The Fibonacci Hourglass Field: A Symbolic and Recursive Alternative to MOND and Dark Matter

a symbolic and recursive gravitational model that offers a compelling alternative to both MOND and dark matter in explaining galactic rotation curves and orbital stability.

The FHF framework is built on spiral shell recursion, Möbius-based polarity inversion, and mirrored topological symmetry. It naturally produces flat and rising velocity profiles through a two-parameter symbolic law:

v^2(r) = (G * M(r) / r) * (1 + A * r^β)

and is empirically validated across 170+ galaxies using SPARC data.

The model also extends to Solar System dynamics, showing resonance with planetary positions via recursive shell structure. With the addition of an embedded unit system (Appendix I), the FHF becomes both symbolically self-consistent and physically scalable.

This paper is intended as both a theoretical proposal and a symbolic exploration of symmetry, recursion, and the beautiful structure of gravitational systems.