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

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 event[cite: 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 parameters[cite: 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 communication[cite: 775, 781, 782]. God does not play dice; the universe operates on pure geometric algorithms [cite: 806-807]. https://zenodo.org/records/19026440