k-Foam Theory: Elastic Foam Model of Space and Unified Description of Physical Phenomena

In 1915, Albert Einstein rewrote gravity not as a force, but as the geometric distortion of space. For the next 40 years, he pursued the dream of describing all physical phenomena—including electromagnetism and quantum mechanics—through pure geometry.

He was right, but one piece was missing: the physical substance of what was doing the distorting.

This paper presents k-Foam Theory (Version 10), a hypothetical framework that proposes a candidate for this missing piece. Beginning from a simple survival simulation, the theory suggests that space is not a continuous void but a discrete elastic foam network composed of regular octahedra (k=6)(k = 6)(k=6).

By replacing the “magic” of unexplained forces with the mechanical topology of k-values (3,4,6)(3, 4, 6)(3,4,6), this theory attempts to complete the landscape Einstein envisioned.

Within this geometric framework, five independent physical constants are derived:

• Proton radius

• Nuclear force range

• Weinberg angle

• Electroweak scale

• Higgs boson mass

All are reproduced with errors within approximately 2%.

Additional derivations include:

• Proton mass (error: 0.073%)

• Lepton generation mass ratios

• Dark matter / baryon ratio

• The geometric slip rate of the Fine-structure constant

  α−1≈137\alpha^{-1} \approx 137α−1≈137

What's New in Version 10

1. Axiom 3 Upgraded to Theorem

The philosophical intuition that “nothingness cannot exist”—that is, P=0P = 0P=0 is forbidden—is proven using Graph Theory.

Existence is therefore redefined as a topological necessity:

Graph≠∅\text{Graph} \neq \emptysetGraph=∅

The connected component of the network can never be zero.

2. Elimination of Singularities

Under the Graph≠∅\text{Graph} \neq \emptysetGraph=∅ theorem, the center of a black hole is no longer treated as an infinite collapse of spacetime.

Instead, it becomes the most densely connected location in the universal network, offering a possible geometric resolution to the Black hole information paradox discussed by Stephen Hawking.

Conclusion

This theory does not negate existing physics. Rather, it proposes a fundamental reinterpretation of its premises.

God does not play dice.
There were never any dice to begin with.

There is only geometry.