The SKB hypothesis proposes that fundamental particles can be modeled as four-dimensional spacetime Klein bottles. Each particle is composed of three sub‑SKBs representing quark-like components that merge into a stable SKB structure.
Two core papers outline this idea:
- A Categorical Framework for Topological Features of Spacetime Klein Bottles in Particle Physics
- 4D Spacetime Klein Bottles as Fundamental Particle Models
These papers describe how topological invariants, such as orientability, Euler characteristic, and intersection forms, correspond to particle properties like mass and charge.
The 4D Manifold Explorer visualizes individual sub‑SKBs and their merged forms using Plotly.js and Three.js. Twist parameters control how sub‑SKBs combine, mirroring the theoretical mechanisms described in the research. The evolutionary algorithm searches parameter space for configurations that satisfy the topological conditions laid out in the SKB hypothesis.
Interactive visualizations let users explore how varying twists and loop factors influence the resulting manifold, providing an engaging way to test the hypothesis.