\begin{thebibliography}{99}\raggedright \bibitem{original} D.~Bhattacharjee and U.~Bhattacharya, \emph{Iterated Nerve Complexes for $k$-Fold Sensor Coverage}, Preprints.org, version 2, 2026. \href{https://doi.org/10.20944/preprints202606.1351.v2}{doi:10.20944/preprints202606.1351.v2}. \bibitem{ecog} A.~Bose, D.~Bhattacharjee and U.~Bhattacharya, \emph{Certified Redundant ECoG Coverage: Exact Geometry, Continuous Mesh Certificates and Reproducible Audits}, research and software archive, version 1.6.0, Zenodo, 2026. \href{https://doi.org/10.5281/zenodo.23731783}{doi:10.5281/zenodo.23731783}. \bibitem{sheehy} D.~R.~Sheehy, \emph{A multicover nerve for geometric inference}, Proceedings of the 24th Canadian Conference on Computational Geometry, Charlottetown, 2012. \url{https://mathtube.org/sites/default/files/lecture-notes/e-proceedings.pdf}. \bibitem{corbet} R.~Corbet, M.~Kerber, M.~Lesnick and G.~Osang, \emph{Computing the multicover bifiltration}, Discrete Comput. Geom. \textbf{70} (2023), 376--405. \href{https://doi.org/10.1007/s00454-022-00476-8}{doi:10.1007/s00454-022-00476-8}. \bibitem{alonso} \'{A}.~J.~Alonso, \emph{A sparse multicover bifiltration of linear size}, Discrete Comput. Geom., published online August 4, 2026. \href{https://doi.org/10.1007/s00454-026-00865-3}{doi:10.1007/s00454-026-00865-3}. \bibitem{dowker} C.~H.~Dowker, \emph{Homology groups of relations}, Ann. of Math. (2) \textbf{56} (1952), 84--95. \href{https://doi.org/10.2307/1969768}{doi:10.2307/1969768}. \bibitem{chowdhury} S.~Chowdhury and F.~M\'emoli, \emph{A functorial Dowker theorem and persistent homology of asymmetric networks}, J. Appl. Comput. Topol. \textbf{2} (2018), 115--175. \href{https://doi.org/10.1007/s41468-018-0020-6}{doi:10.1007/s41468-018-0020-6}. \bibitem{bauer} U.~Bauer, M.~Kerber, F.~Roll and A.~Rolle, \emph{A unified view on the functorial nerve theorem and its variations}, Expo. Math. \textbf{41} (2023), no.~4, article 125503. \href{https://doi.org/10.1016/j.exmath.2023.04.005}{doi:10.1016/j.exmath.2023.04.005}. \bibitem{ghrist} R.~Ghrist and A.~Muhammad, \emph{Coverage and hole-detection in sensor networks via homology}, Proceedings of IPSN 2005, IEEE, 2005, 254--260. \bibitem{desilva} V.~de Silva and R.~Ghrist, \emph{Coverage in sensor networks via persistent homology}, Algebr. Geom. Topol. \textbf{7} (2007), 339--358. \href{https://doi.org/10.2140/agt.2007.7.339}{doi:10.2140/agt.2007.7.339}. \bibitem{controlled} V.~de Silva and R.~Ghrist, \emph{Coordinate-free coverage in sensor networks with controlled boundaries via homology}, Int. J. Robot. Res. \textbf{25} (2006), 1205--1222. \bibitem{realalgebraic} J.~Bochnak, M.~Coste and M.-F.~Roy, \emph{Real Algebraic Geometry}, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol.~36, Springer, Berlin, 1998. \href{https://doi.org/10.1007/978-3-662-03718-8}{doi:10.1007/978-3-662-03718-8}. \bibitem{topoi} D.~Bhattacharjee, \emph{Neuromorphic Grothendieck topoi for grid-embedded circuit architectures}, SSRN, 2026. \href{https://doi.org/10.2139/ssrn.6194939}{doi:10.2139/ssrn.6194939}. \bibitem{suspension} D.~Bhattacharjee, \emph{Suspension of structures in two-dimensional topologies with or without the presence of $\mathcal X\ge1$ genus deformations for canonical $2^{2\eta}$ stabilizer points}, Research Square, version 1, 2022. \href{https://doi.org/10.21203/rs.3.rs-1798323/v1}{doi:10.21203/rs.3.rs-1798323/v1}. \bibitem{linkage} S.~Singha Roy, D.~Bhattacharjee and R.~Sadhu, \emph{Instability in the linkage of topological spaces due to background ghosts}, EPRA Int. J. Res. Dev. \textbf{8} (2023), no.~4, 276--279. \href{https://doi.org/10.36713/epra13019}{doi:10.36713/epra13019}. \bibitem{arrangements} E.~Fogel, D.~Halperin and R.~Wein, \emph{CGAL Arrangements and Their Applications: A Step-by-Step Guide}, Geometry and Computing, vol.~7, Springer, 2012. \href{https://doi.org/10.1007/978-3-642-17283-0}{doi:10.1007/978-3-642-17283-0}. \bibitem{coverage2003} C.-F.~Huang and Y.-C.~Tseng, \emph{The coverage problem in a wireless sensor network}, Proceedings of WSNA 2003, ACM, 2003, 115--121. \bibitem{integrated} X.~Wang, G.~Xing, Y.~Zhang, C.~Lu, R.~Pless and C.~Gill, \emph{Integrated coverage and connectivity configuration in wireless sensor networks}, Proceedings of SenSys 2003, ACM, 2003, 28--39. \bibitem{barlow} R.~E.~Barlow and F.~Proschan, \emph{Statistical Theory of Reliability and Life Testing: Probability Models}, Holt, Rinehart and Winston, New York, 1975. \bibitem{polychromatic} B.~Bollob\'as, D.~Pritchard, T.~Rothvoss and A.~Scott, \emph{Cover-decomposition and polychromatic numbers}, SIAM J. Discrete Math. \textbf{27} (2013), no.~1, 240--256. \href{https://doi.org/10.1137/110856332}{doi:10.1137/110856332}. \bibitem{lattice} J.-L.~Marichal, \emph{Weighted lattice polynomials}, Discrete Math. \textbf{309} (2009), no.~4, 814--820. \href{https://doi.org/10.1016/j.disc.2008.01.019}{doi:10.1016/j.disc.2008.01.019}. \bibitem{reliability-lattice} A.~Dukhovny and J.-L.~Marichal, \emph{System reliability and weighted lattice polynomials}, Probab. Engrg. Inform. Sci. \textbf{22} (2008), no.~3, 373--388. \href{https://doi.org/10.1017/S0269964808000223}{doi:10.1017/S0269964808000223}. \bibitem{robustbook} A.~Ben-Tal, L.~El Ghaoui and A.~Nemirovski, \emph{Robust Optimization}, Princeton University Press, Princeton, 2009. \href{https://doi.org/10.1515/9781400831050}{doi:10.1515/9781400831050}. \bibitem{hailperin} T.~Hailperin, \emph{Best possible inequalities for the probability of a logical function of events}, Amer. Math. Monthly \textbf{72} (1965), no.~4, 343--359. \href{https://doi.org/10.1080/00029890.1965.11970533}{doi:10.1080/00029890.1965.11970533}. \bibitem{csikos} B.~Csik\'os, \emph{On the volume of flowers in space forms}, Geom. Dedicata \textbf{86} (2001), 59--79. \href{https://doi.org/10.1023/A:1011983123985}{doi:10.1023/A:1011983123985}. \bibitem{aurenhammer} F.~Aurenhammer, \emph{Power diagrams: properties, algorithms and applications}, SIAM J. Comput. \textbf{16} (1987), no.~1, 78--96. \href{https://doi.org/10.1137/0216006}{doi:10.1137/0216006}. \bibitem{toussaint} G.~T.~Toussaint, \emph{Computing largest empty circles with location constraints}, Int. J. Comput. Inf. Sci. \textbf{12} (1983), no.~5, 347--358. \href{https://doi.org/10.1007/BF01008046}{doi:10.1007/BF01008046}. \bibitem{leekvoronoi} D.-T.~Lee, \emph{On $k$-nearest neighbor Voronoi diagrams in the plane}, IEEE Trans. Comput. \textbf{C-31} (1982), no.~6, 478--487. \href{https://doi.org/10.1109/TC.1982.1676031}{doi:10.1109/TC.1982.1676031}. \bibitem{soye} A.~M.-C.~So and Y.~Ye, \emph{On solving coverage problems in a wireless sensor network using Voronoi diagrams}, in: Internet and Network Economics (WINE 2005), Lecture Notes in Comput. Sci., vol.~3828, Springer, Berlin, 2005, 584--593. \href{https://doi.org/10.1007/11600930_58}{doi:10.1007/11600930\_58}. \end{thebibliography}