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Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Fundamental Resolution Limits

T0 review · 2 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read A pulsar timing array is a diffraction-limited gravitational-wave observatory whose angular resolution is set by the gravitational-wave wavelength divided by pulsar distance, and whose Earth-term approximation is quantitatively justified fo

desk verdict Full response derivation and regime analysis are solid, but the headline 10^11 pulsar threshold double-counts shared measurements and is roughly four orders too high; the Earth-term conclusion still survives. read the letter →

arxiv 2607.19329 v1 pith:7FOSXLTD submitted 2026-07-21 astro-ph.HE gr-qc

S. A. Andrianov , S. M. Kopeikin This is my paper
classification astro-ph.HEgr-qc
keywords pulsartimingarraysgravitational-waveskymappingtensorsphericalharmonicsEarth-termapproximationangularresolutiondiffractionlimitstochasticbackgroundFisherinformationmatrix
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

Pulsar timing arrays (PTAs) are the only instruments sensitive to nanohertz gravitational waves, and current analyses keep only the Earth term of the response. This paper constructs the full Earth-plus-pulsar response in a tensor spherical-harmonic basis and derives closed-form response functions for a single Earth-pulsar baseline. It shows that a PTA is a diffraction-limited observatory: angular resolution is theta ~ lambda/L, with an exponential sensitivity cutoff at multipole l_cut ~ omega L. The same formalism, combined with Fisher-matrix and singular-value analysis, yields the paper's headline result: coherent pulsar-term information can improve full-sky GW mapping only for arrays of order 10^11 precisely timed pulsars. The net conclusion is that the Earth-term approximation adopted in contemporary PTA work is quantitatively justified for full-sky mapping.

What carries the argument

The key object is the multipole response function f_l(y), defined in Eq. (B57) as a linear combination of spherical Bessel functions j_{l-1}(y) and j_l(y) with y = omega L. Inserted into the closed-form baseline response R^G_lm = 2 pi Y_lm(p-hat) e^{-iy} (-i)^l f_l(y), it encodes all angular-sensitivity information: an Earth-term-dominated plateau with sensitivity falling as l^{-2}, an oscillatory pulsar-term regime between l ~ sqrt(y) and l ~ y, and an exponential cutoff at the Airy turning point l_cut ~ y. The whitened design matrix R-tilde is then inverted by singular-value decomposition; the SVD both regularizes the ill-conditioned inverse problem and provides the rank bound N_modes <= N

What would settle it

Build a simulated short-arm PTA with y = omega L in the range 3–13 and 500 pulsars, exactly as in Section 5, and compare the singular-value spectrum and reconstructed sky maps with and without the pulsar term. The paper predicts a clear rise in high-l singular values and recovery of modes up to l ~ 11 when the pulsar term is included (Figs. 4 and 8); if no such enhancement appears, the claimed pulsar-term extension of angular resolution—and the regime analysis behind it—is wrong.

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Extended reading notes

Core claim

The paper's central claim is that the full PTA response—Earth term plus pulsar term—can be written in closed form in a tensor spherical-harmonic basis, and that this closed form exposes a fundamental diffraction limit. For a monochromatic GW of angular frequency omega and a pulsar at distance L, the baseline response is R^G_lm = 2 pi Y_lm(p-hat) e^{-iy} (-i)^l f_l(y), where y = omega L and f_l(y) is a combination of spherical Bessel functions. The analysis of f_l(y) reveals four regimes: Earth-term domination at low multipoles, a transition near l ~ sqrt(y), pulsar-term domination with roughly constant sensitivity up to l ~ y, and an exponential cutoff beyond l_cut ~ omega L. The cutoff mean

Load-bearing premise

The load-bearing premise is the order-of-magnitude SNR scaling in Section 4.2—that an approximately isotropic PTA has singular values falling as l^{-2}, that per-mode SNR grows as sqrt(N_l) sigma_l, and that ten independent measurements per quadrupole mode is a sufficient anchor—so the quoted 10^11 threshold inherits these assumptions; a different normalization shifts the number by orders of magnitude, though the rank bound N_modes <= N_pulsars independently supports the qual

Editorial extensions

If this is right

  • A PTA's finest resolvable angular scale is set by the most distant pulsars in the array: theta ~ lambda/L, independent of the number of pulsars.
  • Multipoles above l_cut ~ omega L are exponentially suppressed and cannot be recovered even with arbitrarily high signal-to-noise.
  • The number of independently measurable GW-sky modes is bounded by the number of pulsars, so angular resolution also requires adequate sky sampling, not just long baselines.
  • For realistic Galactic millisecond-pulsar populations (around 10^5 objects), the Earth-term approximation is quantitatively justified for full-sky GW mapping.
  • Polarization leakage between + and x maps is intrinsic to the PTA response, because the curl response vanishes; it cannot be removed by better noise modeling or inversion.

Reading between the lines

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

  • The diffraction-limit relation suggests that increasing the GW frequency or discovering even a few very distant pulsars extends the accessible multipole range more efficiently than adding many nearby pulsars; the paper does not optimize this trade-off.
  • Although the 10^11 threshold applies to full-sky mapping, the same full-response formalism could be used for targeted continuous-wave localization, where pulsar-phase information may help with far smaller arrays—an application the paper explicitly leaves open.
  • The parity selection rules for the gradient-curl couplings in the stochastic-background likelihood imply that anisotropy measurements could in principle separate parity-even from parity-odd background components; the paper derives the rules but does not pursue this diagnostic.
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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

2 major / 6 minor

Summary. This paper develops a tensor-spherical-harmonic reformulation of the pulsar timing array (PTA) response that retains both Earth and pulsar terms. The key analytic results are the closed-form gradient response R^G_lm = 2π Y_lm(hat p) e^{-iy}(-i)^l f_l(y), the vanishing of the curl response, and an asymptotic classification of f_l(y) into four regimes separated by l_{1→2} ~ sqrt(y), l_{2→3} ~ 2 sqrt(y), and l_{cut} ~ y. The authors then formulate PTA sky reconstruction as a linear inverse problem, analyze conditioning via the Fisher information matrix and SVD, and illustrate the regime picture with long-arm and short-arm simulations. A central quantitative claim is that coherent pulsar-term information improves full-sky mapping only for PTAs with N_trans ~ 10^11 precisely timed pulsars, providing a quantitative justification of the Earth-term approximation. The formalism is also extended to anisotropic stochastic gravitational-wave backgrounds.

Significance. The analytic derivation in Appendices B–C is self-contained, internally consistent, and correctly reproduces the Gair et al. Earth-term limit. The four-regime picture and the diffraction-like cutoff l_cut ~ ωL are genuine contributions, and the numerical experiments qualitatively support the distinction between Earth-term-dominated and pulsar-term-sensitive regimes. The rank bound N_modes ≤ N_pulsars (Eq. 49) is rigorous and useful. However, the headline threshold N_trans ~ 10^11 is inflated by a mode-counting error in Eq. (68); under the paper's own scaling assumptions the corrected order-of-magnitude estimate is ~2.6×10^7. This is still many orders above the Galactic millisecond-pulsar population, so the qualitative conclusion that realistic PTAs cannot exploit pulsar-term information survives, but the central number and the claim that Eq. (68) is a 'conservative lower bound' must be revised.

major comments (2)
  1. [§4.2, Eqs. (62)–(68)] The headline N_trans ~ 10^11 is obtained by summing (2l'+1) per-mode measurement requirements, but in the same isotropic limit used for Eq. (62) the design-matrix columns are orthogonal (Eq. 57), so every pulsar measurement is shared by all modes. The correct scaling is N_puls ≥ N_lmin (l1→2 / lmin)^4, not the sum in Eq. (67). With the authors' fiducials (N_lmin=10, lmin=2, l1→2=80) this gives ~2.6×10^7, about four orders below Eq. (68). The text's caveat that 'the same PTA measurements contribute simultaneously to multiple spherical-harmonic modes' directly contradicts the use of Eq. (67) as a lower bound. The qualitative conclusion survives, but the abstract's numerical claim is not established.
  2. [§4.2, Eqs. (62)–(63)] Even after correcting the mode-counting, N_trans is not a rigorous bound. Equation (62) assumes an idealized isotropic singular-value spectrum σ_l ∝ f_l(y) ∝ l^{-2}, and N_lmin=10 is an ad hoc normalization; both are order-of-magnitude assumptions. The rank bound (49) cannot fix the threshold because N_modes at l1→2=80 is only ~6.4×10^3, far below the SNR-driven requirement. The paper should present N_trans as a fiducial scaling estimate with a plausible range, and should avoid the phrase 'conservative lower bound' in Eq. (68) and the discussion.
minor comments (6)
  1. [Eq. (69)] The phrase 'reduces to a quantity proportional to the analytical sensitivity function, 2π|f_l(y)|,z from Eq. (16)' contains a stray 'z' and should read '2π|f_l(y)| from Eq. (16)'.
  2. [§4.3 title] The heading 'The Uneven Sky Sensitivity Distribution Consequence' is awkward; 'Consequences of Nonuniform Sky Coverage' would be clearer.
  3. [Figure 2 caption] The caption says 'Mean MeerKAT sensitivity,' but the text discusses scatter of individual m-modes about the ideal f_l(y). Please clarify what quantity is plotted and why it is called a 'mean.'
  4. [Eq. (44)] The angular resolution expression θ = 180°/l3→4 mixes degrees with the dimensionless multipole; writing θ = π/l_cut and then converting numerically would be cleaner.
  5. [References] The author name 'Cury lo et al. 2026' should be typeset with the proper diacritic (Curyło) if the journal style permits Unicode, or otherwise with a clear ASCII equivalent.
  6. [Abstract and §7] After correcting Eq. (68), the abstract and Discussion should be updated consistently so that the 'of order 10^11' statement is not repeated as a central quantitative claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the closed-form response is derived, the N_trans estimate is an explicitly labeled scaling calculation, and the central claims do not reduce to their inputs.

full rationale

No circular step is present. The central derivation chain is: (i) the plane-wave timing-residual integral, Eq. (6), is transformed into tensor-harmonic response functions, Eqs. (13)-(15); (ii) the closed-form gradient response, Eq. (16), is derived in Appendix B from the Rayleigh expansion, Wigner-D rotations, and spherical-Bessel identities, with the auxiliary function f_l(y) given explicitly by Eq. (B57); (iii) the four sensitivity regimes and the cutoff l_cut ~ omega*L follow from the asymptotic analysis of spherical Bessel functions in Appendix C; (iv) the rank bound N_modes <= N_pulsars, Eq. (49), is an algebraic identity; and (v) the headline N_trans ~ 10^11, Eq. (68), is an order-of-magnitude scaling estimate built on stated fiducial assumptions. No parameter is fitted to data and then reported as a prediction: the paper explicitly says 'As a fiducial reference, we adopt N_lmin = 10' and labels Eq. (67) an order-of-magnitude relation, noting that 'the same PTA measurements contribute simultaneously to multiple spherical-harmonic modes.' That caveat means the 10^11 threshold is sensitive to normalization and mode-sharing assumptions, which is a numerical fragility rather than a circular reduction. The only self-citations (Kopeikin 1997, 1999) concern binary-pulsar orbital perturbations and are not load-bearing for the sky-mapping derivation. The tensor-harmonic framework is grounded in external prior work (Gair et al. 2014, 2015); where the text says 'Following ... one finds' for Eq. (16), Appendix B supplies the independent derivation. No uniqueness theorem or ansatz is imported from the authors' prior work to force the conclusion.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The central derivation rests on standard GR and Bessel-function asymptotics plus two hand-chosen quantities: the asymptotic tolerance epsilon=50% and the fiducial normalization N_lmin=10. The latter controls the numerical value of N_trans, so the headline '10^11' is not parameter-free; the qualitative conclusion is robust to reasonable changes.

free parameters (2)
  • epsilon (asymptotic tolerance) = 0.50 (50%)
    Chosen in Section 3.2/Appendix C to define the transition multipoles l1→2 and l2→3; it affects Eqs. (37)-(38) and propagates into N_trans through l1→2. Not fitted to data, but arbitrary.
  • N_lmin fiducial normalization = 10 independent measurements at l=2
    Adopted in Section 4.2 before Eq. (68) to anchor the SNR scaling; N_trans ~ 10^11 scales linearly with this choice.
assumptions (7)
  • domain assumption Linearized GR/TT-gauge plane-wave expansion of the GW field (Eq. 2)
    Standard weak-field approximation; the PTA timing-residual response in Eq. (3) is derived in this setting.
  • domain assumption Gaussian noise model with known covariance (Eq. 19)
    Used to define the likelihood and Fisher matrix; real PTA noise includes red processes, but the simulations restrict to white noise.
  • domain assumption Pulsar distances known exactly for coherent pulsar-term phase (ωΔL<<1)
    Stated in Section 5; this is an idealized coherence limit acknowledged by the authors.
  • ad hoc to paper Singular-value spectrum of an isotropic PTA follows σ_l ∝ f_l(y) ∝ l^{-2} (Eq. 62)
    Assumed for the N_trans scaling estimate; not derived from the design matrix for finite nonuniform arrays.
  • ad hoc to paper N_lmin=10 as the fiducial SNR normalization
    Sets the reference SNR for the scaling estimate and directly drives the numerical value of N_trans in Eq. (68).
  • standard math Spherical Bessel, Debye, and Airy asymptotics (DLMF 10.19, 10.20)
    Used in Appendix C to determine the four sensitivity regimes and the cutoff l_cut≃ωL.
  • standard math Tensor-spherical-harmonic orthonormality and l≥2 for TT tensor fields
    Standard CMB-polarization-style decomposition; curl response vanishes because X_l0=0 in the computational frame.

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Pith. "Pith review of Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Fundamental Resolution Limits." pith.science (2026). https://pith.science/paper/7FOSXLTD

@misc{pith2026260719329,
  author       = {Pith},
  title        = {Pith review of: Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Fundamental Resolution Limits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7FOSXLTD}},
  note         = {Machine review of arXiv:2607.19329}
}
abstract

Pulsar timing arrays (PTAs) are the only means to observe nanohertz gravitational waves (GWs). While current analyses primarily exploit the Earth term, the full detector response encodes additional directional information in the pulsar terms. We develop a GW sky-mapping framework based on the complete Earth--pulsar response and a tensor spherical harmonic decomposition of the GW field. This yields closed-form response functions for an elementary baseline and casts PTA sky reconstruction as a linear inverse problem. We show that a PTA behaves as a diffraction-limited GW observatory whose angular sensitivity is governed by the dimensionless parameter $\omega L$, where $\omega$ is the GW angular frequency and $L$ is the pulsar distance. The detector response exhibits four distinct regimes: an Earth-term dominated regime, a transition regime, a pulsar-term-dominated regime, and an exponential sensitivity cutoff at $l_{cut}\simeq\omega L$. This cutoff defines the fundamental angular resolution limit of PTA sky maps. Using Fisher-information and singular-value analyses, we show that the achievable angular resolution is constrained not only by the intrinsic detector response but also by the finite number of pulsars, their sky distribution, and timing noise. In particular, we find that coherent pulsar-term information can improve full-sky gravitational-wave mapping only for PTAs containing of order $N_{trans}\sim10^{11}$ precisely timed pulsars. This result demonstrates that, although the transition to a pulsar-term-sensitive regime exists mathematically, it is inaccessible for realistic PTAs and therefore provides a quantitative justification for the Earth-term approximation adopted in contemporary observations. Finally, we extend the formalism to stochastic GW backgrounds, establishing a unified mathematical framework for PTA sky mapping and anisotropy studies.

Figures

Figures reproduced from arXiv: 2607.19329 by the authors.

Figure 1
Figure 1. Point-spread function (PSF) of an ideal pulsar timing array for a unit-ampli￾tude, plus-polarized gravitational-wave point source located at (θ, ϕ) = (90◦ , 180◦ ). The reconstruction is truncated at lmax = 10. The left and right panels show the reconstructed plus- and cross-polarization maps, respectively. The detector’s curl-mode blindness and the finite multipole cutoff produce the characteristic diffraction patt… view at source ↗
Figure 2
Figure 2. Deviation of individual m modes from the ideal sensitivity function fl(y) for the MeerKAT PTA pulsar distribution. Vertical lines separate successive multipole orders l. In an isotropic PTA all modes with the same l would have identical sensitivity. The observed scatter therefore quantifies the loss of rotational symmetry introduced by the finite and nonuniform pulsar distribution. To quantify this effect, we define… view at source ↗
Figure 3
Figure 3. Point-spread function for the MeerKAT PTA. The GW source parameters are identical to those of [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Singular-value spectra of the PTA design matrix for four mock arrays. “Long” and “Short” refer to realistic and reduced pulsar-distance distributions, respectively, while “ET” and “PT” denote the Earth-term approximation and the full Earth–pulsar response. Vertical lin…
Figure 5
Figure 5. Figure 5: Sky reconstruction for a realistic PTA using the Earth-term approximation. Upper panels show the reconstructed plus- and cross-polarization gravitational-wave maps as well as the ideal maps constructed directly from Eq. (11). Lower panel compares the magnitudes of the …
Figure 6
Figure 6. Figure 6: Sky reconstruction for a realistic long-arm PTA using the full Earth–pulsar response. Upper panels display the reconstructed polarization maps as well as the ideal maps constructed directly from Eq. (11). The lower panel compares recovered and injected harmonic coeffic…
Figure 7
Figure 7. Figure 7: Sky reconstruction for a short-arm PTA in the Earth-term approximation. Upper panels show the reconstructed polarization maps as well as the ideal maps con￾structed directly from Eq. (11). The lower panel compares recovered and injected harmonic coefficients. Despite t…
Figure 8
Figure 8. Figure 8: Sky reconstruction in the pulsar-term-sensitive regime for the short-arm PTA in the PT regime. Upper panels show the reconstructed polarization maps as well as the ideal maps constructed directly from Eq. (11). The lower panel compares injected and recovered harmonic c…
Figure 9
Figure 9. Figure 9: Absolute value of the sensitivity function fl(y), with y = ωL, shown as a func￾tion of multipole number l. Four asymptotic regimes can be identified: (I) an Earth-term– dominated regime at low multipoles; (II) a transition region; (III) a pulsar-term-dominated regime a…

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Works this paper leans on

178 extracted references · 23 canonical work pages

  1. [1]

    Abbott, B. P. and Abbott, R. and Abbott, T. D. and Acernese, F. and Ackley, K. and Adams, C. and Adams, T. and Addesso, P. and Adhikari, R. X. and Adya, V. B. and Affeldt, C. and Afrough, M. and Agarwal, B. and Agathos, M. and Agatsuma, K. and Aggarwal, N. and Aguiar, O. D. and Aiello, L. and Ain, A. and Ajith, P. and Allen, B. and Allen, G. and Allocca, ...

  2. [2]

    and Abe, H

    Abbott, R. and Abe, H. and Acernese, F. and Ackley, K. and Adhikari, N. and Adhikari, R. X. and Adkins, V. K. and Adya, V. B. and Affeldt, C. and Agarwal, D. and Agathos, M. and Agatsuma, K. and Aggarwal, N. and Aguiar, O. D. and Aiello, L. and Ain, A. and Ajith, P. and Akutsu, T. and Albanesi, S. and Alfaidi, R. A. and Allocca, A. and Altin, P. A. and Am...

  3. [3]

    , year = 1965, month = jan, publisher =

    Abramowitz, Milton and Stegun, Irene A. , year = 1965, month = jan, publisher =. Handbook of

    1965

  4. [4]

    and Alshourbagy, M

    Acernese, F. and Alshourbagy, M. and Amico, P. and Antonucci, F. and Aoudia, S. and Astone, P. and Avino, S. and Baggio, L. and Barone, F. and Barsotti, L. and Barsuglia, M. and Bauer, T. S. and Bigotta, S. and Birindelli, S. and Bizouard, M. and Boccara, C. and Bondu, F. and Bosi, L. and Braccini, S. and Bradaschia, C. and Brillet, A. and Brisson, V. and...

  5. [5]

    and Arzoumanian, Zaven and Baier, Jeremy G

    Agarwal, Nikita and Agazie, Gabriella and Anumarlapudi, Akash and Archibald, Anne M. and Arzoumanian, Zaven and Baier, Jeremy G. and Baker, Paul T. and Bécsy, Bence and Blecha, Laura and Brazier, Adam and Brook, Paul R. and. The. The Astrophysical Journal , volume =. doi:10.3847/2041-8213/ae3719 , url =

    doi:10.3847/2041-8213/ae3719

  6. [6]

    and Arzoumanian, Zaven and Baker, Paul T

    Agazie, Gabriella and Anumarlapudi, Akash and Archibald, Anne M. and Arzoumanian, Zaven and Baker, Paul T. and Bécsy, Bence and Blecha, Laura and Brazier, Adam and Brook, Paul R. and. The. The Astrophysical Journal , volume =. doi:10.3847/2041-8213/acdac6 , url =

    doi:10.3847/2041-8213/acdac6

  7. [7]

    and Arzoumanian, Zaven and Baker, Paul T

    Agazie, Gabriella and Anumarlapudi, Akash and Archibald, Anne M. and Arzoumanian, Zaven and Baker, Paul T. and Bécsy, Bence and Blecha, Laura and Brazier, Adam and Brook, Paul R. and. The. The Astrophysical Journal Letters , volume =. doi:10.3847/2041-8213/acda88 , url =

    doi:10.3847/2041-8213/acda88

  8. [8]

    and Ando, M

    Akutsu, T. and Ando, M. and Arai, K. and Arai, Y. and Araki, S. and Araya, A. and Aritomi, N. and Asada, H. and Aso, Y. and Atsuta, S. and Awai, K. and Bae, S. and Baiotti, L. and Barton, M. A. and Cannon, K. and Capocasa, E. and Chen, C.-S. and Chiu, T.-W. and Cho, K. and Chu, Y.-K. and Craig, K. and Creus, W. and Doi, K. and Eda, K. and Enomoto, Y. and ...

Show all 178 references
  1. [9]

    , year = 1999, month = mar, journal =

    Allen, Bruce and Romano, Joseph D. , year = 1999, month = mar, journal =. Detecting a Stochastic Background of Gravitational Radiation:. doi:10.1103/PhysRevD.59.102001 , url =

    1999 doi

  2. [10]

    Variance of the

    Allen, Bruce , year = 2023, month = feb, journal =. Variance of the. doi:10.1103/PhysRevD.107.043018 , url =

    2023 doi

  3. [11]

    , year = 2023, month = aug, journal =

    Allen, Bruce and Romano, Joseph D. , year = 2023, month = aug, journal =. Hellings and. doi:10.1103/PhysRevD.108.043026 , url =

    2023 doi

  4. [12]

    Physical Review D , volume =

    Pulsar Timing Array Harmonic Analysis and Source Angular Correlations , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.110.043043 , url =

    doi

  5. [13]

    , year = 2025, month = jan, journal =

    Allen, Bruce and Romano, Joseph D. , year = 2025, month = jan, journal =. Optimal. doi:10.1103/PhysRevLett.134.031401 , url =

    2025 doi

  6. [14]

    Обработка Наблюдений Пульсарного Тайминга , author =

  7. [15]

    Andrianov, S. A. , year = 2023, pages =

    2023

  8. [16]

    Andrianov, S. A. , year = 2024, pages =. doi:10.15826/B978-5-7996-3848-1.10 , url =

    2024 doi

  9. [17]

    Andrianov, S. A. , year = 2025, pages =. doi:10.15826/B978-5-7996-3986-0.12 , url =

    2025 doi

  10. [18]

    Andrianov, S. A. and Potapov, V. A. and Tyul'bashev, S. A. and Logvinenko, S. V. and Oreshko, V. V. , year = 2025, month = nov, journal =. The. doi:10.1134/S1063772925702294 , url =

    2025 doi

  11. [19]

    Andrianov, S. A. and Potapov, V. A. and Tyul'bashev, S. A. , year = 2025, month = nov, journal =. The. doi:10.1134/S1063772925702300 , url =

    2025 doi

  12. [20]

    Andrianov, S. A. , year = 2026, pages =

    2026

  13. [21]

    Physical Review D , volume =

    Optimal Strategies for Gravitational Wave Stochastic Background Searches in Pulsar Timing Data , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.79.084030 , url =

    doi

  14. [22]

    The Astrophysical Journal , volume =

    The. The Astrophysical Journal , volume =. doi:10.3847/1538-4357/ac7c74 , url =

    doi

  15. [23]

    doi:10.5281/zenodo.17081336 , url =

    The Spherical Package , author =. doi:10.5281/zenodo.17081336 , url =

    doi

  16. [24]

    Detection of Gravitational Waves from the

    Caprini, Chiara and Durrer, Ruth and Siemens, Xavier , year = 2010, month = sep, journal =. Detection of Gravitational Waves from the. doi:10.1103/PhysRevD.82.063511 , url =

    2010 doi

  17. [25]

    Chen, Siyuan and Xu, Heng and Guo, Yanjun and Wang, Bojun and Caballero, R. Nicolas and Jiang, Jinchen and Xu, Jiangwei and Xue, Zihan and Lee, Kejia and Yuan, Jianping and Xu, Yonghua and Wang, Jingbo and Hao, Longfei and Luo, Jintao and Han, Jinlin and Jiang, Peng and Shen, ...

    2025 doi

  18. [26]

    , year = 2010, month = aug, publisher =

    Corbin, Vincent and Cornish, Neil J. , year = 2010, month = aug, publisher =. Pulsar. doi:10.48550/arXiv.1008.1782 , url =

    2010 doi arXiv

  19. [27]

    Cornish, Neil J. and. Mapping the Nano-. doi:10.48550/arXiv.1406.4511 , url =

    doi arXiv

  20. [28]

    doi:10.48550/arXiv.2604.19073 , url =

    A Comprehensive Framework for Phase-Coherent Mapping of the Gravitational-Wave Sky with Pulsar Timing Arrays , author =. doi:10.48550/arXiv.2604.19073 , url =

    doi arXiv

  21. [29]

    and Deruelle, N

    Damour, T. and Deruelle, N. , year = 1985, month = jan, journal =. General Relativistic Celestial Mechanics of Binary Systems

    1985

  22. [30]

    and Deruelle, N

    Damour, T. and Deruelle, N. , year = 1986, month = jan, journal =. General Relativistic Celestial Mechanics of Binary Systems

    1986

  23. [31]

    doi:10.1088/0264-9381/20/10/301 , url =

    Danzmann, Karsten and Rüdiger, Albrecht , year = 2003, month = may, journal =. doi:10.1088/0264-9381/20/10/301 , url =

    2003 doi

  24. [32]

    Davis, M. M. and Taylor, J. H. and Weisberg, J. M. and Backer, D. C. , year = 1985, month = jun, journal =. High-Precision Timing Observations of the Millisecond Pulsar. doi:10.1038/315547a0 , url =

    1985 doi

  25. [33]

    IEEE Transactions on Antennas and Propagation , volume =

    Antenna Synthesis and Solution of Inverse Problems by Regularization Methods , author =. IEEE Transactions on Antennas and Propagation , volume =. doi:10.1109/TAP.1972.1140197 , url =

    1972

  26. [34]

    The Astrophysical Journal , volume =

    Pulsar Timing Measurements and the Search for Gravitational Waves , author =. The Astrophysical Journal , volume =. doi:10.1086/157593 , url =

    doi

  27. [35]

    Dirac, Paul Adrien Maurice , year = 1975, publisher =. General

    1975

  28. [36]

    , year = 2002, month = jul, journal =

    Dong, Shi-hai and Lemus, R. , year = 2002, month = jul, journal =. The Overlap Integral of Three Associated. doi:10.1016/S0893-9659(02)80004-0 , url =

    2002 doi

  29. [37]

    Doroshenko, O. V. and Kopeikin, S. M. , year = 1990, month = oct, journal =. High

    1990

  30. [39]

    Näherungsweise

    Einstein, Albert , year = 1916, month = jan, journal =. Näherungsweise

    1916

  31. [40]

    Einstein, Albert , year = 1918, month = jan, journal =. Über

    1918

  32. [41]

    Ellis, J. A. , year = 2013, month = nov, journal =. A. doi:10.1088/0264-9381/30/22/224004 , url =

    2013 doi

  33. [42]

    , title =

    Ellis, Justin A. , title =. 2014 , month = aug, advisor =

    2014

  34. [43]

    and Vallisneri, Michele and Taylor, Stephen R

    Ellis, Justin A. and Vallisneri, Michele and Taylor, Stephen R. and Baker, Paul T. , title =. 2020 , month = sep, publisher =. doi:10.5281/zenodo.4059815 , url =

    2020 doi

  35. [44]

    Astronomy and Astrophysics , volume =

    The Second Data Release from the. Astronomy and Astrophysics , volume =. doi:10.1051/0004-6361/202346844 , url =

    doi

  36. [45]

    Astronomy and Astrophysics , volume =

    The Second Data Release from the. Astronomy and Astrophysics , volume =. doi:10.1051/0004-6361/202346842 , url =

    doi

  37. [46]

    Estabrook, F. B. and Wahlquist, H. D. , year = 1975, month = oct, journal =. Response of. doi:10.1007/BF00762449 , url =

    1975 doi

  38. [47]

    Foster, R. S. and Backer, D. C. , year = 1990, month = sep, journal =. Constructing a. doi:10.1086/169195 , url =

    1990 doi

  39. [48]

    and Taylor, Stephen and Mingarelli, Chiara M

    Gair, Jonathan and Romano, Joseph D. and Taylor, Stephen and Mingarelli, Chiara M. F. , year = 2014, month = oct, journal =. Mapping Gravitational-Wave Backgrounds Using Methods from. doi:10.1103/PhysRevD.90.082001 , url =

    2014 doi

  40. [49]

    Physical Review D , volume =

    Mapping Gravitational-Wave Backgrounds in Modified Theories of Gravity Using Pulsar Timing Arrays , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.92.102003 , url =. arXiv , keywords =:1506.08668 , primaryclass =

    arXiv

  41. [50]

    Table of Integrals, Series, and Products , author =

  42. [51]

    Soviet Journal of Experimental and Theoretical Physics Letters , volume =

    Primordial Gravitons and Possibility of Their Observation , author =. Soviet Journal of Experimental and Theoretical Physics Letters , volume =

  43. [52]

    and Thrane, Eric and Champion, David J

    Grunthal, Kathrin and Nathan, Rowina S. and Thrane, Eric and Champion, David J. and Miles, Matthew T. and Shannon, Ryan M. and Kulkarni, Atharva D. and Abbate, Federico and Buchner, Sarah and Cameron, Andrew D. and Geyer, Marisa and Gitika, Pratyasha and Keith, Michael J. and ...

    2024 arXiv

  44. [53]

    and Millman, K

    Harris, Charles R. and Millman, K. Jarrod and. Array Programming with. Nature , volume =. doi:10.1038/s41586-020-2649-2 , url =

    doi

  45. [54]

    , author =

    Upper Limits on the Isotropic Gravitational Radiation Background from Pulsar Timing Analysis. , author =. The Astrophysical Journal , volume =. doi:10.1086/183954 , url =

    doi

  46. [55]

    Hobbs, G. B. , url =

  47. [56]

    Hobbs, G. B. and Edwards, R. T. and Manchester, R. N. , year = 2006, month = jun, journal =. doi:10.1111/j.1365-2966.2006.10302.x , url =

    2006

  48. [57]

    and Archibald, A

    Hobbs, G. and Archibald, A. and Arzoumanian, Z. and Backer, D. and Bailes, M. and Bhat, N. D. R. and Burgay, M. and. The. Classical and Quantum Gravity , volume =. doi:10.1088/0264-9381/27/8/084013 , url =

    doi

  49. [58]

    Hobbs, G. B. and Edwards, R. T. , url =

  50. [59]

    Högbom, J. A. , year = 1974, month = jun, journal =. Aperture

    1974

  51. [60]

    , author =

    Discovery of a Pulsar in a Binary System. , author =. The Astrophysical Journal , volume =. doi:10.1086/181708 , url =

    doi

  52. [61]

    , year = 2007, month = jan, journal =

    Hunter, John D. , year = 2007, month = jan, journal =. Matplotlib:. doi:10.1109/MCSE.2007.55 , url =

    2007 doi

  53. [62]

    , year = 1918, journal =

    Isserlis, L. , year = 1918, journal =. On a. doi:10.2307/2331932 , url =. 2331932 , eprinttype =

    1918 doi

  54. [63]

    and Finn, L

    Jenet, F. and Finn, L. S. and Lazio, J. and Lommen, A. and McLaughlin, M. and Stairs, I. and Stinebring, D. and Verbiest, J. and Archibald, A. and Arzoumanian, Z. and Backer, D. and Cordes, J. and Demorest, P. and Ferdman, R. and Freire, P. and Gonzalez, M. and Kaspi, V. and K...

    2009 doi arXiv

  55. [64]

    and Romano, Joseph D

    Jenet, Fredrick A. and Romano, Joseph D. , year = 2015, month = jul, journal =. Understanding the Gravitational-Wave. doi:10.1119/1.4916358 , url =

    2015 doi

  56. [65]

    and Meyers, Patrick M

    Johnson, Aaron D. and Meyers, Patrick M. and Baker, Paul T. and Cornish, Neil J. and Hazboun, Jeffrey S. and Littenberg, Tyson B. and Romano, Joseph D. and Taylor, Stephen R. and Vallisneri, Michele and Vigeland, Sarah J. and Olum, Ken D. and Siemens, Xavier and Ellis, Justin ...

    doi

  57. [66]

    Physical Review D , volume =

    Statistics of Cosmic Microwave Background Polarization , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.55.7368 , url =

    doi

  58. [67]

    Kaspi, V. M. and Taylor, J. H. and Ryba, M. F. , year = 1994, month = jun, journal =. High-. doi:10.1086/174280 , url =

    1994 doi

  59. [68]

    Journal of the American Statistical Association , volume =

    Bayes Factors , author =. Journal of the American Statistical Association , volume =. doi:10.1080/01621459.1995.10476572 , url =. https://doi.org/10.1080/01621459.1995.10476572 , pages =

    1995

  60. [69]

    Kopeikin, S. M. , year = 1989, month = dec, journal =. Asymptotic

    1989

  61. [70]

    Костина, М. В. , file =. Лекции

  62. [71]

    and Stairs, I

    Kramer, M. and Stairs, I. H. and Manchester, R. N. and Wex, N. and Deller, A. T. and Coles, W. A. and Ali, M. and Burgay, M. and Camilo, F. and Cognard, I. and Damour, T. and Desvignes, G. and Ferdman, R. D. and Freire, P. C. C. and Grondin, S. and Guillemot, L. and Hobbs, G. ...

    2021

  63. [72]

    Ландау, Л. Д. and Лифшиц, Е. М. , year = 2003, url =

    2003

  64. [73]

    , year = 2009, month = jan, pages =

    Lazio, J. , year = 2009, month = jan, pages =. The. Panoramic. doi:10.22323/1.089.0058 , url =

    2009 doi

  65. [74]

    and Hobson, M

    Lentati, Lindley and Alexander, P. and Hobson, M. P. and Taylor, S. and Gair, J. and Balan, S. T. and. Hyper-Efficient Model-Independent. Physical Review D , volume =. doi:10.1103/PhysRevD.87.104021 , url =

    doi

  66. [75]

    Abbott, B. P. and others , collaboration =. Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters , volume =. 2016 , doi =

    2016

  67. [76]

    Handbook of Pulsar Astronomy , author =

  68. [77]

    , year = 2008, month = dec, journal =

    Lorimer, Duncan R. , year = 2008, month = dec, journal =. Binary and. doi:10.12942/lrr-2008-8 , url =

    2008 doi

  69. [78]

    , year = 2013, month = mar, volume =

    Lorimer, Duncan R. , year = 2013, month = mar, volume =. The. Neutron. doi:10.1017/S1743921312023769 , url =

    2013 doi

  70. [79]

    Manchester, R. N. , year = 2008, month = feb, volume =. The. 40. doi:10.1063/1.2900303 , url =

    2008 doi

  71. [80]

    and Shannon, Ryan M

    Miles, Matthew T. and Shannon, Ryan M. and Reardon, Daniel J. and Bailes, Matthew and Champion, David J. and Geyer, Marisa and Gitika, Pratyasha and Grunthal, Kathrin and Keith, Michael J. and Kramer, Michael and Kulkarni, Atharva D. and Nathan, Rowina S. and Parthasarathy, Ad...

    2025

  72. [81]

    Physical Review D , volume =

    Characterizing Gravitational Wave Stochastic Background Anisotropy with Pulsar Timing Arrays , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.88.062005 , url =

    doi

  73. [82]

    Physical Review D , volume =

    Effect of Small Interpulsar Distances in Stochastic Gravitational Wave Background Searches with Pulsar Timing Arrays , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.90.062011 , url =

    doi

  74. [83]

    and Pearson, E

    Neyman, J. and Pearson, E. S. , year = 1933, journal =. On the. 91247 , eprinttype =

    1933

  75. [84]

    Physical Review D , volume =

    Gravitational-Wave Stochastic Background from Kinks and Cusps on Cosmic Strings , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.81.104028 , url =

    doi

  76. [85]

    Potapov, V. A. and Andrianov, S. A. , year = 2023, month = oct, journal =. Testing the. doi:10.31857/S0320010823100066 , url =

    2023 doi

  77. [86]

    and Zic, Andrew and Shannon, Ryan M

    Reardon, Daniel J. and Zic, Andrew and Shannon, Ryan M. and Hobbs, George B. and Bailes, Matthew and Di Marco, Valentina and Kapur, Agastya and Rogers, Axl F. and Thrane, Eric and Askew, Jacob and Bhat, N. D. Ramesh and Cameron, Andrew and Curyło, Małgorzata and Coles, William...

    2023

  78. [87]

    and Cornish,

    Romano, Joseph D. and Cornish,. Detection Methods for Stochastic Gravitational-Wave Backgrounds: A Unified Treatment , shorttitle =. Living Reviews in Relativity , volume =. doi:10.1007/s41114-017-0004-1 , url =

    doi

  79. [88]

    Лекции Python , author =

  80. [89]

    Савченко, С. С. , file =. Лекции

  81. [90]

    Обработка Астрономических Изображений , author =

  82. [91]

    Soviet Astronomy , volume =

    Opportunities for Detecting Ultralong Gravitational Waves , author =. Soviet Astronomy , volume =

  83. [92]

    doi:10.48550/arXiv.2404.11173 , url =

    A Simple Derivation of the Integrals of Products of. doi:10.48550/arXiv.2404.11173 , url =. arXiv , keywords =:2404.11173 , primaryclass =

    doi arXiv

  84. [93]

    and Pol, Nihan and Laal, Nima and Charisi, Maria and Ma, Chung-Pei , year = 2025, month = oct, publisher =

    Schult, Levi and Petrov, Polina and Taylor, Stephen R. and Pol, Nihan and Laal, Nima and Charisi, Maria and Ma, Chung-Pei , year = 2025, month = oct, publisher =. Expectations for the First Supermassive Black-Hole Binary Resolved by. doi:10.48550/arXiv.2510.01317 , url =

    2025 doi arXiv

  85. [94]

    and Vecchio, A

    Sesana, A. and Vecchio, A. and Colacino, C. N. , year = 2008, month = oct, journal =. The Stochastic Gravitational-Wave Background from Massive Black Hole Binary Systems: Implications for Observations with. doi:10.1111/j.1365-2966.2008.13682.x , url =

    2008

  86. [95]

    Gravitational Waves and Pulsar Timing: Stochastic Background, Individual Sources and Parameter Estimation , shorttitle =

    Sesana, A and Vecchio, A , year = 2010, month = apr, journal =. Gravitational Waves and Pulsar Timing: Stochastic Background, Individual Sources and Parameter Estimation , shorttitle =. doi:10.1088/0264-9381/27/8/084016 , url =

    2010 doi

  87. [96]

    Шнейвайс, А. Б. , file =. Лекции

  88. [97]

    Smirnova, T. V. and Zhou, D. J. and Kitaeva, M. A. and Andrianov, S. A. and Wang, C. and Wang, P. F. and Han, J. L. and Tyul'bashev, S. A. , year = 2025, month = nov, publisher =. A Nearby Pulsar. doi:10.48550/arXiv.2511.14191 , url =

    2025 doi

  89. [98]

    and Bailes, M

    Spiewak, R. and Bailes, M. and Miles, M. T. and Parthasarathy, A. and Reardon, D. J. and Shamohammadi, M. and Shannon, R. M. and Bhat, N. D. R. and Buchner, S. and Cameron, A. D. and Camilo, F. and Geyer, M. and Johnston, S. and Karastergiou, A. and Keith, M. and Kramer, M. an...

    2022 doi

  90. [99]

    Stappers, B. W. and Kramer, M. and Lyne, A. G. and D'Amico, N. and Jessner, A. , year = 2006, month = dec, journal =. The. doi:10.1088/1009-9271/6/S2/56 , url =

    2006 doi

  91. [100]

    ZhETF Pisma Redaktsiiu , volume =

    Spectrum of Relict Gravitational Radiation and the Early State of the Universe , author =. ZhETF Pisma Redaktsiiu , volume =

  92. [101]

    and Rana, Prerna and Singha, Jaikhomba and Krishnakumar, M

    Tarafdar, Pratik and Nobleson, K. and Rana, Prerna and Singha, Jaikhomba and Krishnakumar, M. A. and Joshi, Bhal Chandra and Paladi, Avinash Kumar and Kolhe, Neel and Batra, Neelam Dhanda and Agarwal, Nikita and Bathula, Adarsh and Dandapat, Subhajit and Desai, Shantanu and De...

    2022

  93. [102]

    Тараканов, П. А. , file =. Введение в

  94. [103]

    Тараканов, П. А. , langid =

  95. [104]

    Тараканов, П. А. , file =. Лекции

  96. [105]

    Taylor, J. H. and Weisberg, J. M. , year = 1982, month = feb, journal =. A New Test of General Relativity -. doi:10.1086/159690 , url =

    1982 doi

  97. [106]

    Physical Review D , volume =

    Searching for Anisotropic Gravitational-Wave Backgrounds Using Pulsar Timing Arrays , author =. Physical Review D , volume =. doi:10.1103/PhysRevD.88.084001 , url =

    doi

  98. [107]

    , year = 2021, month = may, publisher =

    Taylor, Stephen R. , year = 2021, month = may, publisher =. The. doi:10.48550/arXiv.2105.13270 , url =

    2021 doi arXiv

  99. [108]

    Richard and Moran, James M

    Thompson, A. Richard and Moran, James M. and Swenson, George W. , year = 2017, pages =. Introductory. Interferometry and. doi:10.1007/978-3-319-44431-4_2 , url =

    2017 doi

  100. [109]

    Доклады АН СССР , volume =

    О Решении Некорректно Поставленных Задач и Методе Регуляризации , author =. Доклады АН СССР , volume =

  101. [110]

    Tyul'bashev, S. A. and Tyul'basheva, G. E. and Andrianov, S. A. and Kitaeva, M. A. , year = 2025, month = dec, journal =. The. doi:10.1134/S106377292570252X , url =

    2025 doi

  102. [111]

    Веселова, А. В. , file =. Лекции

  103. [112]

    Physics Letters B , volume =

    Gravitational Radiation from Cosmic Strings , author =. Physics Letters B , volume =. doi:10.1016/0370-2693(81)91144-8 , url =

    doi

  104. [113]

    and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and

    Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and. Nature Medicine , volume =. doi:10.1038/s41592-019-0686-2 , url =

    doi

  105. [114]

    Wahlquist, Hugo , year = 1987, month = nov, journal =. The. doi:10.1007/BF00759146 , url =

    1987 doi

  106. [115]

    , year = 2007, publisher =

    Wald, Robert M. , year = 2007, publisher =

    2007

  107. [116]

    Waldman, S. J. , year = 2011, month = mar, publisher =. The. doi:10.48550/arXiv.1103.2728 , url =

    2011 doi arXiv

  108. [117]

    Wall, J. V. and Jenkins, C. R. , year = 2012, month = apr, journal =. Practical

    2012

  109. [118]

    Gravitation and

    Weinberg, Steven , year = 1972, publisher =. Gravitation and

    1972

  110. [119]

    Extrapolation,

    Wiener, Norbert , year = 1964, publisher =. Extrapolation,

    1964

  111. [120]

    Xu, Heng and Chen, Siyuan and Guo, Yanjun and Jiang, Jinchen and Wang, Bojun and Xu, Jiangwei and Xue, Zihan and Caballero, R. Nicolas and Yuan, Jianping and Xu, Yonghua and Wang, Jingbo and Hao, Longfei and Luo, Jingtao and Lee, Kejia and Han, Jinlin and Jiang, Peng and Shen,...

    2023

  112. [121]

    Zhou, D. J. and Han, J. L. and Xu, Jun and Wang, Chen and Wang, P. F. and Wang, Tao and Jing, Wei-Cong and Chen, Xue and Yan, Yi and Su, Wei-Qi. and Gan, Heng-Qian and Jiang, Peng and Sun, Jing-Hai and Wang, Hong-Guang and Wang, Na and Wang, Shuang-Qiang and Xu, Ren-Xin and Yo...

    2023 doi

  113. [122]

    Healpy: Equal Area Pixelization and Spherical Harmonics Transforms for Data on the Sphere in

    Zonca, Andrea and Singer, Leo and Lenz, Daniel and Reinecke, Martin and Rosset, Cyrille and Hivon, Eric and Gorski, Krzysztof , year = 2019, month = mar, journal =. Healpy: Equal Area Pixelization and Spherical Harmonics Transforms for Data on the Sphere in. doi:10.21105/joss....

    2019 doi

  114. [123]

    and Thorne, Kip S

    Misner, Charles W. and Thorne, Kip S. and Wheeler, John A. , title =

  115. [124]

    Maggiore, Michele , title =

  116. [125]

    Abbott, B. P. and others , collaboration =. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral , journal =. 2017 , doi =

    2017

  117. [126]

    Abbott, B. P. and others , collaboration =. Multi-messenger Observations of a Binary Neutron Star Merger , journal =. 2017 , doi =

    2017

  118. [127]

    and O'Connor, E

    Andresen, H. and O'Connor, E. P. and Janka, H.-T. and Müller, E. and Summa, A. , title =. Living Reviews in Computational Astrophysics , volume =. 2022 , doi =

    2022

  119. [128]

    Annual Review of Nuclear and Particle Science , volume =

    Kamionkowski, Marc and Kosowsky, Arthur , title =. Annual Review of Nuclear and Particle Science , volume =. 1999 , doi =

    1999

  120. [129]

    , title =

    Caprini, Chiara and Figueroa, Daniel G. , title =. Classical and Quantum Gravity , volume =. 2018 , doi =

    2018

  121. [130]

    Physical Review , volume =

    Weber, Joseph , title =. Physical Review , volume =. 1960 , doi =

    1960

  122. [131]

    Physical Review Letters , volume =

    Weber, Joseph , title =. Physical Review Letters , volume =. 1969 , doi =

    1969

  123. [132]

    , title =

    Garwin, Richard L. , title =. Nature , volume =. 1974 , doi =

    1974

  124. [133]

    Peters, P. C. and Mathews, J. , title =. Physical Review , volume =. 1963 , doi =

    1963

  125. [134]

    Peters, P. C. , title =. Physical Review , volume =. 1964 , doi =

    1964

  126. [135]

    Landau, L. D. and Lifshitz, E. M. , title =

  127. [136]

    Taylor, J. H. and Fowler, L. A. and McCulloch, P. M. , title =. Nature , volume =. 1979 , doi =

    1979

  128. [137]

    and Huang, Yuhan , title =

    Weisberg, Joel M. and Huang, Yuhan , title =. Astrophysical Journal , volume =. 2016 , doi =

    2016

  129. [138]

    Nature , volume =

    Burgay, Marta and others , title =. Nature , volume =. 2003 , doi =

    2003

  130. [139]

    Lyne, A. G. and others , title =. Science , volume =. 2004 , doi =

    2004

  131. [140]

    and others , title =

    Kramer, M. and others , title =. Science , volume =. 2006 , doi =

    2006

  132. [141]

    , title =

    Wolszczan, A. , title =. Nature , volume =. 1991 , doi =

    1991

  133. [142]

    Kaspi, V. M. and Lyne, A. G. and Manchester, R. N. and others , title =. Astrophysical Journal , volume =. 2000 , doi =

    2000

  134. [143]

    , title =

    Schutz, Bernard F. , title =. Classical and Quantum Gravity , volume =. 2009 , doi =

    2009

  135. [144]

    , title =

    Stairs, Ingrid H. , title =. Living Reviews in Relativity , volume =. 2003 , doi =

    2003

  136. [145]

    Frontiers in Relativistic Celestial Mechanics: Applications and Experiments , editor =

    Wex, Norbert , title =. Frontiers in Relativistic Celestial Mechanics: Applications and Experiments , editor =. 2014 , doi =

    2014

  137. [146]

    and others , collaboration =

    Abbott, R. and others , collaboration =. GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run , journal =. 2023 , doi =

    2023

  138. [147]

    Jenet, F. A. and Hobbs, G. B. and van Straten, W. and Manchester, R. N. and Bailes, M. and Verbiest, J. P. W. and Edwards, R. T. and Hotan, A. W. and Sarkissian, J. M. and Ord, S. M. , title =. Astrophysical Journal , volume =. 2006 , doi =

    2006

  139. [148]

    Kopeikin, S. M. , title =. Physical Review D , volume =. 1997 , doi =

    1997

  140. [149]

    Kopeikin, S. M. , title =. Monthly Notices of the Royal Astronomical Society , volume =. 1999 , doi =

    1999

  141. [150]

    Shannon, R. M. and Ravi, V. and Lentati, L. T. and Lasky, P. D. and Hobbs, G. and Kerr, M. and Manchester, R. N. and Coles, W. A. and Levin, Y. and Bailes, M. and others , title =. Science , volume =. 2015 , doi =

    2015

  142. [151]

    Jaffe, A. H. and Backer, D. C. , title =. Astrophysical Journal , volume =

  143. [152]

    , title =

    Sesana, A. , title =. MNRAS , volume =

  144. [153]

    and Vilenkin, A

    Damour, T. and Vilenkin, A. , title =. Physical Review D , volume =

  145. [154]

    and Figueroa, D

    Caprini, C. and Figueroa, D. G. , title =. Classical and Quantum Gravity , volume =

  146. [155]

    Lee, K. J. and Wex, N. and Kramer, M. and Stappers, B. W. and others , title =. MNRAS , volume =

  147. [156]

    Ellis, J. A. and Jenet, F. A. and McLaughlin, M. A. , title =. ApJ , volume =

  148. [157]

    Janssen, G. H. and others , title =. Proceedings of Science , volume =

  149. [158]

    and others , title =

    Kramer, M. and others , title =. Experimental Astronomy , volume =

  150. [159]

    , keywords =

    Optimal Reconstruction of the Hellings and Downs Correlation. , keywords =. doi:10.1103/PhysRevLett.134.031401 , archivePrefix =. 2407.10968 , primaryClass =

    arXiv

  151. [160]

    Classical and Quantum Gravity , keywords =

    Answers to frequently asked questions about the pulsar timing array Hellings and Downs curve. Classical and Quantum Gravity , keywords =. doi:10.1088/1361-6382/ad4c4c , archivePrefix =. 2308.05847 , primaryClass =

    arXiv

  152. [161]

    , keywords =

    Variance of the Hellings-Downs correlation. , keywords =. doi:10.1103/PhysRevD.107.043018 , archivePrefix =. 2205.05637 , primaryClass =

    arXiv

  153. [162]

    , keywords =

    Hellings and Downs correlation of an arbitrary set of pulsars. , keywords =. doi:10.1103/PhysRevD.108.043026 , archivePrefix =. 2208.07230 , primaryClass =

    arXiv

  154. [163]

    Tarantola, Albert , title =

  155. [164]

    Hansen, Per Christian , title =

  156. [165]

    Thorne, K. S. , title =. Rev. Mod. Phys. , volume =

  157. [166]

    Cornish, N. J. and van Haasteren, R. , title =. Phys. Rev. D , volume =

  158. [167]

    van Haasteren, R. et al. , title =. MNRAS , volume =

  159. [168]

    Ellis, J. A. and Siemens, X. and Creighton, J. D. E. , title =. ApJ , volume =

  160. [169]

    and Van Loan, Charles F

    Golub, Gene H. and Van Loan, Charles F. , title =

  161. [170]

    Varshalovich, D. A. and Moskalev, A. N. and Khersonskii, V. K. , title =

  162. [171]

    2008 , publisher =

    Steven Weinberg , title =. 2008 , publisher =

    2008

  163. [172]

    and Bhat, N

    Shannon, Ryan M. and Bhat, N. D. Ramesh and Chalumeau, Aurelien and Chen, Siyuan and Cromartie, H. Thankful and Gopukumar, A. and Grunthal, Kathrin and Hazboun, Jeffrey S. and Iraci, Francesco and Joshi, Bhal Chandra and Kato, Ryo and Keith, Michael J. and Lee, Kejia and Liu, ...

    doi

  164. [173]

    Deller, A. T. and Brisken, W. F. and Chatterjee, S. and Cordes, J. M. and Goss, W. M. and Janssen, G. H. and Kovalev, Y. Y. and Lazio, T. J. W. and Petrov, L. and Stappers, B. W. , year = 2011, month = jul, publisher =. doi:10.48550/arXiv.1110.1979 , url =

    2011 doi arXiv

  165. [174]

    Inference with Finite Time Series:

    Talbot, Colm and Thrane, Eric and Biscoveanu, Sylvia and Smith, Rory , year = 2021, month = oct, journal =. Inference with Finite Time Series:. doi:10.1103/PhysRevResearch.3.043049 , url =

    2021 doi

  166. [175]

    doi:10.48550/arXiv.2603.10120 , url =

    On the Angular Localization of Gravitational-Wave Signals by Pulsar Timing Arrays , author =. doi:10.48550/arXiv.2603.10120 , url =. arXiv , keywords =:2603.10120 , primaryclass =

    doi

  167. [176]

    and Jow, Dylan L

    Tsai, Anna C. and Jow, Dylan L. and Pen, Ue-Li , year = 2026, month = may, number =. Reaching Diffraction-Limited Localization with Coherent. doi:10.48550/arXiv.2512.10795 , url =. arXiv , keywords =:2512.10795 , primaryclass =

    2026 doi arXiv

  168. [177]

    Libstempo:

    Vallisneri, Michele , year = 2020, month = feb, journal =. Libstempo:

    2020

  169. [178]

    Moore, E. H. , title = ". Bull. Amer. Math. Soc. , volume =. 1920 , url =

    1920

  170. [179]

    , title = "

    Penrose, R. , title = ". Math. Proc. Cambridge Philos. Soc. , volume =. 1955 , doi =

    1955

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