The Hypothesis
Everything is Spacetime
A monistic geometric framework in which all particles and forces emerge as non-orientable topological defects — geons — in a 4-dimensional Lorentzian manifold with dynamical torsion.
◈ Core Premise
Spacetime is the sole fundamental entity — a 4-dimensional Lorentzian manifold . There are no additional quantum fields “living on” the manifold. Instead, matter, charge, and force are emergent descriptions of the manifold's own structural complexity — its topology, torsion, and curvature.
The framework is rooted in the Metric-Affine approach: the connection is independent of the metric, unlocking axial torsion as a dynamical degree of freedom. A symmetry-breaking “Mexican hat” potential forces the torsion field to acquire a non-zero vacuum expectation value, making the vacuum a torsionful medium.
◈ Key Ideas
Non-Orientable Geons
Stable particles are non-orientable worldtubes — Möbius-like structures extended into 4D. A double traversal of the non-orientable cycle reproduces spinor (fermion) behavior.
Pin⁻ Structures & Fermions
The manifold admits a global Pin⁻ structure, the non-orientable generalization of Spin. This lets topological defects carry half-integer spin intrinsically.
Causal Compensation
Internal closed timelike curves (CTCs) inside geon cores are shielded from external observers, preserving global causality while enabling exotic internal geometry.
Crosscap Particle Model
Quarks and leptons are classified by crosscap count n. The charge rule Q(n) = (2 − n)/3 reproduces the fractional charges of the Standard Model.
Bordism Classification
Composite particles (baryons) are classified by the Pin⁻ bordism group Ω₄^{Pin⁻} ≅ ℤ₁₆, providing a topological explanation for baryon stability.
Twist-State Neutrality
The strong force emerges as a topological constraint: bound states must achieve twist-state neutrality, analogous to color confinement in QCD.
◈ Crosscap Charge Table
| Particle | Crosscaps (n) | Q = (2−n)/3 | Topology |
|---|---|---|---|
| Neutrino (ν) | 1 | ⅓ → 0 (neutral) | S¹ ×̃ S³ |
| Up quark (u) | 2 | 0 → +⅔ | 2-crosscap mapping torus |
| Down quark (d) | 3 | −⅓ | 3-crosscap mapping torus |
| Electron (e⁻) | 5 | −1 | 5-crosscap RP⁴ variant |
“Everything emerges from pure geometry — curvature, holonomy, and the interaction of geon worldtubes.”
— James B. Cupps, 2025