The evolution module searches for compatible Spacetime Klein Bottle (SKB) configurations. It uses a genetic algorithm to evolve sub‑SKB parameters until they meet topological criteria such as Euler characteristic, orientability, and intersection form alignment.
- Initialization: Generate a population of random sub‑SKB twist values and genus selections.
- Fitness Evaluation: Compute each candidate's fitness using weighted sums of Stiefel‑Whitney class match, Euler characteristic proximity, intersection form type, twist alignment, and closed‑timelike‑curve (CTC) stability.
- Selection and Mutation: Choose the best candidates and apply random mutations to twists and genus to create the next generation.
- Compatibility Tracking: Record individuals whose topological properties are mutually compatible, allowing visual inspection of promising pairs.
The /evolution page renders a 3D Plotly scene showing sub‑SKBs as surfaces with
color gradients. Evolution progress is displayed in real time with fitness
metrics in a population grid. Users can adjust generation count, population size,
and mutation rate.
The algorithm uses well‑known topological invariants:
- Euler characteristic and orientability determine manifold type.
- Intersection forms classify four‑manifolds by quadratic form.
- Twist alignment ensures geometric consistency when merging sub‑SKBs. These metrics follow the SKB hypothesis of modeling particles as four‑dimensional Klein bottles.