{"id":"b02e2c85-5453-46e1-a77b-444922bfb427","arxiv_id":"2507.00954","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Solar Orbiter observed 10 solar energetic proton events with inverse velocity dispersion, which the authors explain as delayed release from diffusive shock acceleration and use to infer shock acceleration parameters.","lead":"This paper reports 10 solar proton events where higher-energy protons arrived after lower-energy ones, opposite to the usual pattern, and interprets the delay as evidence that a shock wave took longer to accelerate faster particles. The result gives a new way to measure, from spacecraft data alone, how long and how efficiently solar shock waves accelerate protons.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The derived release times that constitute the DSA evidence are generated by an unvalidated path-length assumption (L(E') = L0 − R_DBM(t_release)); if that assumption is wrong, the IVD can be explained without energy-dependent acceleration.","rationale":"The reader's weakest-assumption analysis identified the same crux: the derived release times and all downstream DSA parameters depend on the unvalidated path-length subtraction L(E') = L0 − R_DBM(t_release). My reading of the paper confirms this is the single most load-bearing step in the argument. The observational detection of IVD in 10 SolO events is credible and well documented, and the DSA interpretation is quantitatively developed, but the inversion that produces the energy-dependent release times is not checked against an independent transport or connectivity model. A synthetic test with fixed injection time, or a recomputation with alternative path models, would determine whether the sequential release is real or manufactured by the method. Because the concern is serious but addressable, the conditional verdict is appropriate; I would not reject the paper outright, but the DSA conclusion should not be accepted as established until the path assumption is validated. The reader's proposed strengthening—releasing onset-selection data, performing a DSA-versus-connectivity model comparison, and propagating uncertainties—directly addresses this concern, so no change to the reader's verdict is needed.","tokens_in":28713,"tokens_out":4582,"duration_ms":116579,"concrete_test":"Re-run the IVDA inversion on the three detailed events (2023-11-09, 2023-12-24, 2023-12-31) under two alternative path models: (i) a constant path L(E') = L0 with no shock-distance subtraction, and (ii) a path length computed from a field-line/cobpoint model connecting the moving shock to SolO (e.g., using an MHD shock simulation or the transport model of Ding et al.). If the inferred trelease(E') versus E' slope, or the fitted λ0, changes qualitatively—or if a zero-slope release-time model reproduces the observed IVD onsets under model (ii)—then the DSA signature in Fig. 3(c) and Table 1 is an artifact of Methods step 2. This single check would settle whether the path-length assumption is load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—that trelease(E') increases monotonically with energy and that this ordering is evidence of diffusive shock acceleration—rests on Methods 4.2, step 2, where the particle path is set to L(E') = L0 − R(t_release(E')), with R taken from the DBM shock propagation. This is an assumption, not a measurement: the observed quantities are only tonset(E'), and the release times are solved from Eq. 8 after imposing this path model. If high-energy protons actually travel a longer or differently shaped path—for example because the cobpoint slides along the shock to a different location, or because cross-field transport lengthens their trajectory—the observed later arrival of high energies could be produced without any energy-dependent release time. Even within the moving-source picture, the correct path is the magnetic field line from the shock cobpoint to SolO, not the low-energy VDA path minus the radial distance of the shock nose. The subtraction is especially consequential because it is iterative: a later trelease(E') for a high-energy proton reduces its path, which pushes trelease still later, amplifying exactly the monotonic release-time curve that is later fitted by the DSA expression. The paper's Table 2 shows IVD events over a wide range of separations, which weakens the connectivity alternative as a universal explanation, but it does not validate the path-subtraction rule. The claimed sequential release is therefore not an independent measurement of DSA; it is largely a consequence of the path model used to invert the onsets.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports 10 solar energetic proton events observed by Solar Orbiter in which the onset pattern shows normal velocity dispersion (VD) at low energies and inverse velocity dispersion (IVD) above a few MeV, meaning that higher-energy protons arrive later. For three well-observed events (2023-11-09, 2023-12-24, 2023-12-31), the authors combine a standard velocity-dispersion analysis for low-energy protons with an iterative inversion of Eq. (8) in which the propagation path at each energy is shortened by the drag-based-model shock distance at the derived release time. This yields energy-dependent release times that increase with energy and release distances of 0.05-0.38 au. The authors interpret this as evidence for diffusive shock acceleration (DSA) at the propagating CME shock, and use the observed spectral indices plus DSA expressions to infer shock compression ratios, acceleration times, and reference mean free paths near the shock. The paper also discusses an alternative connectivity-change scenario and argues that it cannot explain all events.","tokens_in":28921,"tokens_out":3727,"duration_ms":50140,"significance":"The observational discovery is valuable and timely. The manuscript carefully documents 10 IVD events with clear dynamic spectra, provides multi-spacecraft context, checks sunward anisotropy at onset, and presents a useful parameter table. If the delayed high-energy release were established independently of the transport-path assumption, the inferred energy-dependent release times would be a genuinely new probe of shock acceleration in the inner heliosphere, and the fitted mean free paths near 10^-4 au would be an important quantitative constraint. The paper is also honest about several limitations, including possible shock evolution and the need for future coupled MHD-particle modeling. However, the central quantitative result is currently conditional on a path-length subtraction rule that is not independently validated, and the 'evidence for DSA' wording in Supplementary Section C overstates what the analysis can establish. The work is therefore suitable for a major revision rather than acceptance in its present form.","major_comments":[{"comment":"The derivation of energy-dependent release times is load-bearing, but it relies entirely on the unvalidated path-length rule L(E') = L0 - R(t_release(E')), with R taken from the DBM shock propagation. The observed quantity is only t_onset(E'); Eq. (8) contains two unknowns per energy. Step 2 of the iteration imposes a specific moving-source path model rather than measuring it. If high-energy protons instead travel along a longer or differently shaped path (for example, because the cobpoint slides along the shock or because cross-field transport lengthens their trajectory), the observed later arrival of higher energies could be produced without any energy-dependent release time. The paper should either validate this path rule with independent constraints (e.g., modeled field-line connectivity to the shock nose versus cobpoint, or multi-spacecraft comparisons) or present a sensitivity study showing how the release-time ordering, and hence the DSA conclusion, changes under alternative path assumptions. Table 2's wide range of source-observer separations weakens a simple connectivity explanation, but it does not validate the path subtraction.","section":"Methods 4.2, Eq. (8), step 2"},{"comment":"The apparent agreement between the observation-derived release times and the DSA curve is a fit, not an independent prediction. The reference mean free path lambda_0 is not predicted a priori; it is fitted so that the theoretical acceleration time tau_a(E') matches the observation-derived t_release(E') markers in Fig. 3(c), and the same fitted lambda_0 is then used to draw the dotted curve in Fig. 2(b). Additionally, the compression ratio r used in Eq. (5) is derived from the observed IVD spectral index using the DSA formula itself, so the consistency between the observed spectrum and DSA is partly built in by construction. To support the central claim, the authors should show a test that does not use the IVD release times to determine the DSA parameters, for example by predicting the release-time slope from independently constrained shock parameters and transport conditions, or by reporting the goodness of fit of the DSA curve against a null model with no energy-dependent release.","section":"Section 3.1 and Fig. 3(c); Fig. 2(b)"},{"comment":"The IVD onset times are selected manually from the 2-d flux histograms, with the paper stating only that the process was 'repeated multiple times until the result is stabilised.' Because the derived t_release(E') and all subsequent DSA parameters depend linearly on these onsets, manual selection is a load-bearing part of the analysis. The manuscript should provide a quantitative reproducibility assessment: for example, independent selections by two or more observers, Monte Carlo perturbations of the chosen onset times within the 5-minute resolution, or comparison with an objective automated onset algorithm adapted to low count rates. Without this, it is difficult to judge whether the increasing release-time ordering in Fig. 2(b) is robust or partly an artifact of the selection procedure.","section":"Methods 4.2, onset-time determination"},{"comment":"The inference of near-Sun shock parameters uses the in-situ upstream flow speed u_u measured at SolO after shock arrival, together with IVD spectral indices, to derive the compression ratio and downstream speed for shock distances of only 0.05-0.14 au. The paper acknowledges the assumption that shock properties and seed spectra do not evolve between these distances, but this assumption is central to the quantitative claims about acceleration times and mean free paths. A short assessment of how much the inferred lambda_0 values would change under plausible evolution of the compression ratio (for example, r varying between 1.3 and 2.0) would materially strengthen the paper and should be added.","section":"Section 3.1, Eqs. (4)-(6)"}],"minor_comments":[{"comment":"The text says 'In panel (b) we plot the 3-hour-integrated spectra' while the caption describes panel (b) as the release-time/path-length result and panel (c) as the spectra; this labeling should be corrected for consistency.","section":"Supplementary Section E, Fig. 9 caption and text"},{"comment":"There are several missing spaces and typos in the paragraph beginning 'With both trelease(E') and L(E') being variables,' including 'First, based on the initial properties' and the later 'withtheconsiderationthatthao' run-together words; the section needs a careful proofread.","section":"Section 4.2, text after Eq. (8)"},{"comment":"The definition of lambda_rr should be clarified: Eq. (6) and the following sentence introduce the radial mean free path lambda_rr and equate it to lambda_0 (R/R0)^(1/3), but later lambda_r is written as lambda_parallel cos^2 Psi and compared to lambda_rr. The relationship between the radial mean free path used in the acceleration-time formula and the parallel mean free path used in the ESP analysis should be stated more precisely.","section":"Section 3.1, Eq. (6) and Fig. 3(d)"},{"comment":"For the 2023-08-07 event, the table lists onset IVD duration 8 and associated source angle 83 degrees, but the supplementary text notes that the onset phase 'could not be determined using CUSUM or manual selection'; the table and the supplementary text should be reconciled so that readers know which entries are uncertain.","section":"Table 2, event 9"}],"recommendation":"major_revision","confidential_remarks":"The manuscript presents a novel and potentially important event sample, but the central DSA interpretation rests on a path-length subtraction that is not independently tested. I would recommend that the revised version include a robustness analysis of the inversion with respect to the path assumption and a clear separation between fitted and predicted quantities. The paper is within scope for the journal and, with these additions, could become a solid contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The 10-event IVD catalog is a real, useful observational result. The DSA interpretation, however, is more fragile than it looks: the energy-dependent release times that constitute the 'sequential release' evidence are generated by an assumed path-length rule, not measured from the data. If that rule is wrong, the ordering can be explained without energy-dependent acceleration.\n\nThe novel content: the first multi-event catalog of IVD at 0.49-0.95 au, plus the first attempt to convert IVD into quantitative shock parameters (acceleration time, λ0, diffusion coefficient). The event selection and documentation are careful, the dynamic spectra are convincing, and the authors do report the prior single-event work (Cohen et al. 2024, Ding et al. 2025) properly. They also check their fitted λ0 against an independent in-situ ESP-based mean free path and find the same order of magnitude. That is real cross-validation.\n\nThe soft spots. Methods 4.2 sets L(E′) = L0 − R_DBM(trelease). This is an assumption, not an observation. The observed quantities are only onset times; release times are solved from Eq. 8 after imposing this path. The iteration tends to amplify the monotonicity: a later release time at higher energy shortens the path, pushing release still later. So the derived trelease(E′) curve that is later fitted by the DSA expression is largely built into the inversion. In the Supplementary, the authors state these particles 'are released sequentially from lowest to highest energy' and call that 'evidence of the diffusive acceleration'; that is circular unless the path model is independently validated. The compression ratio is also derived from DSA theory applied to the observed spectral index, so the internal consistency is not an independent test. The connectivity-change alternative is discussed and reasonably argued against as a universal explanation (the events span a wide longitude range), but it is not quantitatively modeled. The absence of propagated uncertainties on shock parameters is a minor rather than fatal issue; the uncertainty statements in the figures are hard to interpret.\n\nBottom line: this is a genuine observational discovery that deserves publication, but the mechanism claim needs to be reframed as scenario-based inference, not direct evidence. The authors should be asked to show the sensitivity of trelease(E′) to the path assumption, release the manual onset picks, and ideally run a full shock-particle model for at least one event. A serious referee can handle this. Conditional acceptance, with the path assumption as the primary point to address.","headline":"A credible 10-event catalog of inverse velocity dispersion, but the DSA explanation rests on an unvalidated path-length assumption that shapes the very release-time curve it claims to explain.","tokens_in":29605,"tokens_out":2891,"would_cite":false,"duration_ms":31893,"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":"Solar Orbiter observations of ten solar energetic proton events show inverse velocity dispersion: higher-energy protons arrive later, and the paper explains this as sequential release from a CME shock undergoing diffusive shock…","keywords":["solar energetic particles","inverse velocity dispersion","diffusive shock acceleration","Solar Orbiter","CME-driven shocks","energy-dependent particle release","proton mean free path","SEP onset times"],"falsifier":"Take any one of the ten events and recompute the high-energy release times without subtracting $R(t_{\\mathrm{release}}(E'))$ from the path length, forcing all protons onto a single shared path as in the standard VD analysis; if the high-energy onsets then fall on the same linear relation as the low-energy ones, the IVD would be an artifact of the path-length modification rather than delayed release. Alternatively, a single shock observed as a clear IVD event at one spacecraft and as normal VD at another well-connected spacecraft could test whether the energy-dependent release time is a common source property.","tokens_in":28435,"feed_emoji":"☀️","tokens_out":8039,"duration_ms":88324,"temperature":0.7,"pith_summary":"The paper reports that Solar Orbiter has observed at least ten solar energetic proton events in which protons above a few MeV show inverse velocity dispersion: higher-energy protons arrive later than lower-energy ones, opposite to the usual velocity-dispersion pattern. The authors argue that this inversion is not a transport artifact but a signature of energy-dependent release, with protons released sequentially from lowest to highest energy while the CME shock was still within roughly 0.2 au of the Sun. They interpret the delayed release as the expected behavior of diffusive shock acceleration, in which higher-energy protons need more time to be accelerated, and they use the measured delays to infer shock conditions that cannot be observed directly. A sympathetic reader would care because, if correct, the paper turns a puzzling new observational pattern into a quantitative probe of the acceleration process and of the timing of radiation-hazardous tens-of-MeV protons.","feed_headline":"10 solar proton events show reversed arrival order","feed_subtitle":"The delayed high-energy arrivals trace sequential release by a CME shock, giving a direct look at shock acceleration time.","key_machinery":"The central object is the energy-dependent release time $t_{\\mathrm{release}}(E')$ obtained from the onset equation $t_{\\mathrm{onset}}(E') = t_{\\mathrm{release}}(E') + (8.33\\,\\mathrm{min/au})\\, L(E')/\\beta(E')$, where $L(E')$ is the particle path length and $\\beta(E')$ the proton speed in units of $c$. For the low-energy VD part, $L$ and the release time are fitted by the standard velocity dispersion analysis; the paper's innovation is to iterate the high-energy part with the path shortened by the shock distance $R(t_{\\mathrm{release}}(E'))$ taken from a drag-based model of CME propagation. The physical mechanism invoked is diffusive shock acceleration (DSA), first-order Fermi acceleration at a quasi-parallel shock, whose mean acceleration time $\\tau_a(E') = \\frac{3}{u_u-u_d} \\int \\kappa_{rr} (1/u_u + 1/u_d)\\, dp'/p'$ produces longer acceleration times for higher final energies. The comparison of observed release delays with this formula is what lets the authors infer the otherwise unobservable mean free path and diffusion coefficient at the shock.","core_discovery":"The central claim is that the inverse velocity dispersion (IVD) seen by Solar Orbiter is caused by delayed, energy-dependent release of protons from a CME-driven shock undergoing diffusive shock acceleration. In each of the ten events the low-energy part shows normal velocity dispersion with a common release time and path length, while the high-energy part, above roughly 7 MeV, has onset times that increase with energy. Applying the iterative IVD analysis, the paper derives release times $t_{\\mathrm{release}}(E')$ that grow from lowest to highest energy, with the shock located between about 0.05 and 0.38 au at release. The observed release-time-versus-energy relation is then compared with the diffusive shock acceleration (DSA) acceleration-time formula, and the agreement fixes the mean free path at the shock, $\\lambda_0 \\sim 10^{-4}$ au, the diffusion coefficient $\\sim 10^{13}$ m$^2$/s, and the shock compression ratio around 1.5. The paper argues that DSA, rather than magnetic reconnection or changing magnetic connectivity, is the most likely dominant mechanism producing these tens-of-MeV protons.","pith_inferences":["If this interpretation survives, a testable extension is to compare IVD events observed by two spacecraft at different longitudes: DSA delayed release predicts the same energy-dependent release time for the same shock, whereas the connectivity scenario predicts different onset patterns for observers connected to different shock regions.","The derived $\\lambda_0$ near shocks could be cross-checked against direct measurements of magnetic turbulence and energetic-particle mean free paths made by close-in spacecraft, rather than only against e-folding-derived values at 0.66–0.94 au.","Applying the same analysis to heavy ions or to electrons would test whether the inferred acceleration time scales with rigidity as DSA predicts; a different scaling would point toward a different acceleration process.","The path-length correction $L(E') - R(t_{\\mathrm{release}}(E'))$ assumes the shock position sets the release point; a future model that computes particle trajectories through the expanding shock layer could test whether this simplification changes the inferred release ordering."],"forward_implications":["If the interpretation is right, IVD is a common SEP feature rather than a rare close-to-the-Sun curiosity: ten events by 2024, at a wide range of heliocentric distances and observer-source longitudes.","Energy-dependent release times mean that multi-MeV proton onset at an observer is not a direct measure of flare or CME launch time; the onset delay itself encodes the shock acceleration time.","The inferred mean free path near the shock ($\\lambda_0$ of order $10^{-4}$ au) is much shorter than quiet-solar-wind values, implying strong self-generated turbulence around the accelerating shock.","Because the acceleration time grows with final energy, radiation-risk assessments for tens-of-MeV protons must fold in shock acceleration time, not just transport time.","The connectivity-change alternative is disfavoured as a general explanation, since IVD events occur over a wide range of observer-source longitudinal separations."],"supporting_citations":[{"why":"reports the first single-case IVD observation by a near-Sun spacecraft that this paper extends to ten Solar Orbiter events","marker":"[14]"},{"why":"models the 2022-09-05 event with combined shock and particle transport, providing the connectivity-change alternative that the paper compares against","marker":"[15]"},{"why":"supplies the velocity dispersion analysis method and the linear onset-versus-inverse-speed fit used for the VD protons","marker":"[23]"},{"why":"derives the mean acceleration time expression for diffusive shock acceleration that the paper fits to the observed release delays","marker":"[33]"},{"why":"gives the crossing-probability argument and power-law spectrum from which the shock compression ratio and downstream speed are inferred","marker":"[34]"},{"why":"reproduces an observed Solar Orbiter IVD event in modeling, supporting the delayed-release interpretation","marker":"[52]"},{"why":"provides the drag-based model used to propagate the CME shock and evaluate $R(t_{\\mathrm{release}}(E'))$ for the path-length correction","marker":"[58]"},{"why":"supplies the e-folding method used to obtain the in-situ parallel mean free path for comparison with the fitted $\\lambda_0$","marker":"[42]"}],"fun_headline_variants":["Inverse velocity dispersion: protons arrive in reverse order","High-energy protons lag low-energy ones in 10 solar events","Shock acceleration flips arrival order of solar protons","Delayed high-energy protons reveal shock acceleration times","Proton energy arrival order reversed by CME shock in 10 events"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the high-energy protons travelled the same path length as the low-energy protons minus the drag-based-model shock distance at release, and that the shock conditions did not change appreciably between roughly 0.05 and 0.38 au.","fun_headline_variants_meta":{"raw":{"variants":["Inverse velocity dispersion: protons arrive in reverse order","High-energy protons lag low-energy ones in 10 solar events","Shock acceleration flips arrival order of solar protons","Delayed high-energy protons reveal shock acceleration times","Proton energy arrival order reversed by CME shock in 10 events"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000215,"raw_usage":{"total_tokens":1452,"prompt_tokens":989,"completion_tokens":463,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":382}},"tokens_in":605,"tokens_out":463,"duration_ms":5234,"temperature":1.0,"reasoning_tokens":382,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:01:24.028009+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take any one of the ten events and recompute the high-energy release times without subtracting $R(t_{\\mathrm{release}}(E'))$ from the path length, forcing all protons onto a single shared path as in the standard VD analysis; if the high-energy onsets then fall on the same linear relation as the low-energy ones, the IVD would be an artifact of the path-length modification rather than delayed release. Alternatively, a single shock observed as a clear IVD event at one spacecraft and as normal VD at another well-connected spacecraft could test whether the energy-dependent release time is a common source property.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reports the first single-case IVD observation by a near-Sun spacecraft that this paper extends to ten Solar Orbiter events"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"models the 2022-09-05 event with combined shock and particle transport, providing the connectivity-change alternative that the paper compares against"},{"cited_title":"Particle acceleration at the Sun and in the helio- sphere","cited_arxiv_id":null,"evidence_quote":"supplies the velocity dispersion analysis method and the linear onset-versus-inverse-speed fit used for the VD protons"},{"cited_title":"Vainio.Diffusive Shock Acceleration","cited_arxiv_id":null,"evidence_quote":"derives the mean acceleration time expression for diffusive shock acceleration that the paper fits to the observed release delays"},{"cited_title":"An introduction to the theory of diffusive shock acceler- ation of energetic particles in tenuous plasmas.Reports on Progress in Physics, 46(8):973–1027, August 1983","cited_arxiv_id":null,"evidence_quote":"gives the crossing-probability argument and power-law spectrum from which the shock compression ratio and downstream speed are inferred"},{"cited_title":"Bruno, G","cited_arxiv_id":null,"evidence_quote":"reproduces an observed Solar Orbiter IVD event in modeling, supporting the delayed-release interpretation"},{"cited_title":"Huttunen-Heikinmaa, E","cited_arxiv_id":null,"evidence_quote":"provides the drag-based model used to propagate the CME shock and evaluate $R(t_{\\mathrm{release}}(E'))$ for the path-length correction"},{"cited_title":"Li and G","cited_arxiv_id":null,"evidence_quote":"supplies the e-folding method used to obtain the in-situ parallel mean free path for comparison with the fitted $\\lambda_0$"}],"review_version":1}