Winding Number as Hidden Variable

In the paper's words

This paper proposes that physical reality emerges from a pre-geometric substrate based on the circle S¹, with its integer winding numbers providing a deterministic foundation for physics. A universal computation of pattern writing, evolution, and projection generates spacetime and particles, reinterpreting fundamental constants as geometric scaling factors. Particle mass and identity are determined by the magnitude and prime factorization of the winding number n.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Observations from the Planck satellite and galaxy rotation curves indicate that dark matter constitutes about 27% of the universe’s energy content, yet its particle nature remains unknown, making this a viable hypothesis (Planck Collaboration, 2020).

   from Resolution of

2. The fine-structure constant, approximately 1/137, remains a mystery in this regard, but its dimensionless nature suggests it may be a pure number arising from such a geometric ratio (Mohr, Newell, & Taylor, 2016).

   from The

3. Gravity The numerical factor of $8\pi$ that appears in the Einstein field equations, $G_{\mu\nu} = 8\pi G T_{\mu\nu}$, is conventionally treated as a normalization constant chosen for convenience to match Newtonian gravity in the weak-field limit (Einstein, 1915).

   from The $8\pi$ Projection Factor and Emergent

4. The Bekenstein bound quantifies this limit as $I \leq 2\pi R E / (\hbar c \ln 2)$, where $R$ is the radius and $E$ is the energy (Bekenstein, 1981).

   from The $8\pi$ Projection Factor and Emergent

5. The $8\pi$ factor in gravity can thus be seen as a consequence of how information encoded on a one-dimensional boundary is distributed across a three-dimensional bulk, a concept central to the AdS/CFT correspondence in string theory (Maldacena, 1999).

   from The $8\pi$ Projection Factor and Emergent

6. For instance, the predicted muon-to-electron mass ratio, calculated using $n=207$ for the muon and $n=1$ for the electron, yields a value of 206.76828304.

   from The Unified Particle

How it is done

1. Critically, the winding number serves as a global, topological hidden variable, evading Bell’s theorem and providing a deterministic basis for quantum mechanics without violating experimental results.

   from A

2. This leads to the proposition of a Universal Computational Protocol, a minimal set of operations that define the algorithmic nature of reality.

   from The

3. This interpretation finds support in information-theoretic principles, particularly the holographic principle and the Bekenstein bound.

   from The $8\pi$ Projection Factor and Emergent

4. Precision spectroscopy offers a method to determine the correction coefficients ($\alpha$, $\beta$, $\delta$) in the mass formula.

   from Experimental

What would falsify it

1. The model makes falsifiable predictions for gravitational wave modulation and gamma-ray dispersion.

   from A

2. Similarly, the proton-to-electron mass ratio, derived from the winding number $n=1836$, predicts a value of 1836.152673, which matches the experimental value of 1836.15267343(11) with extraordinary accuracy (Tanabashi et al., 2018).

   from The Unified Particle

3. This refinement allows the model to predict not only the gross properties of particles but also subtle effects like mass splittings within multiplets and the running of coupling constants, bringing it into closer alignment with the full complexity of the Standard Model (Nayak et al., 2008).

   from The Unified Particle

Where the claim stops

1. However, within this framework, they are reinterpreted as emergent scaling factors of the geometric projection map.

   from The

2. They do not represent arbitrary knobs tuned by nature but are mathematical artifacts that arise when translating information from the compact, one-dimensional computational space to the expansive, three-dimensional observational space.

   from The

3. The fine-structure constant, approximately 1/137, remains a mystery in this regard, but its dimensionless nature suggests it may be a pure number arising from such a geometric ratio (Mohr, Newell, & Taylor, 2016).

   from The

Where to read

1. A4,659 words · 20 min