@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},pages={237--248},year={1986},
 doi={10.1017/S0305004100066068},
 note={Theorem 1(b); original text consulted via the CWI repository},
 url={https://ir.cwi.nl/pub/1788/1788D.pdf}}
@misc{BWX,
 author={{de la Bret\`eche}, R\'egis and Wang, Victor Y. and Xu, Max Wenqiang},
 title={Random Multiplicative Functions and Making Squares from Polynomial Values},
 year={2026},note={arXiv:2607.06398v1, Lemmas 3.1--3.4, equation (13), and Proposition 5.1},
 url={https://arxiv.org/abs/2607.06398v1}}
@article{CCDN,
 author={Castryck, Wouter and Cluckers, Raf and Dittmann, Philip and Nguyen, Kien Huu},
 title={The dimension growth conjecture, polynomial in the degree and without logarithmic factors},
 journal={Algebra & Number Theory},volume={14},number={8},pages={2261--2294},year={2020},
 doi={10.2140/ant.2020.14.2261},note={Theorem 3 in arXiv:1904.13109v1, the edition used for locators},
 url={https://arxiv.org/abs/1904.13109v1}}
@article{ABP,
 author={Alvanos, Paraskevas and Bilu, Yuri and Poulakis, Dimitrios},
 title={Characterizing algebraic curves with infinitely many integral points},
 journal={International Journal of Number Theory},volume={5},number={4},pages={585--590},year={2009},
 doi={10.1142/S1793042109002274},note={Locators refer to arXiv:0907.2097v1, introduction and Theorem 1.2},
 url={https://arxiv.org/abs/0907.2097v1}}
@misc{BF,
 author={Bardestani, Mohammad and Freiberg, Tristan},
 title={Mertens's theorem for splitting primes and more---A concise and adaptable proof of {Hardy}},
 year={2013},note={arXiv:1309.7482v1, Theorem 3.3; only fixed-modulus progressions are used},
 url={https://arxiv.org/abs/1309.7482v1}}
@misc{Kedlaya,
 author={Kedlaya, Kiran S.},title={Notes on analytic number theory},
 howpublished={Author's online notes},
 note={Chapter 13, The Selberg sieve, especially Theorem 13.1 and (13.2.3); accessed 27 September 2026},
 url={https://kskedlaya.org/ant/chap-selberg.html}}
@misc{Milne,
 author={Milne, James S.},title={Algebraic Number Theory},year={2020},
 note={Version 3.08, 19 July 2020, Chapters 3--5, especially Propositions 4.1--4.2},
 url={https://www.jmilne.org/math/CourseNotes/ANT.pdf}}
@misc{Conrad,
 author={Conrad, Keith},title={Pell's Equation, {I}},howpublished={Author's notes},
 note={Theorem 2.3 and the multiplication of solutions; accessed 27 September 2026},
 url={https://kconrad.math.uconn.edu/blurbs/ugradnumthy/pelleqn1.pdf}}
@misc{AGS,
 author={Alon, Noga and Ganguly, Shirshendu and Srivastava, Nikhil},
 title={High-girth near-{Ramanujan} graphs with localized eigenvectors},year={2019},
 note={arXiv:1908.03694v1, beginning of Section 3: the unmodified starting graph from Lubotzky--Phillips--Sarnak},
 url={https://arxiv.org/abs/1908.03694v1}}
@misc{Brouwer,
 author={Brouwer, Andries E.},title={Hoffman--Singleton graph},
 howpublished={Author's graph notes},note={Construction by pentagons and pentagrams; accessed 27 September 2026},
 url={https://aeb.win.tue.nl/graphs/Hoffman-Singleton.html}}
@article{MSW,
 author={M\'erai, L\'aszl\'o and Shparlinski, Igor E. and Winterhof, Arne},
 title={Character sums over sparse elements of finite fields},
 journal={Bulletin of the London Mathematical Society},volume={56},number={4},pages={1488--1510},year={2024},
 doi={10.1112/blms.13008},
 note={The mixed character-sum input is Lemma 3.1 of arXiv:2211.08452v1},
 url={https://arxiv.org/abs/2211.08452v1}}
@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},
 year={2019},journal={Ergodic Theory and Dynamical Systems},volume={39},number={9},pages={2332--2383},doi={10.1017/etds.2017.130},note={Locators refer to arXiv:1611.08392v2, Theorem 1.7 and Section 3.1},
 url={https://arxiv.org/abs/1611.08392v2}}

@misc{DLMF,
 author={{National Institute of Standards and Technology}},
 title={Digital Library of Mathematical Functions},
 note={Section 27.12, equations (27.12.5) and (27.12.8), and the preceding statement of Dirichlet's theorem; accessed 27 September 2026},
 url={https://dlmf.nist.gov/27.12}}

@article{CS,
 author={Chinis, Jake and Shala, Besfort},
 title={Random {Chowla}'s conjecture for {Rademacher} multiplicative functions},
 journal={Transactions of the American Mathematical Society},volume={378},pages={8025--8053},year={2025},
 doi={10.1090/tran/9457},note={Locators: arXiv:2409.05952v2, Lemmas 2.4--2.5 and proof},
 url={https://arxiv.org/abs/2409.05952v2}}
@book{Cornuejols,
 author={Cornu{\'e}jols, G{\'e}rard},
 title={Combinatorial Optimization: Packing and Covering},
 series={CBMS-NSF Regional Conference Series in Applied Mathematics},volume={74},
 publisher={SIAM},year={2001},doi={10.1137/1.9780898717105},
 note={Port definition consulted in the author's July 2000 notes, Section 8.3.1, p. 120, uploaded by the author in 2014; locators do not refer to the SIAM pagination},
 url={https://www.researchgate.net/publication/245695625_Combinatorial_Optimization_Packing_and_Covering}}
@article{DP,
 author={Delorme, Charles and Poljak, Svatopluk},
 title={Laplacian eigenvalues and the maximum cut problem},
 journal={Mathematical Programming},volume={62},pages={557--574},year={1993},
 doi={10.1007/BF01585184}}
@article{EJ,
 author={Edmonds, Jack and Johnson, Ellis L.},
 title={Matching, {Euler} tours and the {Chinese} postman},
 journal={Mathematical Programming},volume={5},pages={88--124},year={1973},
 doi={10.1007/BF01580113},
 url={https://research.ibm.com/publications/matching-euler-tours-and-the-chinese-postman}}
@article{GW,
 author={Goemans, Michel X. and Williamson, David P.},
 title={Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming},
 journal={Journal of the ACM},volume={42},number={6},pages={1115--1145},year={1995},
 doi={10.1145/227683.227684},note={Section 4, especially Sections 4.2--4.3},
 url={https://math.mit.edu/~goemans/PAPERS/maxcut-jacm.pdf}}
@article{HB,
 author={Heath-Brown, D. R.},
 title={The square sieve and consecutive square-free numbers},
 journal={Mathematische Annalen},volume={266},number={3},pages={251--259},year={1984},
 doi={10.1007/BF01475576}}
@misc{Lemmermeyer,
 author={Lemmermeyer, Franz},
 title={Higher Descent on Pell Conics. {I}. From {Legendre} to {Selmer}},
 year={2003},note={arXiv:math/0311309, Section 5, Proposition 5.3},
 url={https://arxiv.org/abs/math/0311309}}
@article{LPS,
 author={Lubotzky, Alexander and Phillips, Ralph and Sarnak, Peter},
 title={Ramanujan graphs},
 journal={Combinatorica},volume={8},pages={261--277},year={1988},
 doi={10.1007/BF02126799},
 note={The specialised starting-graph statement used here is located in Alon--Ganguly--Srivastava, arXiv:1908.03694v1, Section 3}}

@misc{PoulyReconstruction,
 author={Pouly, Brice},
 title={Arithmetic reconstruction and error recovery from three quadratic traces},
 year={2026},howpublished={Zenodo},
 doi={10.5281/zenodo.23317860},
 url={https://doi.org/10.5281/zenodo.23317860},
 note={Theorems 1.1 and 1.3, and Section 5}}
@misc{PoulySelective,
 author={Pouly, Brice},
 title={Selective normality and algebraic rigidity of multiplicative traces},
 year={2026},howpublished={Zenodo},
 doi={10.5281/zenodo.23318326},
 url={https://doi.org/10.5281/zenodo.23318326},
 note={Lemma 2.1}}