First-Principles Mechanism of Hadron Jet Production: The Universe's Topological Purge Protocol (k-Foam Theory)

In high-energy proton–proton collisions (such as those studied at the LHC or RHIC), hadron jet production is commonly described using phenomenological models such as the Lund string model, in which extended objects stretch and fragment. While successful in practice, such models do not directly address the underlying mechanism by which localized excitations emerge from the vacuum. This working paper, within the k-Foam framework, explores an alternative interpretation in which hadron production is described as a topological relaxation process of an underlying discrete spatial structure. By modeling the vacuum as a k = 6 elastic network, the study investigates whether aspects of jet formation can be described in terms of geometric constraints and local tension redistribution, based on a small set of simplifying assumptions. Key Observations and Hypotheses: On the emergence of hadronic states:Hadron production is interpreted as a release of localized excess tension within the network, potentially corresponding to topological reconfigurations that stabilize the structure.On multiplicity scaling behavior:The dissipation of high local tension may follow branching patterns resembling Fibonacci-like structures, suggesting a possible connection to logarithmic scaling relations of the form N ∝ log(E).On phase-like transitions in collision energy:Experimental data may indicate a transition between different regimes of behavior (e.g., logarithmic vs. enhanced multiplicity growth) in the exactly 19.7 GeV range, which could be interpreted within this framework as a change in dissipation mode.On the geometric interpretation of internal degrees of freedom:Internal quantum numbers (such as color charge) may admit an alternative representation in terms of occupancy configurations within the discrete network structure.On potential observable signatures:The model suggests that underlying geometric symmetries could, in principle, manifest as angular correlations in particle distributions, though this remains speculative. This work is exploratory and does not claim a complete or empirically validated description. Rather, it proposes a geometric perspective in which aspects of high-energy collision phenomena may be reinterpreted in terms of discrete structure and topology.