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REVIEW 3 major objections 6 minor 15 references

Reconstruction of inclined cosmic-ray properties with GRAND data

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Fitting the ADF radio-emission model directly to raw antenna voltages—skipping electric-field reconstruction—recovers inclined cosmic-ray directions to a median 0.09 degrees and first-order energies.

desk verdict A solid commissioning-stage methods paper: direct voltage-based ADF reconstruction is genuinely new and the simulation validation is strong, but the voltage-field proportionality is asserted rather than shown. read the letter →

arxiv 2507.04324 v1 pith:RSODZYDR submitted 2025-07-06 astro-ph.IM astro-ph.HEhep-ex

Marion Guelfand , Pauline Fritsch , Valentin Decoene , Olivier Martineau-Huynh , Mauricio Bustamante (for the GRAND collaboration) This is my paper · ORCID
classification astro-ph.IMastro-ph.HEhep-ex
keywords ultra-high-energycosmicraysradiodetectionextensiveairshowersangulardistributionfunctionGRANDProto300directionreconstructionenergyestimationvoltagetraces
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the Angular Distribution Function (ADF), a phenomenological model of radio emission from inclined air showers, can be fitted directly to the raw voltage traces recorded by GRANDProto300 antennas, without first reconstructing the electric field. On 13,000 simulated showers with zenith angles above 60 degrees, this voltage-level fit reaches a median angular resolution of 0.09 degrees and yields a scaling factor that tracks the shower's electromagnetic energy to first order. Applied to commissioning data, the same fit separates 41 cosmic-ray candidates from background and gives energy estimates that agree with electric-field-based estimates to within about 32%. If correct, the result means large radio arrays can do event selection, direction reconstruction, and first-order energy estimation straight from the detector's raw output.

What carries the argument

The central object is the Angular Distribution Function (ADF), a phenomenological model of the angular pattern of radio amplitudes in the 50–200 MHz band, parametrized by a global amplitude $A$, the shower direction $\theta,\phi$, and a profile width $\delta\omega$, evaluated at each antenna's angular coordinates $\omega$ and $\eta$ in the shower plane. It encodes the Cherenkov-ring enhancement through $\tan\omega/\tan\omega_c$, the geomagnetic asymmetry through $G_A \cos\eta/\sin\alpha$, and the early-late effect through the source distance $l$. The load-bearing step is fitting this model to raw voltage peaks rather than to deconvolved electric-field peaks, relying on the flat GRAND Horizon antenna gain over 70–85 degrees zenith to make voltages proportional to fields; the fitted $A$ then feeds the first-order energy estimator $E^*_{\rm em}=A/[\sin\alpha \, f(\rho,\sin\alpha)]$, and the fit's $\chi^2_\nu$ acts as an event-selection and background-rejection statistic.

What would settle it

Take a set of triggered air-shower events with known simulated or well-reconstructed directions and compare the ADF fit on raw voltages with the fit on fully deconvolved electric fields; if the median direction difference grows well beyond 0.09 degrees, or if voltage-based energies scatter by much more than 32% against field-based energies, the linear voltage-to-field scaling is violated. A direct laboratory measurement of the 50–200 MHz gain spread across deployed GP300 antennas would also settle whether the antenna response is uniform enough.

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Extended reading notes

Core claim

The central claim is that the ADF—a model originally built for electric-field amplitudes—remains valid on raw voltages, so the electric-field reconstruction step can be bypassed. Because the GRAND Horizon antennas have a wide, flat gain for zenith angles between 70 and 85 degrees, the viewing angles across the array are nearly uniform, and the voltage recorded by each antenna is expected to scale approximately linearly with the electric field. With this assumption, the paper shows on simulations that the fitted amplitude parameter $A$, corrected as $A/\sin(\alpha)$, correlates linearly with the electromagnetic energy of the shower, and that the reconstructed directions have a median error of about 0.09 degrees. On the 41 experimental candidates, a reduced $\chi^2_\nu$ cut around 25 removes events with poor fits, the measured amplitudes show the predicted enhancement at the Cherenkov angle, and voltage-based energies agree with the deconvolved electric-field energies to about 32%. The authors note that amplitude calibration has not yet been applied, so the experimental results are preliminary.

Load-bearing premise

The method depends on the premise that each antenna's raw voltage tracks the radio field essentially linearly, with antenna response varying little across the array; this was inferred from the antenna's flat gain and checked only through simulations, not with a dedicated measurement.

Editorial extensions

If this is right

  • A reduced chi-squared cut at 25 applied to the voltage-based ADF fit selects cosmic-ray showers while rejecting about 84% of the random background events tested here.
  • For simulated showers at zenith angles above 60 degrees, the voltage-based reconstruction reaches a median angular resolution of about 0.09 degrees, matching electric-field-based fits.
  • The voltage-derived scaling factor $A/\sin(\alpha)$ correlates linearly with electromagnetic energy to first order, and voltage-based energies agree with electric-field-based energies to within about 32%.
  • A combined cut on the ADF fit and a simple isotropic-emission fit should give stronger background rejection once the detector reaches its full configuration.
  • The same approach extends to upward-going trajectories, the geometry relevant for Earth-skimming neutrino searches at full GRAND scale.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: because the voltage fit skips deconvolution, it could plausibly run as an online or trigger-stage filter, reserving full electric-field reconstruction for candidate events.
  • Editorial extension: the paper shows the ADF and isotropic-background chi-squared distributions are separated but does not construct a joint cut; a two-dimensional selection could yield better background rejection than either cut alone.
  • Editorial extension: the linear-scaling argument is tuned to the GRAND Horizon antenna's flat 70–85 degree gain; whether similar voltage-level fitting works for other radio arrays with different antenna response is not established by this paper.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript presents a reconstruction method for highly inclined cosmic-ray air showers detected by GRANDProto300 (GP300), based on fitting the phenomenological Angular Distribution Function (ADF) directly to raw voltage traces rather than to reconstructed electric fields. The pipeline combines a plane-wave timing fit, a spherical-wavefront emission-point fit, and an ADF amplitude-profile fit, followed by a voltage-based energy proxy A/sin(alpha). The method is validated on 13,000 simulated ZHAireS showers (0.1-3.98 EeV, 60-88 degrees zenith) with realistic electronics, noise, and timing jitter, yielding a median angular resolution of 0.09 degrees and a linear correlation between the corrected amplitude and electromagnetic energy. The approach is then applied to 41 cosmic-ray candidate events from GP300 commissioning data, with a cross-check between voltage-based and electric-field-based energy estimates showing about 32% relative spread. The paper concludes that the ADF method works directly on voltages, enabling event selection, direction reconstruction, and first-order energy estimation without antenna-response deconvolution.

Significance. If the voltage-based ADF approach is validated, it would be practically valuable for large sparse arrays like GRAND: it bypasses electric-field reconstruction, reduces processing complexity, and enables quick event identification and preliminary energy estimation. The simulation study is a clear strength: large statistics, realistic electronics and noise modeling, and a direct, machine-checked comparison against true shower directions. The reported 0.09-degree median angular resolution on simulated data is an explicit, falsifiable quantity. The experimental demonstration on 41 candidates, while preliminary, indicates the method works on real detector outputs. However, the central voltage-field proportionality assumption is only qualitatively motivated and the energy calibration is simulation-based and not independently anchored, so the quantitative claims (especially the energy proxy) are not yet fully established.

major comments (3)
  1. [Section 3.1, Eq. (1)] The load-bearing assumption that voltage traces scale approximately linearly with the electric field across the array is asserted but not quantitatively demonstrated. The text says this was 'checked with simulations presented in the following section, by comparing the amplitudes of electric field traces with those of ADC traces,' but Section 3.2 contains no such comparison figure, table, or numerical spread. A flat antenna gain at 70-85 degrees is not sufficient, because the ADF fit uses the peak of the Hilbert envelope of the vector sum of three polarization channels; flat total power gain does not guarantee uniform per-channel amplitude and phase response with direction or frequency over 50-200 MHz. Please add a direct per-antenna test on the simulated events: for each event, compute the ratio of the peak Hilbert-envelope amplitude of the ADC trace to that of the corresponding electric-field trace, and show its RMS variation across antennas, events, zenith angles, and frequency sub-bands. Without this, the median 0.09-degree resolution and the A/sin(alpha) energy proxy could be biased by an unmodeled voltage distortion, even if the simulation chain is internally consistent.
  2. [Section 4.4, Figure 5 (Top Right)] The cross-check between voltage-based and electric-field-based energies is not an independent validation: both estimates use the same ADF model, the same simulation-derived correction factor f(rho, sin alpha), and the same underlying voltage traces through the same electronics model. The observed 32% relative spread therefore measures internal consistency, not absolute accuracy, and a common systematic bias would not appear in this comparison. Please state this explicitly and, if possible, validate the absolute energy scale with an external reference (e.g., a measured energy spectrum, coincidence with another detector, or a calibrated test source). The sentence in Section 4.4 noting that amplitude calibration has not yet been applied is important and should be moved to the main claims rather than only a closing caveat.
  3. [Sections 4.2-4.3] The event-selection claim is based on the fraction of events passing chi2_nu <= 25 in simulated cosmic rays (86%) versus random CD events (16%), but the 41 candidates were not drawn from a pure background sample: they were pre-selected by an independent analysis [10] whose criteria are not described here. The statement that the ADF fit 'refines the initial selection' is therefore not a controlled test of the ADF's background-rejection power. Please provide at least the selection criteria used in [10], or state explicitly that the 85% passing fraction is conditional on an already high-quality candidate set. A simple false-positive estimate for the combined cut would also strengthen the 'efficient event selection' claim.
minor comments (6)
  1. [Abstract and Section 1] The abstract and introduction state that the method is 'applicable as well to upward-going trajectories,' but no upward-going showers are simulated, reconstructed, or tested in this work. This is an overclaim; either add a sentence explaining how the method extends trivially to upward-going geometries, or move this remark to the outlook section.
  2. [Section 3.2.2] The choice of the chi2_nu <= 25 selection threshold is arbitrary and is justified only by the observed separation between signal and background. Please specify how this value was chosen (e.g., optimization on simulations or signal efficiency) and how the median angular resolution changes if the threshold is varied.
  3. [Section 4.3 and Figure 2] The error bars on measured amplitudes are said to represent 'estimated 7.5% uncertainties,' but no derivation or reference for this value is given. Please state how the 7.5% was estimated (e.g., from noise covariance, calibration residuals, or simulation).
  4. [Throughout] There are several typographical errors: 'istropic' should be 'isotropic' in Section 4.2; 'quiet distinct trends' should be 'quite distinct trends' in Section 4.2; 'Bij' and 'Ceopenhagen' appear in the author affiliations. A careful proofread is recommended.
  5. [Figure 3] The caption states that the reconstructed footprint is 'derived from the Cherenkov angle (from the toy model), the core position, and the shower axis,' but the text does not define this toy model or how the footprint is drawn. Please add a brief definition or reference.
  6. [Section 4.4] The statement that the reconstructed energy distribution spans 10^17 eV to 5x10^18 eV and 'matches expectations based on our exposure calculations' is not quantified; a plot of the reconstructed energy distribution compared with the expected distribution would be more convincing.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity: the ADF model is a cited phenomenological input, direction reconstruction is checked against true simulated directions, and the only mild circularity is an internal-consistency energy cross-check.

  1. other [Section 4.4, Figure 5 (Top Right)]
    "the energy is also reconstructed directly from the voltage traces using the empirical scaling law derived from simulations (Section 3.2.1). ... A good agreement is observed ... indicating that voltage-based reconstruction provides a reliable first-order energy estimate."

    Both energy estimators are applications of the same ADF model (Eq. 1): the electric-field energy uses the ADF amplitude A with the simulation-derived factor f(rho, sin alpha), and the voltage energy uses an 'empirical scaling law derived from simulations' that is also based on the ADF amplitude extracted from voltage. The agreement between the two is therefore a consistency check between two uses of the same model and the same simulation calibration, not an independent absolute validation of the energy scale. This is a mild validation circularity, but it does not affect the direction-reconstruction claim, which is benchmarked against true shower directions in simulations independent of the ADF fit.

full rationale

The paper's derivation chain does not reduce to its own inputs by construction. The ADF model (Eq. 1) is adopted from prior work ([2]) as an explicit phenomenological fitting function, not derived from the data being reconstructed. The central quantitative result, a median angular resolution of 0.09 degrees, comes from comparing ADF-fitted directions to true shower directions in 13,000 ZHAireS simulations; those truths are external to the ADF model and independent of its fitted parameters. The energy claim is presented as a first-order proxy: A/sin(alpha) is plotted against true electromagnetic energy in simulations and a linear correlation is reported; this is a calibration, not a prediction manufactured from the fitted values themselves. On experimental data, the voltage versus electric-field energy comparison in Section 4.4 is an internal-consistency check because both reconstructions share the ADF model and the same simulation-derived correction factor; the paper calls it a cross-check, and while it should not be read as an external validation, it is not a definitional reduction of one result into another. The voltage-linear-in-electric-field assumption of Section 3.1 is asserted from flat antenna gain and checked only indirectly through simulations; this is a limitation in support strength, not a circular step, because the simulated angular-resolution test could in principle fail if the assumption were wrong. Self-citations ([2], [3]) are not used to import a uniqueness theorem or to forbid alternative models, and the paper explicitly labels the ADF a phenomenological model. Overall, the central claims have independent grounding in simulation truth, and the identified issue is a minor internal-consistency cross-check rather than substantive circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method rests on the ADF phenomenological model from prior work, the spherical wavefront model for inclined showers, and a simulation-calibrated energy correction. The main free parameters are per-event fit scales (A, delta_omega) and a simulation-determined correction factor f(rho, sin alpha); the chi-squared cut is a hand-chosen selection threshold. No new physical entities are introduced.

free parameters (5)
  • A (ADF amplitude scale) = per event, fitted
    Global amplitude scaling in Eq. 1; its corrected value A/sin(alpha) is the energy proxy.
  • delta_omega (ADF profile width) = per event, fitted
    Width of the angular amplitude profile in Eq. 1; absorbs lateral spread of the radio signal.
  • f(rho, sin alpha) energy correction factor = not specified in paper; determined from simulations
    Multiplicative correction in E*_em = A / (sin(alpha) f(rho, sin(alpha))); claimed to depend primarily on air density at the emission point. Its functional form is not given.
  • chi-squared selection threshold = 25 (reduced chi-squared)
    Hand-chosen cut that keeps 86% of simulated triggered events and 85% of candidates; affects event selection efficiency.
  • kappa (background fit amplitude) = per event, fitted
    Amplitude parameter in the isotropic background model A = kappa/l used to separate background from cosmic-ray candidates.
assumptions (5)
  • domain assumption ADF model (Eq. 1) adequately describes the angular amplitude pattern of radio emission from inclined air showers in the 50-200 MHz band.
    Phenomenological model taken from ref [2]; not re-derived here, yet it is the basis of the fit and the energy proxy.
  • domain assumption The radio wavefront from a very inclined shower can be modeled as spherical, with a single emission point X_e.
    Assumed in step 2 of the reconstruction pipeline, citing ref [5]; supports the geometry of the fit.
  • ad hoc to paper Voltage traces scale approximately linearly with the electric field across the triggered antennas.
    Introduced in Section 3.1 to justify applying the ADF model directly to voltages; checked only indirectly via simulations.
  • domain assumption ZHAireS simulations with the modeled electronics chain and measured on-site noise reproduce GP300 voltage signals.
    The 13,000-event validation set relies on this simulation chain (refs [6,8]); no comparison to real pulses is shown except through candidates.
  • domain assumption The Cherenkov angle can be predicted from the emission point and atmospheric refractive index along the line of sight.
    Used in Eq. 1 and in the footprint comparison of Section 4.3; accuracy is assumed from the toy model.

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Cite this review

Pith. "Pith review of Reconstruction of inclined cosmic-ray properties with GRAND data." pith.science (2026). https://pith.science/paper/RSODZYDR

@misc{pith2026250704324,
  author       = {Pith},
  title        = {Pith review of: Reconstruction of inclined cosmic-ray properties with GRAND data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RSODZYDR}},
  note         = {Machine review of arXiv:2507.04324}
}
abstract

Radio-detection is now an established technique for studying ultra-high-energy (UHE) cosmic rays with energies exceeding $\sim 10^{17}$ eV. The next generation of radio experiments, such as the Giant Radio Array for Neutrino Detection (GRAND), aims to expand this technique to the observation of Earth-skimming UHE neutrinos, which requires the detection of very inclined extensive air showers (EAS). Currently, GRAND is validating its detection principle -- autonomous radio detection -- in particular through the prototype array GRANDProto300, deployed in the Gobi Desert. In this phase, the array is limited to detecting inclined EAS from cosmic rays. Neutrinos cannot be observed because of the restricted detector size. We present a method to reconstruct the arrival direction and energy of EAS with zenith angles above $60^\circ$, applicable as well to upward-going trajectories. The approach combines a point-source-like description of the radio wavefront with the so-called Angular Distribution Function (ADF), a phenomenological model describing the angular pattern of radio signal amplitudes in the 50--200 MHz band. Applied directly to the voltage traces, this method enables efficient event selection with accurate direction reconstruction and a first-order energy estimate. We validate the approach with both simulations and experimental data, and reconstruct the first cosmic-ray candidates detected by GRANDProto300.

Figures

Figures reproduced from arXiv: 2507.04324 by the authors.

Figure 1
Figure 1. Left: Angular resolution 𝜓 obtained directly from voltage using the ADF fit on simulations. Right: Corrected scaling factor 𝐴/sin(𝛼) extracted from voltage as a function of the electromagnetic energy in simulations. A first-order linear dependence is observed, with a small spread. selected background events exhibit similar amplitudes on all antennas, with reconstructed angular distances 𝜔 close to the Cherenkov angl… view at source ↗
Figure 2
Figure 2. Left: Distribution of the 𝜒 2 𝜈 from the ADF and background fits for cosmic-ray simulations, random CD (interpreted as background events), and cosmic-ray candidates. A clear separation is observed between background and cosmic-ray events. Most CR candidates fall within the cosmic-ray distribution, while those with 𝜒 2 𝜈 > 25 are excluded from further reconstruction, as they are considered likely background. Right: A… view at source ↗
Figure 3
Figure 3. Left: Map of active antennas on site for the cosmic-ray candidate (CR0), with amplitudes shown at triggered antennas. The reconstructed radio footprint is displayed. Right: Triggered antennas projected onto the reconstructed shower plane. 4.4 Reconstruction on Voltage and Electric Field As shown in Section 3.2.1, ADF treatment of voltages offers excellent angular resolution in simulations [PITH_FULL_IMAGE:figures/f… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Left: Amplitude profile of a cosmic-ray candidate (CR16: 𝜃 = 80.8°, 𝜙 = 178.5°) fitted with the ADF model, which does not meet the selection criterion 𝜒 2 𝜈 ≤ 25. Right: Amplitude profile of the same event using the background fit. Blue points represent the amplitudes …
Figure 5
Figure 5. Figure 5: Top Left: ADF fit applied to the reconstructed electric field for a selected candidate (CR20: 𝜃 = 77.41°, 𝜙 = 310.35°). Bottom: Reconstructed arrival directions (zenith 𝜃 and azimuth 𝜙) of the cosmic-ray candidates from voltages. The zenith is at the center, the horizo…

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Works this paper leans on

15 extracted references · 14 canonical work pages

  1. [10]

    Lavoisieret al.inPoS(ICRC2025)314

    J. Lavoisieret al.inPoS(ICRC2025)314

    work page

  2. [1]

    Martineau-Huynh inPoS(ICRC2025)1114

    O. Martineau-Huynh inPoS(ICRC2025)1114

    work page

  3. [2]

    Guelfandet al

    M. Guelfandet al. Astroparticle Physics171 (2025) 103120

    work page 2025

  4. [3]

    Decoeneet al

    V. Decoeneet al. PoSICRC2021(2021) 211. 7 Reconstruction of inclined cosmic rays on GRAND Marion Guelfand Preliminary Preliminary Preliminary Figure 5: Top Left: ADF fit applied to the reconstructed electric field for a selected candidate (CR20: 𝜃 = 77.41°, 𝜙 = 310.35°). Bottom: Reconstructed arrival directions (zenith𝜃 and azimuth 𝜙) of the cosmic-ray ca...

    work page 2021

  5. [4]

    Ferrièreet al

    A. Ferrièreet al. Nucl. Instrum. Methods Phys. Res. A1072(2025) 170178

    work page 2025

  6. [5]

    Decoeneet al

    V. Decoeneet al. Astroparticle Physics145 (Mar., 2023) 102779

    work page 2023

  7. [6]

    Chicheet al

    S. Chicheet al. Phys. Rev. Lett.132 no. 23, (2024) 231001

    work page 2024

  8. [7]

    Álvarez-Muñiz et al.)Sci

    GRAND Collaboration (J. Álvarez-Muñiz et al.)Sci. China Phys. Mech. Astron.63no. 1, (Aug., 2019)

    work page 2019

Show all 15 references
  1. [8]

    Alves Batista et al.)Comput

    GRAND Collaboration (R. Alves Batista et al.)Comput. Phys. Commun.308(Mar., 2025)

    2025

  2. [9]

    Ma inPoS(ICRC2025)453

    P. Ma inPoS(ICRC2025)453

  3. [11]

    Corstanjeet al

    A. Corstanjeet al. Astroparticle Physics89(Mar., 2017) 23–29

    2017

  4. [12]

    K. D. de Vrieset al. PRL107 no. 6, (Aug., 2011) 061101

    2011

  5. [13]

    Álvarez-Muñizet al

    J. Álvarez-Muñizet al. PRD81 no. 12, (June, 2010) 123009

    2010

  6. [14]

    Zhanget al., 2025

    K. Zhanget al., 2025. https://arxiv.org/abs/2501.12614

    2025 arXiv

  7. [15]

    Emergences

    S. Katoet al.in PoS(ICRC2025)298. 8 Reconstruction of inclined cosmic rays on GRAND Marion Guelfand Full Author List: GRAND Collaboration J. Álvarez-Muñiz1, R. Alves Batista2,3, A. Benoit-Lévy4, T. Bister5,6, M. Bohacova7, M. Bustamante8, W. Carvalho9, Y. Chen10,11, L.Cheng 12...

    1900

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