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\title[Explicit string vacua and the Geometric Selection Conjecture]{Explicit String Vacua and the Geometric Selection Conjecture}

\author{Deep Bhattacharjee\,\orcidlink{0000-0003-0466-750X}}
\address{Formerly, Electro-Gravitational Space Propulsion Laboratory (EGSPL), Bhubaneswar, Odisha 751030, India}
\address{Formerly, University of Calcutta, Senate House, 87/1 College Street, Kolkata 700073, West Bengal, India}
\email{d.bhattacharjee@erl-forschung.de}
\email{itsdeep@live.com}
\email{egspl@proton.me}
\thanks{\sloppy Corresponding author: Deep Bhattacharjee. Email: \href{mailto:d.bhattacharjee@erl-forschung.de}{d.bhattacharjee@erl-forschung.de}, \href{mailto:itsdeep@live.com}{itsdeep@live.com}, \href{mailto:egspl@proton.me}{egspl@proton.me}; ORCID \href{https://orcid.org/0000-0003-0466-750X}{0000-0003-0466-750X}}
\author{Ushashi Bhattacharya\,\orcidlink{0009-0002-2254-3914}}
\address{Formerly, National Taiwan University, Taipei 106319, Taiwan}
\email{rai.bhattacharya.in@gmail.com}
\thanks{Ushashi Bhattacharya: email \href{mailto:rai.bhattacharya.in@gmail.com}{rai.bhattacharya.in@gmail.com}; ORCID \href{https://orcid.org/0009-0002-2254-3914}{0009-0002-2254-3914}.}

\subjclass[2020]{14J32; 81T30; 14J33; 32G20}
\keywords{heterotic compactification; Calabi--Yau threefold; Dwork pencil; line-bundle model}
\date{27 October 2026}

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