About This Site
Spacetime Manifolds is a free, interactive resource for exploring the topology and geometry behind the Spacetime Klein Bottle (SKB) hypothesis — a monistic framework in which all particles and forces emerge as non-orientable topological defects in a 4-dimensional Lorentzian manifold with dynamical torsion.
Every demo runs entirely in your browser — no downloads, no plugins, no accounts. The goal is to make beautiful, abstract mathematics tangible: drag a Möbius strip to see its single side, rotate a Klein bottle through its figure-8 self-intersection, explore crosscap particles and their β-decay lifecycle, or spin a tesseract through the fourth dimension.
The Author
This site and the underlying theoretical framework were developed by James B. Cupps. The “Everything is Spacetime” paper (2025) presents the complete 4D Torsional-Topological Spacetime Ontology (4D-TTSO), including the Metric-Affine primitive, axial torsion dynamics, crosscap charge rule, Pin⁻-structure fermion classification, and bordism-based baryon stability.
“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.”
— William Paul Thurston
What You Can Explore
- 01Möbius Strip — Non-orientable surfaces and half-twist counting
- 02Klein Bottle — Closed surfaces that can't be embedded without self-intersection
- 03Crosscap Particles — Quarks, neutrinos & beta decay from non-orientable 4-manifolds
- 04Real Projective Plane — Boy's surface and antipodal identification
- 054D Immersions — Tesseract stereographic projection
- 06Closed Curves — Fundamental groups and winding numbers on the torus
Technology
All visualizations use Three.js for real-time 3D rendering with custom Fresnel glow shaders and reactive lighting. Mathematical formulas are typeset with KaTeX. The application is built on a modern web framework with interactive controls powered by OrbitControls for mouse drag/zoom/rotate.