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Two dense passive spheres in highly eccentric Earth orbits, tracked by laser ranging, can act as resonant detectors of microhertz gravitational waves, filling the gap between pulsar timing arrays and planned space interferometers.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-01 15:31 UTC pith:5R2GIIZP

load-bearing objection A serious white paper for a clever microhertz GW mission, but the headline sensitivity is the authors' own 'likely overly optimistic' no-arc case, and the conservative case is orders weaker. the 4 major comments →

arxiv 2607.18390 v1 pith:5R2GIIZP submitted 2026-07-20 astro-ph.CO gr-qchep-phphysics.ins-det

GUEST: Gravitational Universe Exploration with Satellite Tracking. A passive satellite laser-ranging mission for the dark gravitational Universe

classification astro-ph.CO gr-qchep-phphysics.ins-det
keywords gravitational wavesmicrohertz bandsatellite laser rangingresonant detectoreccentric orbitssupermassive black hole binariesultra-light dark matterfifth forces
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper makes the case that two dense, passive spheres — each covered with corner-cube retroreflectors — can be placed in highly eccentric Earth orbits with ~34-hour periods and, by being continuously tracked with laser ranging from the ground for a decade, act as resonant detectors of gravitational waves in the microhertz band. The central physical claim is that a gravitational wave whose frequency matches an integer multiple of the orbital frequency causes a small acceleration that accumulates into a quadratic drift in the satellite's orbital angle, so that even a strain of h0 ~ 1e-19 becomes visible over years. If this holds, GUEST would be the first experiment to probe the frequency gap between reported pulsar-timing signals and planned space interferometers, enabling searches for supermassive black-hole binaries, primordial gravitational-wave backgrounds, ultra-light dark matter, superradiant boson clouds, and fifth forces. The same data would yield an improved determination of Earth's gravitational parameter GM⊕. The mission concept is deliberately low-cost: two passive spheres and existing laser-ranging stations.

Core claim

The paper's central claim is that a highly eccentric Earth satellite orbit is a practical resonant gravitational-wave detector. A GW with frequency close to n times the orbital frequency induces a transverse-traceless acceleration that, over many orbits, produces a quadratic drift in the orbital angle (the true anomaly) — a drift that grows with observation time and survives a simultaneous fit of all other orbital parameters. With two spheres in 33.8-hour, e≈0.75 orbits tracked at ~10 cm precision (10 normal points per orbit per satellite) for ten years, the projected reach is h0 ≲ 1e-19 for monochromatic sources and hc ≲ 1e-17 for stochastic backgrounds in the 1e-7 to 1e-4 Hz range. The pap

What carries the argument

The central object is the orbit-as-resonator: the satellite's trajectory itself accumulates the gravitational-wave signal. The key identity is the resonance condition P ≈ n/ω_gw, where the orbital period stays near an integer multiple of the GW period; the resulting quadratic growth of the orbital-angle drift is amplified by high eccentricity and by higher harmonics. The long orbital period (33.8 h) places the fundamental resonances in the microhertz band, and the high eccentricity (e≈0.75) boosts the effect and excites higher resonances that extend the sensitive band upward. Two spheres in differently oriented planes (inclinations 75° and 50°, differing ascending nodes) decorrelate systemat

Load-bearing premise

The detection requires that the satellite's orbit remain near a fixed resonance with the gravitational-wave frequency long enough for the quadratic drift to accumulate over years, and that all systematic non-gravitational accelerations can be modelled well enough to separate them from the signal; the paper states that its 7-day-arc analysis destroys long-term signals and that the 10-year-arc analysis is 'likely overly optimistic'.

What would settle it

A concrete test: run a full precise-orbit-determination simulation of the two GUEST orbits — including lunisolar perturbations, the Earth's gravity field, solar radiation pressure, albedo, thermal re-radiation, and measurement noise — and inject a monochromatic GW of h0 = 1e-19 at 1e-5 Hz. If the recovered signal is absorbed by the fitted orbital parameters, or if the quadratic drift only appears in the unrealistic 10-year-arc analysis and not in any arc-based analysis, the central sensitivity claim fails; conversely, successful recovery would validate the concept.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • GUEST would deliver the first coherent search for supermassive black-hole binaries in the microhertz band, with sensitivity to individual chirping mergers up to roughly a billion solar masses at redshifts near 1, and to intermediate-mass black-hole binaries in nearby globular clusters.
  • It would probe stochastic backgrounds from primordial sources such as first-order phase transitions and cosmic strings, at energy scales inaccessible to terrestrial colliders, complementing pulsar-timing and millihertz interferometer observations.
  • It would extend direct searches for ultra-light dark matter (masses around 1e-22 to 1e-19 eV/c^2) into a parameter region untouched by other experiments, and would look for gravitational waves from superradiant boson clouds around nearby supermassive black holes.
  • It would improve bounds on Yukawa fifth forces and quadratic scalar couplings by roughly an order of magnitude at ranges from about a thousand to ten billion kilometres, and test the relativistic precession of the orbit's closest-approach point at the few-percent level.
  • The high-eccentricity, long-period orbits would break the correlation between range biases, station positions, and GM⊕, yielding an absolute determination of Earth's gravitational parameter approaching the 1-mm geodetic goals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the resonant response could also act as a monitor of local transient perturbations — for example, a planetary-mass primordial black hole passing through the inner Solar System might produce a detectable non-resonant disturbance; this is a natural extension worth quantifying.
  • Because the sensitivity curves are bracketed by two extremes (7-day arc breaks that erase long signals, and a 10-year arc the paper calls 'likely overly optimistic'), the real sensitivity will probably fall between them; a practical data-analysis scheme that keeps some arc structure while retaining long-period signal would sharpen the forecast.
  • A testable near-term extension is to apply the same resonant-drift formalism to existing long-arc objects that are already laser-tracked, such as the Moon, to search for an injected known monochromatic signal; success would validate the detection pipeline before launch.
  • The proposed scientific overlap with the planned millihertz interferometer turns GUEST into a possible pre-alert system: a source identified in the microhertz band can be followed into the higher band years later, improving sky localization and enabling archival searches — a multi-band synergy the paper mentions but does not fully develop.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes GUEST, a mission concept consisting of two dense, passive, retroreflector-covered spheres in highly eccentric Earth orbits (e~0.75, P~33.8 h), tracked by the ILRS satellite laser ranging network. The central claim is that the orbits act as resonant GW detectors, accumulating a quadratic drift in orbital elements when a GW frequency matches a harmonic of the orbital motion. The authors claim sensitivity to monochromatic strains h0≲1e-19 and stochastic backgrounds hc≲1e-17 in the microhertz band, and from these derive a broad science programme: SMBHB searches, primordial GW backgrounds, ultralight dark matter, superradiant boson clouds, fifth forces, and improved GM⊕ determination. The paper is a white paper presenting the motivation, orbit choices, sensitivity curves, science goals, and mission implementation, but it does not provide the underlying simulation code, covariance matrices, or a detailed error budget.

Significance. If the central sensitivity claim is correct, GUEST would open a genuinely unexplored frequency window between PTAs and LISA, with impact on GW astronomy, cosmology, particle physics, and geodesy. The concept is attractively simple and builds on mature SLR technology, and the two-satellite configuration for sky coverage and systematic decorrelation is thoughtful. The paper also contains useful concrete engineering work, including the dual-CCR optical cross-section design and the re-entry analysis. However, the quantitative forecasts are not yet demonstrated: the headline sensitivity relies on an admittedly optimistic data-analysis scenario, and the realistic 'with arcs' scenario is admitted to destroy the long-term coherent signal that is the basis of the detection concept. The scientific payoff therefore rests on an unquantified ability to perform decade-long precise orbit determination, which is the manuscript's principal weakness.

major comments (4)
  1. [Sec. 2.2, Fig. 2, Abstract and Sec. 3.5] The abstract and Sec. 3.5 state that GUEST will be sensitive to h0≲1e-19 and hc≲1e-17, but Fig. 2 shows that the h0≲1e-19 curve is the 'no arc' case, i.e. a single 10-year arc. The text immediately before Fig. 2 calls this scenario 'likely overly optimistic'. The 'with arcs' case (7-day POD arcs) is described as the realistic conservative scenario, and the paper admits that arcs are 'highly unfavorable for long-term signals'. No quantitative argument is given for how unmodeled non-gravitational accelerations (solar radiation pressure, Earth albedo, thermal/Yarkovsky effects, geopotential harmonics, station range biases) would be mitigated to allow a 10-year global arc. Thus the headline sensitivity is not supported as stated; the paper must either adopt the with-arcs sensitivity as the headline or provide an error budget demonstrating that decade-long arcs are feasible.
  2. [Sec. 2.1 and Sec. 2.2] The paper claims that 'we fit the GW signal simultaneously with all other parameters considered in standard POD', but no covariance matrix, simulation setup, or analysis software is provided, and no end-to-end simulation results are shown. The only quantitative basis for the sensitivity curves is therefore opaque. To make the central claim reproducible and checkable, the authors need to release at least the relevant covariance analysis, or describe the simulation in enough detail for an independent group to reproduce the curves. This is not a mere documentation issue: the feasibility of the whole mission depends on whether systematics can be separated from the GW signal over the relevant timescales.
  3. [Fig. 4 and Sec. 2.1] The sensitivity curves in Fig. 2 appear to assume fixed orbital elements, but Fig. 4 shows large Lidov-Kozai-driven variations in eccentricity, inclination, and argument of perigee over the 30-year mission. These variations change the resonance condition, the orbital harmonics, and the accumulated phase drift. The paper does not convolve the time-dependent orbital elements with the sensitivity calculation. Even the 'no arc' curve is therefore a best-case snapshot, not a mission-integrated sensitivity. The authors should show the sensitivity obtained by propagating the actual time-dependent orbits, or justify why the static approximation is adequate.
  4. [Sec. 3.1.A and Fig. 5] The reach claims for individual SMBHB mergers and IMBH systems in Fig. 5 are based on 'dedicated waveforms' and 'estimates for individual sources' that 'will appear in future work'. Since these figures are used to support science goals SGA1 and SGA2, the analysis should be described at least in outline here, or the figures should be clearly labelled as preliminary and not used as quantitative mission statements. The same applies to the GM⊕ forecast in Fig. 10, whose caption notes that additional parameters are not included.
minor comments (5)
  1. [Title] The title contains a typo: 'T racking' should be 'Tracking'.
  2. [Throughout] The acronym 'GUEST' is written as 'Guest' in several places (e.g., first sentence of the abstract and in Sec. 2.2). Please use one consistent capitalization.
  3. [Sec. 4.4 and Sec. 2.2] The data cadence is given as '10 NPs per orbit' in Sec. 2.2, but Sec. 4.4 says '20 NPs observations per orbit (10 per satellite)', and Fig. 10 refers to '2x10NPs/day'. Please clarify the intended number per satellite and per day, and ensure the sensitivity calculations use a consistent value.
  4. [Fig. 2] The left-panel x-axis is labelled 'f [Hz]' but the tick values run from 0 to 140; presumably the intended unit is microhertz or the axis should be scaled. Please correct the axis label and ticks.
  5. [Fig. 8] The axes are labelled only '[m]' and '[-]'; the meaning (λ and α) should be included in the axis labels.

Circularity Check

0 steps flagged

No significant circularity: sensitivity forecasts follow from standard, independently checkable orbital-resonance physics; the optimistic no-arc case is explicitly labeled as optimistic, not disguised as a fitted prediction.

full rationale

The paper's central derivation is not circular. Its detection concept relies on the standard transverse-traceless acceleration formula (Eq. 2) and the published result that a resonantly-driven eccentric orbit accumulates a quadratic drift in true anomaly; the ensemble of Refs. [14-18] provides the underlying physics, but that physics is external to the mission claim and is checkable from general-relativistic perturbation theory rather than being defined by GUEST's sensitivity. The mission parameters (e~0.75, P~33.8 h, 10 NPs/orbit, 10 cm precision, 10 years) are chosen design inputs, not fit parameters tuned to reproduce a target signal, and the sensitivity curves are explicitly presented as SNR=1 forecasts under two data-analysis scenarios. The paper is transparent that the 'no arc' curve is 'likely overly optimistic' while the 'with arcs' curve is 'overly pessimistic', so quoting the no-arc headline is a best-case caveat, not a constructed equivalence. The overlap of some authors with Refs. [14-18] and [31] is real, but those works are published, parameter-free derivations of the resonant response, not unverified claims whose sole support is the present collaboration. Any weaknesses — arc length, non-gravitational accelerations, Lidov-Kozai secular evolution, or the deferred source-specific waveform details — are feasibility and modelling limitations, openly acknowledged in the text, and do not reduce the forecast to its own inputs. No fitted parameter is renamed as a prediction, and no self-citation chain is invoked to forbid alternatives, so no circular step can be exhibited.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claims rest on the published resonant-orbit theory (Refs. [14-18], overlapping authorship) and on mission design choices (precision, cadence, arc length) that are not validated with shipped code or data. No new physical entities are introduced. The largest source of uncertainty is the arc-length modeling choice, which changes the forecast by orders of magnitude.

free parameters (5)
  • Normal-point precision = 10 cm (baseline); cm-level stated as possible
    Assumed data quality that directly sets the strain sensitivity; chosen as a conservative baseline, not derived.
  • Data cadence = 10 NPs per orbit per satellite
    Assumed tracking rate from the ILRS network; sensitivity scales with this number.
  • Observation duration = 10 years nominal, 30 years extended
    The resonant accumulation time is proportional to observation duration; 10 years is a mission design choice.
  • Arc length in POD = 7-day arcs (conservative) or 10-year single arc (optimistic)
    The paper's own Fig. 2 shows this choice changes sensitivity by orders of magnitude; the 10-year arc is called 'likely overly optimistic'.
  • Orbital elements = e=0.75, P=33.8h, i=75/50 deg, RAAN=0/220 deg
    Chosen design parameters to target the microhertz band and comply with re-entry requirements; not fitted to data.
axioms (4)
  • standard math Linearized TT-gauge equation δ¨r_i = 1/2 h¨_ij^TT r_j (Eq. 2)
    Standard GR linearized geodesic deviation, used for the GW effect on the orbit.
  • domain assumption Resonance condition P ≈ n/ω_gw produces a quadratic drift of the true anomaly (Refs. [14-18])
    The core detection mechanism is taken from prior work by overlapping authors; the paper states it 'qualitatively holds as long as the resonance conditions are satisfied' (Sec. 2.1).
  • domain assumption The local DM density ρ⊙ = 0.4 GeV/cm^3
    Standard value used in the ULDM reach (Sec. 3.2.A), not derived in this paper.
  • domain assumption SMBHB stochastic background extends from the PTA band into the μHz band (Sec. 3.1.A, Fig. 2 right)
    The astrophysical model is adopted from literature (e.g., Ref. [21]) to motivate the science case.

pith-pipeline@v1.3.0-alltime-deepseek · 23187 in / 9451 out tokens · 84369 ms · 2026-08-01T15:31:24.354470+00:00 · methodology

0 comments
read the original abstract

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band -- a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in {highly eccentric} Earth orbits ($e \gtrsim 0.7$, period $P \gtrsim 33$ h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the $\mu$Hz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of $GM_\oplus$ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.

Figures

Figures reproduced from arXiv: 2607.18390 by Adrien Bourgoin, Alberto Sesana, Albert Roura, Alessandro Di Marco, Alexander C. Jenkins, Alfonso Caldiero, Alice Paun, Alice Perego, Ana Caramete, Andrea Caputo, Angela Serrano, Angus Macdonald, Anja Schlicht, Antonio J. Iovino, Ariadna Farr\'es, Aur\'elien Hees, Bruno Bertrand, Carlos F. Sopuerta, Clare Burrage, Cl\'ement Courde, Crist\'obal Padilla, Daniel Serrano Lombillo, Dario Vetrano, David Lucchesi, Diego Blas, Elisa Todarello, Fco. Rogelio Palomo Pinto, Feliciana Sapio, F. Javier Atapuerca, Florentina-Crenguta Pislan, Florin Adrian Popescu, Florin-Ioan Constantin, Francesco Santoli, Gabriel Chiritoi, Giada Bargiacchi, Hanxi Wang, Ignasi Ribas, Ilia Musco, Jean-Paul Kneib, Joan Manel Casalta Escuer, Jorge Mart\'in Camalich, Jos\'e C. Rodr\'iguez, Josep J. Masdemont, Joshua N. Benabou, Joshua W. Foster, Julien Chab\'e, Justin Janquart, Krzysztof So\'snica, Laurentiu Caramete, Luca Porcelli, Malcolm Fairbairn, Marco Cinelli, Marco Lucente, Marco Reyes, Maria-Catalina Isfan, Mariano S\'anchez Nogales, Marta Goli, Massimo Bassan, Massimo Visco, Michael H\"afner, Miguel Vanvlasselaer, Miguel Zumalac\'arregui, Nanda Rea, Neil J. Cornish, Nicola Tamanini, Nicol\`o Burzill\`a, Pascal Rosenblatt, Rafael Rebolo, Roberto Campagnola, Roberto Peron, Rosa Mart\'inez Rubiella, Sebastian Ellis, S\'ebastien Le Maistre, Silvia Gasparotto, Simone Dell'Agnello, Sokratis Trifinopoulos, Soumen Roy, Toshimichi Otsubo, Ulrich Schreiber, Xiao Xue, Yann Gouttenoire.

Figure 1
Figure 1. Figure 1: The gravitational-wave landscape. Current facilities (dark grey) and planned or approved next-generation missions (light grey) leave the µHz band essentially uncovered. Astrometric missions [13] may offer complementary sensitivity, but do not reach astrophysically-motivated signals, and suffer from calibration issues that make robust analyses challenging. Guest makes a decisive step toward closing this gap… view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: Reach of guest for individual monochromatic GW sources. The “with arcs” case corresponds to a very conservative approach to data analysis, while the “no arc” case is related to a best-case scenario. The curves correspond to SNR = 1. Right panel: Possible stochastic GW sources probed by guest. Pulsar timing arrays (represented here by NANOGrav-15yr [4], light blue) provide strong evidence for a … view at source ↗
Figure 3
Figure 3. Figure 3: Sensitivity to monochromatic GWs as a function of sky location for one month of data, for each of the two guest spacecraft separately and for their combination. The colour code is such that darker means stronger bounds, while the global scale is not relevant. The single-spacecraft response is anisotropic; the joint response, and the natural drift of the orbital planes over the mission, restore near-uniform… view at source ↗
Figure 5
Figure 5. Figure 5: Upper panel: Guest distance reach for slowly evolving SMBHB sources. Colour indicates the binary frequency at the start of the mission; solid and dashed lines indicate conservative and optimistic data-analysis scenarios (7-day arcs and 10-year arcs, respectively). Lower panels: Guest distance reach for merging SMBHBs. The “with arcs” curve corresponds to the conservative data-analysis scenario; coloured cu… view at source ↗
Figure 6
Figure 6. Figure 6: Left panel: Guest reach for ULDM detection via coherent gravitational oscillations, in the (mDM, βρDM/ρ⊙) plane. β = 1 corresponds to the universal (unavoidable) gravitational coupling. Bounds from PTAs, Cassini, and expected LISA constraints are shown for comparison. The unshaded region is open parameter space. Right panel: Predicted strain from scalar and vector boson clouds around three nearby supermass… view at source ↗
Figure 7
Figure 7. Figure 7: PLI sensitivity curve of guest vs. the spectra for benchmark scenarios of PBHs. ∆ is the width of the initial overdensity [31]. Part or all of DM may be in the form of primordial black holes (PBH) [32]. In the standard formation scenario, PBHs arise from the collapse of large-amplitude curva￾ture perturbations at horizon re-entry, and the same per￾turbations unavoidably source a stochastic background of sc… view at source ↗
Figure 8
Figure 8. Figure 8: Existing constraints on a Yukawa fifth force (strength α, range λ) and the region opened by guest. The novelty of tracking orbits with much higher eccen￾tricity and longer periods than those of other satellites deployed for precise laser tracking (cf. the LARES and LAGEOS satellites, which are in circular orbits from 1450 to 5800 km altitude) opens new possible searches for fundamental forces sourced by th… view at source ↗
Figure 9
Figure 9. Figure 9: Existing constraints on the mass and coupling strength of ultra-light dark mat￾ter scalars with quadratic couplings to matter from existing experiments, and forecast con￾straints from measurements of GUEST perigee precession. A new scalar ϕ coupled quadratically to matter also induces scalar-mediated fifth forces on a test body with volume V and density ρ of the form: F⃗ 5 = −2πGβ Z V d 3x ρ ∇⃗ ϕ 2 , (6) w… view at source ↗
Figure 10
Figure 10. Figure 10: Estimated formal errors in GM⊕ obtained from simulations of LAGEOS-2 and GUEST orbits. The simulations do not include additional parameters to be explored in future work. The first term in the multipole expansion of the Earth’s potential is GM⊕, the standard gravitational parameter. This single num￾ber provides the dynamical scale for every Earth-bound orbit and enters every naviga￾tion solution, every sa… view at source ↗
Figure 11
Figure 11. Figure 11: Estimated satellite’s OCS versus altitude for the guest orbit (for the 70 cm sphere, factor 1.5 larger for 86 cm). guest addresses this issue through an innovative design based on two families of corner-cube reflectors mounted on the same sphere. • CCR1 (1 inch): optimised for the high velocity aberration µ ≈ 48 µrad encountered at perigee. The far-field diffraction pattern (FFDP) of these prisms peaks as… view at source ↗
Figure 12
Figure 12. Figure 12: Distribution of 1” and 2 ” CCRs in the 3:1 configuration. Protrusions for CCR2 shown. The distribution of the CCRs on the spheres has been op￾timized accounting for the following factors: (i) sufficient visibility; (ii) isotropy to provide constant visibility and minimize aspects such as thermal noise; (iii) small asym￾metry to determine the spinning properties of the S/Cs; and (iv) sub-cm accuracy in the… view at source ↗
Figure 13
Figure 13. Figure 13: SLR station performance at current and upgraded laser power levels. The upgrade provides the margin needed to track guest at apogee while maintaining millimetre-level normal-point precision. As compared to other geodesy satellites, the guest satellites orbit at altitudes well above 10000 km most of the time, and travel at speeds that decrease their visibility when orbiting closer to the stations near peri… view at source ↗
Figure 14
Figure 14. Figure 14: Geometric visibility of the GUEST-1 orbits from different ranging stations. The continuous colored line represents the GUEST-1 orbit (the color corresponding to its altitude). Note that the orbit ground tracks will change over the mission’s lifetime. The dashed areas represent the visibility areas for the different stations shown. They are classified as LLR (main stations are those with relations to peopl… view at source ↗

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Forward citations

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