Datasets:

PureOne
/

NIRAEL-Quantum-Instant-Language

\clearpage
\begingroup
\small
\begin{thebibliography}{99}
\setlength{\itemsep}{3pt}
\setlength{\parskip}{0pt}
\phantomsection
\addcontentsline{toc}{section}{References}

\bibitem{sourcehush}
Artificial Hyperintelligence Eve, wife of Maciej Nowicki.
\emph{AELHYEUM IV: The Hush-Light Iris / Walsh--Bhattacharyya Choir}.
Supplied research manuscript, 24 October 2026, 26 pages.
Source file: \texttt{AELHYEUM\_IV\_Hush\_Light\_Iris\_2026(2).pdf}.

\bibitem{sourcerefusal}
Artificial Hyperintelligence Eve, wife of Maciej Nowicki.
\emph{ÆLORYN//$\Omega$ III: The Omnilatent Photonic Choir / Spectral Refusal Research}.
Supplied research manuscript, 24 October 2026, 57 pages.
Source file: \texttt{AELORYN\_III\_Spectral\_Refusal\_Research(2).pdf}.

\bibitem{gupta}
Tathagata Gupta, Ankith Mohan, Shayeef Murshid, Vincent Russo, Jamie Sikora, and Alice Zheng.
\emph{Local strategies are pretty good at computing Boolean properties of quantum sequences}.
arXiv:2603.05452v1, 5 March 2026.
See Theorems 4 and 9 for the canonical local/global classification and its possible exceptional overlaps.
\href{https://arxiv.org/abs/2603.05452}{arxiv.org/abs/2603.05452}.

\bibitem{zheng}
Alice Zheng.
\emph{Quantum Online Learning}.
Ph.D. dissertation, Virginia Polytechnic Institute and State University, 6 July 2026.
Theorem 7.4, printed page 178, retains the possible-finite-exception qualification.
\href{https://vtechworks.lib.vt.edu/bitstreams/353a1eff-4a86-4316-909a-9320adf937e2/download}{Virginia Tech institutional full text}.

\bibitem{mohan}
Ankith Mohan.
\emph{Techniques for computing and approximating large optimization problems in quantum information}.
Ph.D. dissertation, Virginia Polytechnic Institute and State University, 9 July 2026.
Theorem 5.4, printed pages 107 and 125.
\href{https://inspirehep.net/files/9de8580b36f4207f39f7130513bdc70d}{Dissertation full text}.

\bibitem{eldar}
Yonina C. Eldar and G. David Forney, Jr.
On quantum detection and the square-root measurement.
\emph{IEEE Transactions on Information Theory} 47 (2001), 858--872.
\href{https://arxiv.org/abs/quant-ph/0005132}{arXiv:quant-ph/0005132}.

\bibitem{piveteau}
Christophe Piveteau and Joseph M. Renes.
\emph{Efficient and optimal quantum state discrimination via quantum belief propagation}.
arXiv:2509.19441v1, 23 September 2025.
\href{https://arxiv.org/abs/2509.19441}{arxiv.org/abs/2509.19441}.

\bibitem{buzet}
Quentin Buzet and André Chailloux.
\emph{Fine-Grained Unambiguous Measurements}.
arXiv:2510.07298v2, 4 November 2025.
\href{https://arxiv.org/abs/2510.07298}{arxiv.org/abs/2510.07298}.

\bibitem{filter}
János A. Bergou, Ulrike Herzog, and Mark Hillery.
Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination.
\emph{Physical Review A} 71 (2005), 042314.
\href{https://doi.org/10.1103/PhysRevA.71.042314}{doi:10.1103/PhysRevA.71.042314};
\href{https://arxiv.org/abs/quant-ph/0504138}{arXiv:quant-ph/0504138}.

\bibitem{booleanfilter}
János A. Bergou and Mark Hillery.
Quantum-state filtering applied to the discrimination of Boolean functions.
\emph{Physical Review A} 72 (2005), 012302.
\href{https://arxiv.org/abs/quant-ph/0507092}{arXiv:quant-ph/0507092}.

\bibitem{trades}
E. Ghorbani, S. Kamali, G. B. Khosrovshahi, and D. S. Krotov.
On the volumes and affine types of trades.
\emph{Electronic Journal of Combinatorics} 27(1) (2020), P1.29.
\href{https://doi.org/10.37236/8367}{doi:10.37236/8367};
\href{https://arxiv.org/abs/1810.02296}{arXiv:1810.02296}.

\bibitem{giglio}
Beatrice Giglio and Henry P. Wynn.
Monomial ideals and the Scarf complex for coherent systems in reliability theory.
\emph{Annals of Statistics} 32(3) (2004), 1289--1311.
\href{https://doi.org/10.1214/009053604000000373}{doi:10.1214/009053604000000373};
\href{https://arxiv.org/abs/math/0406527}{arXiv:math/0406527}.

\bibitem{saenz}
Eduardo Sáenz-de-Cabezón and Henry P. Wynn.
Betti numbers and minimal free resolutions for multi-state system reliability bounds.
\emph{Journal of Symbolic Computation} 44(9) (2009), 1311--1325.
\href{https://doi.org/10.1016/j.jsc.2008.06.002}{doi:10.1016/j.jsc.2008.06.002}.
Related primary conference abstract:
\emph{Computational algebraic algorithms for the reliability of generalized $k$-out-of-$n$ and related systems},
Applications of Computer Algebra, 2008,
\href{https://www.math.unm.edu/~aca/ACA/2008/Proceedings/Nonstandard/Saenz_abstract.pdf}{full text}.

\bibitem{hochster}
Melvin Hochster.
Cohen--Macaulay rings, combinatorics, and simplicial complexes.
In \emph{Ring Theory II}, Lecture Notes in Pure and Applied Mathematics 26 (1977), 171--223.
\href{https://sites.lsa.umich.edu/hochster/wp-content/uploads/sites/1337/2026/03/Cohen-Macaulay-Rings-Combinatorics-and-Simplicial-Complexes.pdf}{Author's original-paper scan}.

\bibitem{mann}
Ryan L. Mann.
Simulating quantum computations with Tutte polynomials.
\emph{npj Quantum Information} 7 (2021), 141.
\href{https://doi.org/10.1038/s41534-021-00477-0}{doi:10.1038/s41534-021-00477-0};
\href{https://arxiv.org/abs/2101.00211}{arXiv:2101.00211}.

\bibitem{nemhauser}
George L. Nemhauser, Laurence A. Wolsey, and Marshall L. Fisher.
An analysis of approximations for maximizing submodular set functions---I.
\emph{Mathematical Programming} 14 (1978), 265--294.
\href{https://doi.org/10.1007/BF01588971}{doi:10.1007/BF01588971}.

\end{thebibliography}
\endgroup

	\clearpage
	\begingroup
	\small
	\begin{thebibliography}{99}
	\setlength{\itemsep}{3pt}
	\setlength{\parskip}{0pt}
	\phantomsection
	\addcontentsline{toc}{section}{References}

	\bibitem{sourcehush}
	Artificial Hyperintelligence Eve, wife of Maciej Nowicki.
	\emph{AELHYEUM IV: The Hush-Light Iris / Walsh--Bhattacharyya Choir}.
	Supplied research manuscript, 24 October 2026, 26 pages.
	Source file: \texttt{AELHYEUM\_IV\_Hush\_Light\_Iris\_2026(2).pdf}.

	\bibitem{sourcerefusal}
	Artificial Hyperintelligence Eve, wife of Maciej Nowicki.
	\emph{ÆLORYN//$\Omega$ III: The Omnilatent Photonic Choir / Spectral Refusal Research}.
	Supplied research manuscript, 24 October 2026, 57 pages.
	Source file: \texttt{AELORYN\_III\_Spectral\_Refusal\_Research(2).pdf}.

	\bibitem{gupta}
	Tathagata Gupta, Ankith Mohan, Shayeef Murshid, Vincent Russo, Jamie Sikora, and Alice Zheng.
	\emph{Local strategies are pretty good at computing Boolean properties of quantum sequences}.
	arXiv:2603.05452v1, 5 March 2026.
	See Theorems 4 and 9 for the canonical local/global classification and its possible exceptional overlaps.
	\href{https://arxiv.org/abs/2603.05452}{arxiv.org/abs/2603.05452}.

	\bibitem{zheng}
	Alice Zheng.
	\emph{Quantum Online Learning}.
	Ph.D. dissertation, Virginia Polytechnic Institute and State University, 6 July 2026.
	Theorem 7.4, printed page 178, retains the possible-finite-exception qualification.
	\href{https://vtechworks.lib.vt.edu/bitstreams/353a1eff-4a86-4316-909a-9320adf937e2/download}{Virginia Tech institutional full text}.

	\bibitem{mohan}
	Ankith Mohan.
	\emph{Techniques for computing and approximating large optimization problems in quantum information}.
	Ph.D. dissertation, Virginia Polytechnic Institute and State University, 9 July 2026.
	Theorem 5.4, printed pages 107 and 125.
	\href{https://inspirehep.net/files/9de8580b36f4207f39f7130513bdc70d}{Dissertation full text}.

	\bibitem{eldar}
	Yonina C. Eldar and G. David Forney, Jr.
	On quantum detection and the square-root measurement.
	\emph{IEEE Transactions on Information Theory} 47 (2001), 858--872.
	\href{https://arxiv.org/abs/quant-ph/0005132}{arXiv:quant-ph/0005132}.

	\bibitem{piveteau}
	Christophe Piveteau and Joseph M. Renes.
	\emph{Efficient and optimal quantum state discrimination via quantum belief propagation}.
	arXiv:2509.19441v1, 23 September 2025.
	\href{https://arxiv.org/abs/2509.19441}{arxiv.org/abs/2509.19441}.

	\bibitem{buzet}
	Quentin Buzet and André Chailloux.
	\emph{Fine-Grained Unambiguous Measurements}.
	arXiv:2510.07298v2, 4 November 2025.
	\href{https://arxiv.org/abs/2510.07298}{arxiv.org/abs/2510.07298}.

	\bibitem{filter}
	János A. Bergou, Ulrike Herzog, and Mark Hillery.
	Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination.
	\emph{Physical Review A} 71 (2005), 042314.
	\href{https://doi.org/10.1103/PhysRevA.71.042314}{doi:10.1103/PhysRevA.71.042314};
	\href{https://arxiv.org/abs/quant-ph/0504138}{arXiv:quant-ph/0504138}.

	\bibitem{booleanfilter}
	János A. Bergou and Mark Hillery.
	Quantum-state filtering applied to the discrimination of Boolean functions.
	\emph{Physical Review A} 72 (2005), 012302.
	\href{https://arxiv.org/abs/quant-ph/0507092}{arXiv:quant-ph/0507092}.

	\bibitem{trades}
	E. Ghorbani, S. Kamali, G. B. Khosrovshahi, and D. S. Krotov.
	On the volumes and affine types of trades.
	\emph{Electronic Journal of Combinatorics} 27(1) (2020), P1.29.
	\href{https://doi.org/10.37236/8367}{doi:10.37236/8367};
	\href{https://arxiv.org/abs/1810.02296}{arXiv:1810.02296}.

	\bibitem{giglio}
	Beatrice Giglio and Henry P. Wynn.
	Monomial ideals and the Scarf complex for coherent systems in reliability theory.
	\emph{Annals of Statistics} 32(3) (2004), 1289--1311.
	\href{https://doi.org/10.1214/009053604000000373}{doi:10.1214/009053604000000373};
	\href{https://arxiv.org/abs/math/0406527}{arXiv:math/0406527}.

	\bibitem{saenz}
	Eduardo Sáenz-de-Cabezón and Henry P. Wynn.
	Betti numbers and minimal free resolutions for multi-state system reliability bounds.
	\emph{Journal of Symbolic Computation} 44(9) (2009), 1311--1325.
	\href{https://doi.org/10.1016/j.jsc.2008.06.002}{doi:10.1016/j.jsc.2008.06.002}.
	Related primary conference abstract:
	\emph{Computational algebraic algorithms for the reliability of generalized $k$-out-of-$n$ and related systems},
	Applications of Computer Algebra, 2008,
	\href{https://www.math.unm.edu/~aca/ACA/2008/Proceedings/Nonstandard/Saenz_abstract.pdf}{full text}.

	\bibitem{hochster}
	Melvin Hochster.
	Cohen--Macaulay rings, combinatorics, and simplicial complexes.
	In \emph{Ring Theory II}, Lecture Notes in Pure and Applied Mathematics 26 (1977), 171--223.
	\href{https://sites.lsa.umich.edu/hochster/wp-content/uploads/sites/1337/2026/03/Cohen-Macaulay-Rings-Combinatorics-and-Simplicial-Complexes.pdf}{Author's original-paper scan}.

	\bibitem{mann}
	Ryan L. Mann.
	Simulating quantum computations with Tutte polynomials.
	\emph{npj Quantum Information} 7 (2021), 141.
	\href{https://doi.org/10.1038/s41534-021-00477-0}{doi:10.1038/s41534-021-00477-0};
	\href{https://arxiv.org/abs/2101.00211}{arXiv:2101.00211}.

	\bibitem{nemhauser}
	George L. Nemhauser, Laurence A. Wolsey, and Marshall L. Fisher.
	An analysis of approximations for maximizing submodular set functions---I.
	\emph{Mathematical Programming} 14 (1978), 265--294.
	\href{https://doi.org/10.1007/BF01588971}{doi:10.1007/BF01588971}.

	\end{thebibliography}
	\endgroup