Dialectical Tensor Framework (DTF): Mathematical Formalization and Empirical Validation of a Critical Transition

We present the Dialectical Tensor Framework (DTF), which operationalizes material contradiction—the measurable divergence between observable state A and latent potential Ā—as the driver of systemic instability. Applied to the 2025 water crisis in the Lower Jaguaribe Valley (Brazil), DTF classified the system as α-level critical (H=0.83, p<0.01). The Collapse Risk Index reached 100%, with Monte Carlo simulations indicating a 5.85% probability of immediate systemic failure in 2026. Files included in this repository: Manuscript2.pdf: Full paper describing the mathematical formalization and results. Supplementary_Material2.pdf: Mathematical proofs and extended validation protocols. Raw_Data_Inputs.zip: Contains the Parquet files for the Environmental Tensor (Precipitation/Temperature 2000-2025) and Appropriation Tensor (Water Grants/Production). Mineração_Limpeza_DTF.ipynb: Python notebook containing the ETL pipeline and tensor alignment logic.