About the κ\kappa-Framework

The κ\kappa-framework is an exploratory initiative in Natural Mathematics: an approach to dynamical systems and physics that prioritizes state-space mechanics and environmental response over static universal constants.

About the Author

Jack Pickett is a Senior Systems Engineer and Independent Researcher based in Cornwall, UK. With over a decade of experience building high-resilience production systems, he brings a software architect's discipline to theoretical physics. His work focuses on the intersection of dynamical systems, numerical simulation, and empirical data analysis.

Environmental Response

What began as a study into the orientation-switching mechanics of quadratic maps has evolved into a unified empirical framework for understanding gravitational anomalies, from planetary perihelion drift to galaxy rotation curves.

Traditional physics often relies on "dark" unobserved entities to balance the books when observations deviate from theory. The κ\kappa-framework proposes an alternative: spacetime curvature responds not just to mass, but to the dynamical environment.

By introducing a curvature-response parameter, κ\kappa, we can model complex systems, whether chaotic mathematical attractors or spiral galaxies, using local deterministic rules within a fully baryonic framework.

Key Research Streams

The Architecture

This site serves as a live laboratory for these ideas. The same principles that govern a high-stakes transaction flow in a production system govern the stability of an orbit in a solar system.

  1. Correctness: grounded in high-precision numerical simulation.
  2. Clarity: visualized through diagnostics that expose internal state.
  3. Reproducibility: supported by public review and open-source implementation.

Code and Reproducibility

The analysis pipeline is implemented in Python. The repository includes data ingestion routines, model fitting procedures, and scripts used to generate the figures and statistical results presented throughout the project.