The Abebe Tensility Framework — The Geometry of Failure —

A candidate cross-domain framework for identifying and monitoring structural instability across heterogeneous systems. At its core is the Abebe Tensility Index (Φ_z), the dimensionless ratio of destabilizing pressure (τ) to cohesive integrity (V_k). Key Contributions • Canonical Ratio: Formalizes Φ_z = τ / V_k and identifies a recurrent transition regime near Φ_z ≈ 2.0, associated with the progression from organized structural coherence toward fragmentation (parity exhaustion). • Cross-Domain Calibration: Provides illustrative empirical alignment across mechanical systems (ductile fracture in structural alloys), biological systems (oxygen extraction limits in human physiology), and macro-financial systems…