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

A Geometric Theory of Everything [k-Foam Theory v12: Geometric Algorithm of Hadron Production and Local Big Bang Hypothesis] ■ OverviewIn 1915, Einstein intuited that "mass distorts the geometry of space" and aimed for a unified description of the universe using pure geometry. The only piece he lacked was the physical substance of "what is distorting." This paper (k-Foam Theory) attempts to redefine the universe not as a continuum, but as a discrete elastic foam grid with a regular octahedron (k=6) as its basic unit. Adding to the geometric derivations of the fine-structure constant (1/137), Higgs mass (125 GeV), and the resolution of UV divergence, Ver 12 introduces the "first-principles derivation of hadron production (jets)." ■ V12 Major Updates (Chapter 22)Modern physics (Standard Model) describes the phenomenon of countless particles being born in high-energy collisions using the empirical "Lund string model," but it lacks a fundamental reason for "why the string breaks." It also treats the direction of spontaneous symmetry breaking as a "random" event (rolling the dice). v12 geometrically redefines hadron production not as particle fragmentation, but as an "emergency defense protocol of the spatial grid." 1. Deterministic Resolution of Symmetry Breaking (k=6 to k=4 phase transition)Stress concentrates deterministically only along the axis of the collision vector (z-axis). When the tension limit is reached, two vertices drop out, and the remaining four vertices snap (phase transition) into a stable spatial block (k=4). God does not need to play dice; the direction of collapse is geometrically determined from the start. 2. Golden Ratio (phi) Damper and Derivation of Hadron MultiplicityTo prevent the spatial freeze (update halt) caused by wave interference under extreme tension, the dissipated energy is distributed into space through a Fibonacci recursive structure converging to the golden ratio (phi). As a result, the logarithmic law of hadron multiplicity N proportional to log_phi(E / 200 MeV) is derived not as an empirical rule, but from first principles. 3. Theoretical Consistency with RHIC Experimental DataThe "particle pair production from the vacuum" and "100% spin correlation" observed in the February 2026 RHIC experiment are completely consistent with the geometric mechanisms of k-Foam's Axiom 3 (prohibition of complete disconnection) and Axiom 5 (preservation and equal distribution of torsion information). Einstein's intuition was right. "God does not play dice." There is only pure geometry (source code) operating on just five axioms. * This paper is a Working Paper at the hypothesis stage. Quantitative refinement is left open as a future task.