We present the Coulon-Cartan Framework, a rigorous mathematical language unifying topology, category theory, functional analysis, and applied rheology. Systems are modeled via the Coulon State Tuple (χ, g, τ, η, ζ), enabling a universal stability functional to quantify deformation resilience across physical, mathematical, and computational domains.

We formalize τ-flows, topological membranes (Coulon Spine), and function composition through minimal Lisp and lambda calculus, providing formal theorems, conjectures, and proof scaffolding.

The framework supports practical applications in economics, GIS, materials, cognition, and proof theory, as well as abstract topological thought experiments exploring connectedness, compactness, and categorical limits.

We present the Coulon-Cartan Framework, a rigorous mathematical language unifying topology, category theory, functional analysis, and applied rheology. Systems are modeled via the Coulon State Tuple (χ, g, τ, η, ζ), enabling a universal stability functional to quantify deformation resilience across physical, mathematical, and computational domains. 

We formalize τ-flows, topological membranes (Coulon Spine), and function composition through minimal Lisp and lambda calculus, providing formal theorems, conjectures, and proof scaffolding. 

The framework supports practical applications in economics, GIS, materials, cognition, and proof theory, as well as abstract topological thought experiments exploring connectedness, compactness, and categorical limits.