Kappa Method v2.5: Formal Proposal with Historical Validation and Transition Taxonomy

Formal proposal of Kappa Method v2.5, a layered framework for analyzing structural vulnerability in complex systems through structural capacity, attractor geometry, and probabilistic hazard modeling. Layer 1 introduces a definitional measure of structural capacity based on accumulated system memory. Layer 2 proposes a geometric extension via attractor reconstruction, testing the hypothesis that dynamical reconfiguration precedes structural degradation. Layer 3 defines a probabilistic hazard model integrating capacity depletion, rigidity, and geometric activation. This version incorporates historical lead-time analysis, an explicit observability taxonomy (including left-censored and degenerate baseline regimes), and a formal distinction between shock-driven geometric spikes and gradual structural ramps. Across multiple system domains, preliminary evidence suggests that geometric activation may precede structural degradation in observable cases, although statistical validation remains limited. Three prospective cases are currently under active monitoring to evaluate predictive consistency. The framework is explicitly falsifiable and distinguishes between structural condition and event occurrence, interpreting geometric signals as modulation of impact sensitivity rather than direct prediction of events.