About the $\kappa$-Framework

The $\kappa$-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. 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.

The Core Philosophy: Environmental Response

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

By introducing a curvature-response parameter, $\kappa$, 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. We believe that logic is universal—the same principles that govern a high-stakes transaction flow in a production system govern the stability of an orbit in a solar system.

Every model presented here is built on three pillars:

1. Correctness: Grounded in high-precision numerical simulation.
2. Clarity: Visualized through interactive diagnostics that expose internal state.
3. Reproducibility: Supported by peer-reviewed research and open-source implementation.

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 — from the scale of global Web3 marketplaces at Dapper Labs to interactive educational platforms — 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.

Code and Reproducibility

The analysis pipeline used is implemented in Python. All code used to generate the figures and statistical results presented in this work is available as open-source software:

github.com/hasjack/OnGravity

This repository includes the full analysis pipeline, data ingestion routines, model fitting procedures, and scripts used to generate the figures presented within the project.

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