Mechanized T-Duality and Frontier String Dynamics on K3 × T²: Closing the Loop via LeanFlow Stiff Solvers with Native Duality, Topological Data Analysis, and Lean 4 Certification

This deposit provides the complete reproducible artifacts for the manuscript 'Mechanized T-Duality and Frontier String Dynamics on K3 × T²: Closing the Loop via LeanFlow Stiff Solvers with Native Duality, Topological Data Analysis, and Lean 4 Certification'. The repository introduces LeanFlow, a neuro-symbolic computational architecture bridging stiff non-linear partial differential equation (PDE) solvers with automated theorem proving (Lean 4) and topological data analysis (TDA). Original computational contributions include: (1) Operational Algorithmic Section Condition in Double Field Theory (DFT) embedding Buscher duality into a 2D×2D generalized metric with in-loop AOT contract assertions executing in 12–18 ns; (2) Formal proofs in Lean 4 verifying Fourier–Mukai spherical reflection auto-equivalences on the Mukai lattice Γ^{4,20}, Kummer orbifold singularity resolution (e(X)=24), and discrete Betti invariants; (3) Closed-loop TDA Mapper extraction (187 nodes, 557 edges, β₁=376) certified through an outer IPC verification gate (45 ms); (4) Stiff simulation telemetry across three frontier string dynamics use cases: Langevin tunneling on Kummer orbifolds, Coleman–De Luccia vacuum decay, and boundary tachyon condensation.