What question did this study set out to answer?

The research aims to establish a theoretical foundation explaining how matter, forces, and spacetime originate from a singular field's dynamics.

April 19, 2026Open Access

Grand Torsion Hypothesis: A Topological Framework for the Origin of Matter, Forces, and Spacetime (v5.6)

Key Points

The research aims to establish a theoretical foundation explaining how matter, forces, and spacetime originate from a singular field's dynamics.
Proposes a framework using non-abelian self-coupling of a primordial field.
Identifies particles and forces with topological structures like knots and loops.
Introduces a method to derive fractional charges based on knot geometry.
Revised identification of protons as (2,3)-torus knots with specific charge characteristics.
Introduced conditions for falsification to strengthen the hypothesis's scientific rigor.
Presented a new observation linking geometric transformations to knot structures.

Abstract

Abstract The Grand Torsion Hypothesis proposes that all physical reality emerges from the self-interacting dynamics of a single primordial field whose non-abelian self-coupling (A ∧ A) gives rise to topological structures — knots, loops, and waves — identified with particles, leptons, and gauge bosons respectively. Version 5. 6 presents a refined qualitative framework in which the proton is identified with the (2, 3) -torus knot (trefoil knot), fractional charges ±2/3e and ∓1/3e are derived from the over/under-strand exposure ratios at the knot's crossings, and the three-dimensionality of space emerges as a necessary condition for stable non-trivial knots. What's new in v5. 6 Reorganized: Reverse-inferred numerical leads (6π⁵ ≈ mₚ/mₑ, 313 MeV crossing-point energy, secondary-twist neutron model) moved from the main text into a standalone Appendix B, explicitly marked as observations rather than claims of the hypothesis. Added: Appendix A "Falsification Conditions" — eight specific experimental outcomes that would refute corresponding parts of the hypothesis, following Popper's criterion of scientific demarcation. Added: A reverse-engineering observation in Appendix B — a 3ds Max modifier stack (Stretch→Twist→Bend) applied to a sphere produces the (2, 3) -torus knot geometry at parameter values corresponding precisely to the knot's topological invariants. Previous versions v4. 1 (2026-04-04, first Zenodo release) established the three-winding proton model and the knot/loop/wave particle classification. v5. 0 (2026-04) added the trefoil charge derivation. v5. 5 (2026-04-17) introduced quantitative leads. v5. 6 (this release) separates unsupported numerical observations from the main claims and explicitly states falsification conditions. Caveat This is a qualitative theoretical framework. The fractional charge derivation in Part II contains a fitting component (see Chapter XXIII honest disclosure). The hypothesis does not yet provide a quantitative particle mass spectrum. Readers interested in the honest assessment of what has and has not been derived are referred to the "Mathematical Feasibility Assessment" section and Appendix A.

Grand Torsion Hypothesis: A Topological Framework for the Origin of Matter, Forces, and Spacetime (v5.6)

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