@article{JK,
  author = {Jaming, Philippe and Kolountzakis, Mihail N.},
  title = {Reconstruction of functions from their triple correlations},
  journal = {New York Journal of Mathematics},
  volume = {9},
  year = {2003},
  pages = {149--164},
  note = {\url{https://nyjm.albany.edu/j/2003/9-12p.pdf}}
}
@article{GB,
  author = {Grimm, Uwe and Baake, Michael},
  title = {Homometric point sets and inverse problems},
  journal = {Zeitschrift f{\"u}r Kristallographie},
  volume = {223},
  year = {2008},
  pages = {777--781},
  note = {arXiv:0808.0094, \url{https://arxiv.org/abs/0808.0094}}
}
@article{BKLR,
  author = {Bergelson, Vitaly and Ku{\l}aga-Przymus, Joanna and Lema{\'n}czyk, Mariusz and Richter, Florian K.},
  title = {Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics},
  journal = {Ergodic Theory and Dynamical Systems},
  volume = {39},
  number = {9},
  year = {2019},
  pages = {2332--2383},
  note = {arXiv:1611.08392v2, \url{https://arxiv.org/abs/1611.08392v2}; doi:10.1017/etds.2017.130}
}
@article{Ding,
  author = {Ding, Cunsheng},
  title = {Pattern distributions of {Legendre} sequences},
  journal = {IEEE Transactions on Information Theory},
  volume = {44},
  number = {4},
  year = {1998},
  pages = {1693--1698},
  note = {Author copy, \url{https://www.cse.ust.hk/faculty/cding/JOURNALS/it982.pdf}}
}
@misc{BWX,
  author = {de la Bret{\`e}che, R{\'e}gis and Wang, Victor Y. and Xu, Max Wenqiang},
  title = {Random multiplicative functions and making squares from polynomial values},
  year = {2026},
  note = {arXiv:2607.06398v1, 7 July 2026. Lemmas 3.2--3.3 and the explicit proof of Lemma 3.3. \url{https://arxiv.org/html/2607.06398v1}}
}
@article{ES,
  author = {Evertse, Jan-Hendrik and Silverman, Joseph H.},
  title = {Uniform bounds for the number of solutions to {$Y^n=f(X)$}},
  journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
  volume = {100},
  number = {2},
  year = {1986},
  pages = {237--248},
  note = {doi:10.1017/S0305004100066068. Original article: \url{https://ir.cwi.nl/pub/1788/1788D.pdf}}
}
@article{GHR,
  author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
  title = {A constructive {Borel--Cantelli} lemma. {Constructing} orbits with required statistical properties},
  journal = {Theoretical Computer Science},
  volume = {410},
  number = {21--23},
  year = {2009},
  pages = {2207--2222},
  note = {doi:10.1016/j.tcs.2009.02.010; arXiv:0711.1478v2, \url{https://arxiv.org/abs/0711.1478v2}}
}
@misc{DLMF,
  author = {{National Institute of Standards and Technology}},
  title = {{NIST Digital Library of Mathematical Functions}},
  note = {\S27.9, Quadratic Characters, and \S27.11, Asymptotic Formulas: Partial Sums, especially equation 27.11.9. Consulted 27 September 2026. \url{https://dlmf.nist.gov/27.9}; \url{https://dlmf.nist.gov/27.11}}
}

@article{Klurman,
  author = {Klurman, Oleksiy},
  title = {Correlations of multiplicative functions and applications},
  journal = {Compositio Mathematica}, volume = {153}, number = {8},
  year = {2017}, pages = {1622--1657},
  note = {doi:10.1112/S0010437X17007163. Theorem 1.3 is cited from arXiv:1603.08453v1, \url{https://arxiv.org/html/1603.08453v1}}
}
@article{KM,
  author = {Klurman, Oleksiy and Mangerel, Alexander P.},
  title = {Rigidity theorems for multiplicative functions},
  journal = {Mathematische Annalen}, volume = {372}, year = {2018}, pages = {651--697},
  note = {doi:10.1007/s00208-018-1724-6. Question 1.11 and Proposition 1.12 are cited from arXiv:1707.07817v2, \url{https://arxiv.org/html/1707.07817v2}}
}
@article{GM,
  author = {Gr{\"u}nbaum, F. Alberto and Moore, Calvin C.},
  title = {The use of higher-order invariants in the determination of generalized {Patterson} cyclotomic sets},
  journal = {Acta Crystallographica Section A}, volume = {51}, number = {3},
  year = {1995}, pages = {310--323},
  note = {doi:10.1107/S0108767394009827. The reconstruction result is used here for historical context via the accounts in Jaming--Kolountzakis, Section 3.4, and Casper--Orozco, Introduction}
}
@misc{CO,
  author = {Casper, W. Riley and Orozco, Bobby},
  title = {Reconstructing rational functions on finite abelian groups with higher autocorrelations},
  year = {2026},
  note = {arXiv:2503.21022v2, 4 July 2026, \url{https://arxiv.org/html/2503.21022v2}. Journal version: doi:10.1016/j.acha.2026.101908. Comparisons use the cited preprint}
}
@article{AG,
  author = {Allouche, Jean-Paul and Goldmakher, Leo},
  title = {Mock characters and the {Kronecker} symbol},
  journal = {Journal of Number Theory}, volume = {192}, year = {2018}, pages = {356--372},
  note = {doi:10.1016/j.jnt.2018.04.022. Theorem 2.11 is cited from arXiv:1608.03957v2, 4 January 2017, \url{https://arxiv.org/html/1608.03957v2}}
}
@article{Najnudel,
  author = {Najnudel, Joseph},
  title = {On consecutive values of random completely multiplicative functions},
  journal = {Electronic Journal of Probability}, volume = {25}, year = {2020},
  pages = {1--28},
  note = {Paper no.~59; doi:10.1214/20-EJP456. Proposition 6.3 is cited from arXiv:1702.01470v2, \url{https://arxiv.org/html/1702.01470v2}}
}
@misc{PoulySN,
  author = {Pouly, Brice},
  title = {Selective normality and algebraic rigidity of multiplicative traces},
  year = {2026},
  doi = {10.5281/zenodo.23318326},
  url = {https://doi.org/10.5281/zenodo.23318326},
  note = {Author's manuscript, 38 pp. \href{https://doi.org/10.5281/zenodo.23318326}{doi:10.5281/zenodo.23318326}. Section 5, pp.~16--19, especially Proposition 5.1 and the marked-law bound in Section 5.3. Edition consulted 30 September 2026; comparison of the shared selection method, not a proof dependency}
}