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April 17, 20260 citationsOpen Access

Toroidal Unification: S¹ × CP¹ × CP² as the Complete Structure of Fundamental Physics

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CGCarlos Javier Perea Gallego

Key Points

  • The aim is to demonstrate that a unique topological structure can explain various physical phenomena without relying on free parameters.
  • Explored spacetime structure S¹ × S² near gravitational sources.
  • Analyzed implications for galaxy rotation curves without dark matter.
  • Predicted physical constants using topological relations.
  • Proposed falsifiable predictions that differentiate this framework from conventional physics.
  • Successfully reproduced classical tests of general relativity.
  • Predicted mass ratio m_p/m_e with high accuracy (0.002%).
  • Matched the inverse fine structure constant 1/α to 0.0002%.
  • Emergence of the Standard Model gauge group from topology alone.
  • Identified exactly three fermion generations based on the Euler characteristic.

Abstract

We show that a single topological ansatz — spacetime near a gravitational source has the structure S¹ × S² — reproduces all classical tests of general relativity, explains galaxy rotation curves without dark matter, and predicts the Schumann resonance from pure geometry. Extending S² = CP¹ to CP² at nuclear scales, the full Standard Model gauge group U (1) × SU (2) × SU (3) emerges from topology alone. The Euler characteristic χ (CP²) = 3 predicts exactly three fermion generations, and the mass ratio mₚ/mₑ = χ (CP¹) × χ (CP²) × π⁵ = 6π⁵ matches observation to 0. 002%. The inverse fine structure constant 1/α = 4π³ + π² + π matches to 0. 0002%. No free parameters are adjusted. Seven falsifiable predictions distinguish this framework from standard physics.

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Cite This Study

Carlos Javier Perea Gallego (2026) studied this question.

synapsesocial.com/papers/69e1cecc5cdc762e9d857c53https://doi.org/10.5281/zenodo.19590356
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