Verification of Mathematical and Observational Consistency from 10-Dimensional Superstring Theory to 4-Dimensional Cosmology: Anomaly Cancellation, Calabi-Yau Compactification, Swampland Constraints, M-Theory Duality Web, and the AdS/CFT Correspondence

This paper comprehensively verifies the consistency chain extending from the math-ematical quantum consistency inherent in 10-dimensional superstring theory (super-gravity as the low-energy effective theory), through compactification of extra dimen-sions, to the physical constraints imposed on observational data in 4-dimensionalmacroscopic cosmology. Furthermore, we venture into the unified framework offive superstring theories via 11-dimensional M-theory and the holographic principlethrough the AdS/CFT correspondence, challenging the elucidation of superstringtheory.Specifically, we proceed along five main pillars of verification: (i) algebraic ver-ification of the Green–Schwarz anomaly cancellation mechanism for the SO(32)and E8 × E8 gauge groups via SymPy (§2); (ii) topological analysis of Calabi–Yaumanifolds yielding |χ| = 6 and Ng = 3 fermion generations (§3); (iii) evaluationof the tension between the de Sitter Swampland Conjecture, the Trans-PlanckianCensorship Conjecture, and the latest cosmological observations (§4); (iv) numer-ical verification of S-duality and T-duality within the M-theory duality web (§5);(v) quantitative verification of the N 2 scaling of Bekenstein–Hawking entropy andthe 3/4 problem in the AdS/CFT correspondence (§6).All verifications are accompanied by fully reproducible Python (SymPy/Matplotlib)code ensuring computational transparency.