What question did this study set out to answer?

This work aims to derive hadron jet formation from first principles using k-Foam Theory, eliminating empirical parameters.

March 19, 2026Open Access

Geometric Algorithm of Hadron Production: Local Big Bang Hypothesis — First-Principles Derivation of Jet Formation from k-Foam Axioms

Key Points

This work aims to derive hadron jet formation from first principles using k-Foam Theory, eliminating empirical parameters.
Utilizes five dynamical axioms of k-Foam Theory to describe particle materialization.
Analyzes the relationship between quarks and spatial grid dynamics under extreme tension.
Applies geometric concepts such as the golden ratio and Fibonacci sequence in the derivation of hadron multiplicity.
Derives a logarithmic law of hadron multiplicity as a geometric necessity.
Establishes deterministic symmetry breaking without randomness in the system.
Demonstrates consistency with recent RHIC data on vacuum materialization and spin correlation.

Abstract

In the Standard Model (QCD), hadron jet formation is calculated using the empirical "Lund string model, " which relies on parameter fitting and lacks a fundamental explanation for the timing of string breaking or particle materialization cite: 733-734. Furthermore, the direction of spontaneous symmetry breaking is conventionally treated as a random, probabilistic eventcite: 795. This working paper derives hadron jet formation from first principles using the five dynamical axioms of k-Foam Theory (a discrete geometric framework) and pure geometry (k=3, 4, 5, 6 and the golden ratio φ), completely eliminating empirical parameterscite: 735. We reframe hadron production not as "particle fragmentation, " but as an "emergency defense protocol of the spatial grid"cite: 810: 1. The 4-Phase Local Big Bang: When the k=2 link between quarks reaches the extreme tension of the k=5 transition pass (1. 25 fm), complete disconnection (Connected component = 0) is mathematically prohibited by Axiom 3 cite: 739-742. To prevent spatial collapse, the system forcibly writes the irresolvable tension into the grid as new k=3 defect pairs (explosive materialization via Axiom 5) cite: 745-747. 2. Golden Ratio (φ) Damper: To avoid wave self-interference that would halt grid updates (Axiom 4), the enormous energy dissipates in a Fibonacci fractal cascade cite: 748-749, 760-761. This derives the logarithmic law of hadron multiplicity (N ∝ log_φ (E / 200 MeV) ) as a geometric necessity, not an empirical rule cite: 768-769. 3. Deterministic Symmetry Breaking: The topological phase transition from k=6 (vacuum) to k=4 (spatial block) is deterministically specified by the collision vector axis. No randomness is involved cite: 785, 796-799. 4. Consistency with RHIC Data: The recent observations at RHIC (Feb 2026) regarding vacuum materialization and 100% spin correlation are shown to be theoretically consistent with Axiom 5 (topology conservation), requiring no "spooky" non-local communicationcite: 775, 781, 782. God does not play dice; the universe operates on pure geometric algorithms cite: 806-807. https: //zenodo. org/records/19026440

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