Geometric Algorithm of Hadron Production: Local Big Bang Hypothesis — First-Principles Derivation of Jet Formation from k-Foam Axioms
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2026
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| _version_ | 1866901353363668992 |
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| author | sato, t |
| author_facet | sato, t |
| contents | <p><br>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].</p> <p>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].</p> <p>We reframe hadron production not as "particle fragmentation," but as an "emergency defense protocol of the spatial grid"[cite: 810]:</p> <p>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].<br>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].<br>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].<br>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].</p> <p>God does not play dice; the universe operates on pure geometric algorithms [cite: 806-807].</p> <p> </p> <p> </p> <p>https://zenodo.org/records/19026440</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19059784 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Geometric Algorithm of Hadron Production: Local Big Bang Hypothesis — First-Principles Derivation of Jet Formation from k-Foam Axioms sato, t Quantum Chromodynamics (QCD) Hadron Jet Lund String Model Spontaneous Symmetry Breaking Golden Ratio Graph Theory k-Foam Theory Determinism RHIC <p><br>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].</p> <p>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].</p> <p>We reframe hadron production not as "particle fragmentation," but as an "emergency defense protocol of the spatial grid"[cite: 810]:</p> <p>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].<br>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].<br>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].<br>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].</p> <p>God does not play dice; the universe operates on pure geometric algorithms [cite: 806-807].</p> <p> </p> <p> </p> <p>https://zenodo.org/records/19026440</p> |
| title | Geometric Algorithm of Hadron Production: Local Big Bang Hypothesis — First-Principles Derivation of Jet Formation from k-Foam Axioms |
| topic | Quantum Chromodynamics (QCD) Hadron Jet Lund String Model Spontaneous Symmetry Breaking Golden Ratio Graph Theory k-Foam Theory Determinism RHIC |
| url | https://doi.org/10.5281/zenodo.19059784 |