistent LV scale from three extreme GRB photons"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001138,"raw_usage":{"total_tokens":4805,"prompt_tokens":1105,"completion_tokens":3700,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":721,"completion_tokens_details":{"reasoning_tokens":3627}},"tokens_in":721,"tokens_out":3700,"duration_ms":24897,"temperature":1.0,"reasoning_tokens":3627,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:52:08.144290+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a GRB with two or more high-energy photons spanning a wide energy range and an unambiguous low-energy peak, then measure the delay versus energy; if the delays do not fall on a single straight line with the same $\\alpha\\sim -0.2$ s GeV$^{-1}$ and the same $E_{\\rm LV}\\sim 3\\times 10^{17}$ GeV used here, Model C is ruled out.","supporting_citations":[],"review_version":1}