% Bibliographic companion to angular_hecke_15_16.tex.
% The reviewed standalone TeX retains its embedded thebibliography environment.
% It does not require a BibTeX run or this file to compile.
% These six records reproduce the references in that manuscript.

@article{Patterson,
  author  = {Patterson, S. J.},
  title   = {A cubic analogue of the theta series},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {296},
  year    = {1977},
  pages   = {125--161},
  doi     = {10.1515/crll.1977.296.125},
  url     = {https://doi.org/10.1515/crll.1977.296.125},
  note    = {Classical background for the cubic theta function}
}

@article{HB,
  author  = {Heath-Brown, D. R.},
  title   = {A mean value estimate for real character sums},
  journal = {Acta Arithmetica},
  volume  = {72},
  number  = {3},
  year    = {1995},
  pages   = {235--275},
  doi     = {10.4064/aa-72-3-235-275},
  url     = {https://doi.org/10.4064/aa-72-3-235-275},
  note    = {Classical quadratic large-sieve background}
}

@article{GL,
  author  = {Goldmakher, L. and Louvel, B.},
  title   = {A quadratic large sieve inequality over number fields},
  journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
  volume  = {154},
  number  = {2},
  year    = {2013},
  pages   = {193--212},
  doi     = {10.1017/S0305004112000370},
  url     = {https://doi.org/10.1017/S0305004112000370},
  eprint  = {1112.1642},
  archivePrefix = {arXiv},
  note    = {Theorem 1.1 supplies the fixed-modulus quadratic Hecke-family inequality discussed in the manuscript}
}

@article{DR,
  author  = {Dunn, A. and Radziwi{\l}{\l}, M.},
  title   = {Bias in cubic {Gauss} sums: {Patterson}'s conjecture},
  journal = {Annals of Mathematics},
  volume  = {200},
  number  = {3},
  year    = {2024},
  pages   = {967--1057},
  doi     = {10.4007/annals.2024.200.3.3},
  url     = {https://doi.org/10.4007/annals.2024.200.3.3},
  note    = {Related cubic theta and Voronoi framework. Its GRH-conditional prime asymptotic is not an input to the manuscript's argument}
}

@misc{OAI,
  author       = {{OpenAI}},
  title        = {{OAI-003} source development},
  year         = {2026},
  howpublished = {GitHub repository openai/math},
  url          = {https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a},
  note         = {Pinned revision adc7f1241b42e322a6451854ab7e4b4c146bf78a. Source material; no peer-reviewed publication status is asserted}
}

@misc{Angular,
  author       = {Winarski, Troy},
  title        = {Angular {Hecke} {$15/16$} frozen source and native {Windows} verification evidence},
  year         = {2026},
  howpublished = {GitHub repository TheRealDubb/angular-hecke-15-16-xenoproof},
  url          = {https://github.com/TheRealDubb/angular-hecke-15-16-xenoproof/releases/tag/v15-16-2026-10-18},
  note         = {Release v15-16-2026-10-18; commit 67bb5d2df315fe5ebe7b6ffe0eb4529ffef225de. Source closure, theorem scope, dependency pins and native Windows replay evidence. Distinct from later explanatory README edits; no independent human certification is asserted}
}