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Abstract

N=1/F-Theory Resolutions

Deep Bhattacharjee

Electro-Gravitational Space Propulsion Laboratory (EGSPL), Bhubaneswar, Odisha, India

945 - 982
Vol.21, Issue 1, Jan-Jun, 2026
Receiving Date: 2026-05-12
Acceptance Date: 2026-06-01
Publication Date: 2026-06-03
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http://doi.org/10.37648/ijps.v21i01.022

Abstract

This paper develops a compact framework for four-dimensional N=1 F-theory on resolved elliptic Calabi–Yau fourfolds. The discussion starts from the Weierstrass model, keeps track of crepant resolution data, and follows the same classes through the Shioda map, the shifted G?-flux law, tadpole cancellation, matter-surface indices, and residue formulae for holomorphic Yukawa couplings. The main point is that these calculations can be placed in one clean sequence of lattice, Chow-ring, and Deligne-cohomology steps. Within the stated admissible class, the flux set is finite, chiral indices are integral, hypercharge masslessness becomes a lattice condition, and local Yukawa entries reduce to finite residue algebra. The paper also gives worked SU(5), SO(10), Pati–Salam, E?, and abelian-sector computations with diagrams and full reference data.


Keywords: F-theory; Calabi–Yau fourfolds; G?-flux; Shioda maps; singularity resolution; N=1 compactifications; moduli stabilization; swampland; Deligne cohomology; Yukawa couplings.


References
  1. C. Vafa, *Evidence for F-Theory*, Nucl. Phys. B 469, 403–418. arXiv:hep-th/9602022.
  2. D. R. Morrison and C. Vafa, Compactifications of F-theory on Calabi–Yau Threefolds II, Nucl. Phys. B 476, 437–469 (1996). doi:10.1016/0550-3213(96)00369-0; arXiv:hep-th/9603161.
  3. T. Weigand, TASI Lectures on F-theory, PoS TASI2017, 016. arXiv:1806.01854.
  4. D. R. Morrison and C. Vafa, Compactifications of F-theory on Calabi–Yau threefolds I, Nucl. Phys. B 473, 74–92 (1996). doi:10.1016/0550-3213(96)00242-8; arXiv:hep-th/9602114.
  5. D. Bhattacharjee, The Critical Line from First Principles: A Complete Unconditional Liouville-Collar Closure of the Riemann Hypothesis, International Journal of Research in Science and Technology 16(2), 9–54. doi:10.37648/ijrst.v16i02.002.
  6. T. W. Grimm, The N=1 effective action of F-theory compactifications, Nucl. Phys. B 845, 48–92. arXiv:1008.4133
  7. V. Braun and D. R. Morrison, F-theory on genus-one fibrations, JHEP 08, 132. arXiv:1401.7844
  8. R. Ghora, D. Bhattacharjee, P. Nandi, et al., O’Neill–Calabi– Yau curvature: Reference implementation v1.0.0, Preprints.org (2026). doi:10.20944/preprints202602.0125.v1.
  9. D. R. Morrison and W. Taylor, Classifying bases for 6D Ftheory models, Central Eur. J. Phys. 10, 1072–1088 (2012). doi:10.2478/s11534-012-0126-3; arXiv:1201.1943
  10. D. Bhattacharjee, Zero-Defect Algebraization from First Principles: A Complete Unconditional Closure of the Hodge Conjecture, International Journal of Inventions in Engineering and Science Technology 12(1), 72–113. doi:10.37648/ijiest.v12i01.009
  11. D. R. Morrison and W. Taylor, Toric bases for 6D F-theory models, Fortsch. Phys. 60, 1187–1216. arXiv:1204.0283.
  12. M. Esole and S.-T. Yau, Small resolutions of SU(5)-models in F-theory, Adv. Theor. Math. Phys. 17, 1195–1253 (2013). doi:10.4310/ATMP.2013.v17.n6.a1; arXiv:1107.0733.
  13. D. Bhattacharjee, Unconditional Closure of P versus NP: Fourier–Entropy Obstruction, Spectral Saturation, and Curvature-Guided Descent, International Journal of Research in Science and Technology 16(2), 62–105. doi:10.37648/ijrst.v16i02.004.
  14. M. Esole, S.-H. Shao and S.-T. Yau, Singularities and gauge theory phases, Adv. Theor. Math. Phys. 19, 1183–1247. arXiv:1402.6331.
  15. A. P. Braun, A. Collinucci and R. Valandro, G-flux in F-theory and algebraic cycles, Nucl. Phys. B 856, 129–179. arXiv:1107.5337
  16. D. Bhattacharjee, U. Bhattacharya and S. Ghosh, One Missing Axiom for the Complete Closure of the Heterotic Landscape: Resonance Classifier of a Vibrating String Creates the Typical Particle Classes, Preprints.org (2026). doi:10.20944/preprints202603.0792.v2.
  17. M. Cvetic and L. Lin, The global gauge group structure of F-theory compactification with U(1)s, JHEP 01, 157. arXiv:1706.08521.
  18. M. Cvetic and L. Lin, TASI lectures on abelian and discrete symmetries in F-theory, PoS TASI2017, 020. arXiv:1809.00012.
  19. D. Bhattacharjee, Calabi–Yau Saturation Universality: Toric Mirror Laws, Hodge Statistics, and the Higher-Dimensional Landscape, International Journal of Professional Studies 21(1), 211–256. doi:10.37648/ijps.v21i01.017.
  20. F. Marchesano, D. Prieto and M. Wiesner, F-theory flux vacua at large complex structure, JHEP 08, 077. arXiv:2105.09326.
  21. Y. Honma and H. Otsuka, On the flux vacua in F-theory compactifications, Phys. Rev. D 96, 126006. arXiv:1706.09417.
  22. D. Bhattacharjee, P. Samal, R. Sadhu and S. Singha Roy, Geometric suppression of the electroweak scale from Calabi–Yau singularities, Preprints.org (2026). doi:10.20944/preprints202603.0916.v1.
  23. W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP 12, 164. arXiv:1511.03209.
  24. M. Cvetic, J. Halverson, L. Lin, M. Liu and J. Tian, A Quadrillion Standard Models from F-theory, Phys. Rev. Lett. 123, 101601 (2019). doi:10.1103/PhysRevLett.123.101601; arXiv:1903.00009.
  25. D. Bhattacharjee, Higher-Dimensional Calabi–Yau Manifolds and Dimensional Saturation, SSRN Electronic Journal. doi:10.2139/ssrn.6429958.
  26. H. Hayashi, T. Kawano, Y. Tsuda and T. Watari, More on dimension-4 proton decay problem in F-theory, Nucl. Phys. B 823, 47–115 (2009). arXiv:0901.4941.
  27. S. Cecotti, M. C. N. Cheng, J. J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv preprint (2009). arXiv:0910.0477.
  28. S. Bhattacharjee, P. Samal, D. Bhattacharjee, S. Singha Roy, P. Nandi and S. N. Thakur, Pontryagin integrals and characteristicclass constraints on Calabi–Yau fourfolds, SSRN preprint (2026). doi:10.2139/ssrn.6226138.
  29. S.-J. Lee and T. Weigand, Swampland bounds on the abelian gauge sector, Phys. Rev. D 100, 026015. arXiv:1905.13213.
  30. M. Bies, M. E. Mikelsons and A. P. Turner, FTheoryTools: Advancing computational capabilities for F-theory research, arXiv preprint (2025). arXiv:2506.13849.
  31. D. Bhattacharjee and S. Singha, Brane-cluster UV completion of quantum gravity, Research Square (2026). doi:10.21203/rs.3.rs9053205/v1.
  32. S. Sethi, C. Vafa and E. Witten, Constraints on low-dimensional string compactifications, Nucl. Phys. B 480, 213–224. arXiv:hepth/9606122.
  33. E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22, 1–13. arXiv:hep-th/9609122.
  34. F. Denef and M. R. Douglas, Distributions of flux vacua, JHEP 05, 072. arXiv:hep-th/0404116.
  35. P. Samal, D. Bhattacharjee, R. Sadhu and coauthors, Buggy loci as pathological subsets of non-compact Calabi–Yau moduli spaces, Preprints.org (2026). doi:10.20944/preprints202601.2065.v1.
  36. S. Ashok and M. R. Douglas, Counting flux vacua, JHEP 01, 060. arXiv:hep-th/0307049.
  37. S. B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66, 106006. arXiv:hep-th/0105097.
  38. R. Friedman, J. Morgan and E. Witten, Vector bundles and F theory, Commun. Math. Phys. 187, 679–743. arXiv:hep-th/9701162.
  39. D. Bhattacharjee and A. Harikant, Perturbative Norm for Associated Spreading of Diseases, Research Square (2020). doi:10.21203/rs.3.rs-117165/v1.
  40. R. Donagi and T. Pantev, Torus fibrations, gerbes, and duality, Mem. Amer. Math. Soc. 193. arXiv:math/0306213.
  41. A. Clingher, R. Donagi and M. Wijnholt, The Sen limit, Adv. Theor. Math. Phys. 18, 613–658. arXiv:1212.4505.
  42. M. Cvetic, D. Klevers, H. Piragua and W. Taylor, General U(1) x U(1) F-theory compactifications and beyond, JHEP 11, 204. arXiv:1507.05954.
  43. D. Bhattacharjee, S. Singha Roy and coauthors, Phase transitions in artificial general intelligence: Scaling laws, predictability limits, and singularity dynamics, Research Square (2026). doi:10.21203/rs.3.rs-9055490/v1.
  44. N. Raghuram and W. Taylor, Large U(1) charges in F-theory, JHEP 10, 182. arXiv:1809.01666.
  45. A. Sen, F-theory and orientifolds, Nucl. Phys. B 475, 562–578. arXiv:hep-th/9605150.
  46. S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68, 046005. arXiv:hep-th/0301240
  47. D. Bhattacharjee, P. N. Bose, P. Samal and coauthors, Ramanujan τ-function and its relationship with PSL(2, Z) for L24(τ) +, E, Research Square (2023). doi:10.21203/rs.3.rs-2796280/v1.
  48. C. Beasley, J. J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory I, JHEP 01, 058. arXiv:0802.3391.
  49. C. Beasley, J. J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory II, JHEP 01, 059. arXiv:0806.0102.
  50. J. J. Heckman and C. Vafa, Flavor hierarchy from F-theory, Nucl. Phys. B 837, 137–151. arXiv:0811.2417.
  51. D. Bhattacharjee, On the hierarchy problem of particle physics, TechRxiv (2023). doi:10.36227/techrxiv.23690364.v1.
  52. J. Marsano, N. Saulina and S. Schafer-Nameki, F-theory compactifications for supersymmetric GUTs, JHEP 08, 030. arXiv:0904.3932.
  53. J. Marsano, N. Saulina and S. Schafer-Nameki, Compact F-theory GUTs with U(1)PQ, JHEP 04, 095 (2010). arXiv:0912.0272.
  54. H. Hayashi, T. Kawano, Y. Tatar and T. Watari, Codimension-3 singularities and Yukawa couplings in F-theory, Nucl. Phys. B 823, 47–115. arXiv:0901.4941.
  55. D. Bhattacharjee, The expulsion of super-intelligence, Preprints.org (2021). doi:10.20944/preprints202104.0353.v1.
  56. T. W. Grimm and T. Hayashi, F-theory fluxes, chirality and Chern-Simons theories, JHEP 03, 027. arXiv:1111.1232.
  57. A. P. Braun, T. W. Grimm and J. Keitel, New global F-theory GUTs with U(1) symmetries, JHEP 09, 154. arXiv:1302.1854.
  58. C. Mayrhofer, E. Palti, O. Till and T. Weigand, Discrete gauge symmetries by Higgsing in four-dimensional F-theory compactifications, JHEP 12, 068. arXiv:1408.6831.
  59. D. Bhattacharjee, Consolidated Closure Dossier and Authorial Research Ledger 2026: Verification-Ledger Approaches to the Riemann Hypothesis, the Hodge Conjecture, and P versus NP, PhilArchive record BHACCD (2026). https://philarchive.org/ rec/BHACCD.
  60. D. Klevers, D. R. Morrison, N. Raghuram and W. Taylor, Exotic matter on singular divisors in F-theory, JHEP 11, 124. arXiv:1706.08194.
  61. L. B. Anderson, J. Gray, N. Raghuram and W. Taylor, Matter in transition, JHEP 04, 080. arXiv:1512.05791.
  62. P. Candelas and X. de la Ossa, Moduli space of Calabi–Yau manifolds, Nucl. Phys. B 355, 455–481.
  63. D. Bhattacharjee, S. Singha Roy and P. Samal, Engineering Macroscopic Wormholes via Planck-Scale Quantum Backreaction, Preprints.org (2025). doi:10.20944/preprints202507.1598.v3.
  64. P. S. Aspinwall and M. Gross, The SO(32) heterotic string on a K3 surface, Phys. Lett. B 387, 735–742. arXiv:hep-th/9605131.
  65. F. Denef, M. R. Douglas and B. Florea, Building a better racetrack, JHEP 06, 034. arXiv:hep-th/0404257.
  66. S. Gukov, C. Vafa and E. Witten, CFTs from Calabi–Yau fourfolds, Nucl. Phys. B 584, 69–108. arXiv:hep-th/9906070.
  67. S. N. Thakur and D. Bhattacharjee, Cosmic speed beyond light: Gravitational and cosmic redshift, Preprints.org (2023). doi:10.20944/preprints202310.0153.v1.
  68. M. R. Douglas, The statistics of string/M theory vacua, JHEP 05, 046. arXiv:hep-th/0303194.
  69. M. Bershadsky, K. Intriligator, S. Kachru, D. R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481, 215–252. arXiv:hep-th/9605200.
  70. E. Witten, Non-perturbative superpotentials in string theory, Nucl. Phys. B 474, 343–360. arXiv:hep-th/9604030.
  71. D. Bhattacharjee, Hopf-like Fibrations on Exotic Spheres and Their Geometric Structures, SSRN Electronic Journal (2026). doi:10.2139/ssrn.6440138.
  72. D. S. Freed, Dirac charge quantization and generalized differential cohomology, Surveys Diff. Geom. 7, 129–194. arXiv:hepth/0011220
  73. M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M-theory, J. Diff. Geom. 70, 329–452. arXiv:math/0211216.
  74. K. Gomi, Twisted differential cohomology, preprint. arXiv:0801.1754.
  75. A. Harikant, S. Singha Roy and D. Bhattacharjee, Computing the temporal intervals by making a Thorne–Morris wormhole from a Kerr black hole in the context of gravity, International Journal of Scientific Research and Management 9(7), AA–2021–72–92 (2021). doi:10.18535/ijsrm/v9i07.aa01.
  76. J. Simons and D. Sullivan, Structured vector bundles define differential K-theory, Quanta of Maths, Clay Math. Proc. 11, 579–599
  77. V. V. Batyrev, Dual polyhedra and mirror symmetry for Calabi– Yau hypersurfaces in toric varieties, J. Alg. Geom. 3, 493–535. arXiv:alg-geom/9310003.
  78. M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four dimensions, Adv. Theor. Math. Phys. 4, 1209– 1230. arXiv:hep-th/0002240.
  79. D. Bhattacharjee, S. Singha Roy and R. Sadhu, The split singularity hypothesis, TechRxiv (2023). doi:10.36227/techrxiv.22817036.v1.
  80. S. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497, 146–154. arXiv:hep-th/9606086.
  81. R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15, 1237–1317. arXiv:0802.2969.
  82. D. Bhattacharjee, Astrophysical signatures of warp-drive activity in the Milky Way, SSRN Electronic Journal (2025). doi:10.2139/ssrn.5341129.
  83. D. Bhattacharjee, Holonomic Quantum Computing, SSRN Electronic Journal. doi:10.2139/ssrn.6066428.
  84. D. Bhattacharjee, Hopf-Like Fibrations on Exotic Spheres and Their Geometric Structures, SSRN Electronic Journal. doi:10.2139/ssrn.6440138.
  85. D. Bhattacharjee, Neuromorphic Grothendieck Topoi for Grid-Embedded Proof Systems, SSRN Electronic Journal. doi:10.2139/ssrn.6194939.
  86. D. Bhattacharjee, Framework for Symplectic Holonomic Quantum Architecture, SSRN Electronic Journal. doi:10.2139/ssrn.6326638
  87. D. Bhattacharjee, Emergent Quantum Gravity via Brane Clustering, SSRN Electronic Journal. doi:10.2139/ssrn.5315196.
  88. D. Bhattacharjee, Quantum Algorithms on Symplectic State Manifolds, SSRN Electronic Journal. doi:10.2139/ssrn.6114107.
  89. D. Bhattacharjee, Constructing Exotic Calabi–Yau 3- Folds via Quantum Inner State Manifolds, Preprints.org. doi:10.20944/preprints202505.0700.v1.
  90. D. Bhattacharjee, Seed Universality for Reflexive Polytopes in Dimension Four, Preprints.org. doi:10.20944/preprints202603.1056.v1.
  91. D. Bhattacharjee, On Equivalences in Calabi– Yau Geometry from String Theory, Preprints.org. doi:10.20944/preprints202602.0462.v1
  92. D. Bhattacharjee, Topological Slice Structures in Calabi–Yau Manifolds, Preprints.org. doi:10.20944/preprints202603.0911.v1
  93. D. Bhattacharjee, SU(n) Holonomy Deviations in Calabi–Yau Manifolds CY1–CY4, Preprints.org. doi:10.20944/preprints202602.0023.v1.
  94. D. Bhattacharjee, Three Generations from Six: Realizing the Standard Model via Calabi–Yau Compactification with Euler Number Six, Preprints.org. doi:10.20944/preprints202505.0080.v1.
  95. D. Bhattacharjee, Enriques and Kummer Surfaces Arising from K3 Involutions, Preprints.org. doi:10.20944/preprints202602.0098.v1.
  96. D. Bhattacharjee, Renormalization of Spacetime Dimension, Preprints.org. doi:10.20944/preprints202602.0531.v1.
  97. D. Bhattacharjee, Partitioning the Critical Strip: A Nyman–Beurling Approach, Preprints.org. doi:10.20944/preprints202506.0772.v1
  98. D. Bhattacharjee, Spectral and Analytic Structure of the Nyman–Beurling–Baez-Duarte Approximation, Preprints.org. doi:10.20944/preprints202506.0772.v2.
  99. D. Bhattacharjee, Calabi–Yau Solutions for Cohomology Classes, TechRxiv. doi:10.36227/techrxiv.23978031.v1.
  100. D. Bhattacharjee, Enumerative Norms through Quantum Cohomological Connectivity over Gromov–Witten Invariants, TechRxiv. doi:10.36227/techrxiv.19524214.v1.
  101. D. Bhattacharjee, Geometry and Topology through Geometrization and Uniformization for Thurston Geometries, TechRxiv. doi:10.36227/techrxiv.20134382.v1.
  102. D. Bhattacharjee, A Coherent Approach Towards Quantum Gravity, TechRxiv. doi:10.36227/techrxiv.19785880.v1.
  103. D. Bhattacharjee, Endomorph L-Current for Infinite Genera Category, TechRxiv. doi:10.36227/techrxiv.23664420.
  104. D. Bhattacharjee, Solutions of Kerr Black Holes Subject to Naked Singularity and Wormholes, TechRxiv. doi:10.36227/techrxiv.23676897.v1.
  105. D. Bhattacharjee, Atiyah–Hirzebruch Spectral Sequence on Reconciled Twisted K-Theory over S-Duality, Authorea. doi:10.22541/au.165212310.01626852/v1.
  106. D. Bhattacharjee, Uniqueness in Poincare–Birkhoff– Witt Theorem over Algebraic Equivalence, Authorea. doi:10.22541/au.165511635.53854231/v1.
  107. D. Bhattacharjee, Positive Energy Driven CTCs in ADM 3+1 Space–Time of Unprotected Chronology, Preprints.org (2021). doi:10.20944/preprints202104.0277.v1.
  108. D. Bhattacharjee, P. Samal, R. Sadhu, S. Singha Roy, S. Bhattacharya and S. N. Thakur, Deciphering Black Hole Spin, Inclination Angle and Charge from Kerr Shadow, Preprints.org (2021), 2021040315. doi:10.20944/preprints202104.0315.v1.
  109. D. Bhattacharjee, Establishing Equivalence among Hypercomplex Structures via Kodaira Embedding, Research Square. doi:10.21203/rs.3.rs-1635957/v1.
  110. D. Bhattacharjee, Generalization of Grothendieck Duality over Serre Duality in Cohen–Macaulay Schemes, Research Square. doi:10.21203/rs.3.rs-1781474/v1.
  111. D. Bhattacharjee, Suspension of Structures in Two-Dimensional Topologies with Genus Deformations, Research Square. doi:10.21203/rs.3.rs-1798323/v1.
  112. D. Bhattacharjee, Generalized Poincare Conjecture via Alexander Trick and h-Cobordism, Research Square. doi:10.21203/rs.3.rs1830184/v1.
  113. D. Bhattacharjee, Generalization of Quartic and Quintic Calabi– Yau Manifolds Fibered by Polarized K3 Surfaces, Research Square. doi:10.21203/rs.3.rs-1965255/v1.
  114. D. Bhattacharjee, Relating Enriques Surfaces with K3 and Kummer Through Involutions, Research Square. doi:10.21203/rs.3.rs2011341/v1.
  115. D. Bhattacharjee, Eliminating Hyperbolic Curvature of Nine Dimensions in Quotient Space, Research Square. doi:10.21203/rs.3.rs-2879172/v1.
  116. R. Sadhu, D. Bhattacharjee, S. Bhattacharya and S. N. Thakur, E8 × E8 Heterotic Gravity and M-Theory, SSRN Electronic Journal (2026). doi:10.2139/ssrn.6326718.
  117. D. Bhattacharjee, Homotopy Group of Spheres, Hopf Fibrations and Villarceau Circles, EPRA International Journal of Multidisciplinary Research (2022). doi:10.36713/epra11212.
  118. D. Bhattacharjee, P. Nandi and S. N. Thakur, Almost Impossible Calabi–Yau Manifolds: Hodge Realization, Full-Measure SYZ Lifting, and Dimensional Saturation, PhilArchive record BHAAIC (2026). URL: https://philarchive.org/rec/BHAAIC.
  119. D. Bhattacharjee, P. Nandi and O. Frederick, Numerical Ricci-flat metrics on the quintic threefold, Preprints.org preprint (2025). doi:10.20944/preprints202505.0202.v1.
  120. D. Bhattacharjee, Hopf-like fibrations on Calabi–Yau manifolds, Preprints.org (2025). doi:10.20944/preprints202504.2581.v4.
  121. D. Bhattacharjee, Homotopy groups of spheres, Hopf fibrations and Villarceau circles II, Preprints.org (2026). doi:10.20944/preprints202602.2038.v1.
  122. R. Ghora, D. Bhattacharjee, P. Nandi, P. Samal, R. Patra, S. Singha Roy and S. Bhattacharya, O’Neill Tensor Bounds for Riemannian Submersions in Fibred Calabi–Yau Manifolds, Preprints 2026, 2026020125. doi:10.20944/preprints202602.0125.v1.
  123. D. Bhattacharjee, Mandela effect and deja vu: Are we living in a simulated reality?, TechRxiv (2021). doi:10.36227/techrxiv.16680904.v1
  124. D. Bhattacharjee, The gateway to parallel universe and connected physics, Preprints.org (2021). doi:10.20944/preprints202104.0350.v1.
  125. D. Bhattacharjee, One missing axiom for the complete closure of the heterotic landscape: Resonance classifier of a vibrating string creates the typical particle classes, Preprints.org (2026). doi:10.20944/preprints202603.0792.v2.
  126. D. Bhattacharjee, M-theory and F-theory over theoretical analysis on cosmic strings and Calabi–Yau manifolds subject to conifold singularity with Randall–Sundrum model, Asian Journal of Research and Reviews in Physics 6(2), 30–42 (2022). doi:10.9734/ajr2p/2022/v6i230181.
  127. D. Bhattacharjee, Particle origins for string vibrations, Asian Journal of Research and Reviews in Physics 7(3), 8–14 (2023). doi:10.9734/ajr2p/2023/v7i3140.
  128. D. Bhattacharjee, KK Theory and K-Theory for Type II Strings Formalism, Asian Research Journal of Mathematics 19(9), 79–94. doi:10.9734/arjom/2023/v19i9701.
  129. D. Bhattacharjee, Universe Before Big Bang, Asian Journal of Research and Reviews in Physics 6(3), 33–47. doi:10.9734/ajr2p/2022/v6i3120.
  130. D. Bhattacharjee, Positive Energy Driven CTCs in ADM Three plus One Space-Time, Preprints.org. doi:10.20944/preprints202104.0277.v1.
  131. D. Bhattacharjee, Deciphering Black Hole Spin, Inclination Angle and Charge from Kerr Shadow, Preprints.org. doi:10.20944/preprints202104.0315.v1
  132. D. Bhattacharjee, Path Tracing Photons Oscillating Through Alternate Universes Inside a Black Hole, Preprints.org. doi:10.20944/preprints202104.0293.v1.
  133. D. Bhattacharjee, P. Nandi, O. Frederick, P. Samal and S. Bhattacharjee, Higher Topos-Theoretic Closure of the Riemann Hypothesis, PhilPapers record BHAHTC (2026). URL: https: //philpapers.org/rec/BHAHTC.
  134. D. Bhattacharjee, P. Samal and S. Bhattacharjee, Chronology Violation in Einstein–Maxwell Binaries, PhilArchive record BHACVI (2026). URL: https://philarchive.org/rec/BHACVI.
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