Carlo Calculus: Core Framework and Extended Behavioural Toolkit

This upload presents the complete Carlo Calculus, a structural framework for describing change, unbounded evolution, and stabilising behaviour without limits or infinitesimals. The calculus is defined through three core components: the Carlo Derivative, Infinity as Direction, and Zero as Attractor. These establish how systems evolve locally, how they behave when growth is unbounded, and how they stabilise when drift weakens. A fourth document provides the extended behavioural toolkit, including Carlo Smoothness, Higher Order Behaviour, Trajectory Classes, and Asymptotic Behaviour. These extensions classify system evolution, describe stability patterns, and outline long range behaviour in a structural, operator‑driven way. The Carlo Calculus is designed to be general, intuitive, and compatible with discrete, continuous, hybrid, and symbolic systems. It removes the need for shrinking intervals and replaces them with structural transitions, making it suitable for theoretical research, computational modelling, and systems analysis. This upload contains all four documents in clean, linear, notepad‑style text, consistent with the Carlo Framework standards and ready for researcher use.