PFUSRC-047 Paths Are Not Stochastic Competition The Estimation-Avoidance-Selection Anchoring Mechanism Ontological Limitations of Feynman Path Integrals and the Unified Meta-Framework of the Global Path Formula

The Feynman path integral is a foundational mathematical tool in quantum mechanics. Its popular interpretation often portrays microscopic processes as “particles traversing all possible paths simultaneously, with paths canceling one another until only one remains.” This paper argues that the path integral itself carries no ontological commitment; the issue lies in the popular interpretation that mistakes mathematical equivalence for physical reality, implicitly assuming an ontology of stochastic competition and passive cancellation. Drawing on the PFUSRC biconic ontology, this paper demonstrates that no continuous paths exist at the ontological layer; only discrete \Psi-\Xi anchoring events are present. The actual microscopic process is an ordered anchoring sequence of Estimation → Avoidance → Selection, wherein the \Xi-field performs proactive topological risk avoidance rather than passive behavior. A fourfold logical falsification of the “stochastic competition / passive cancellation” hypothesis is presented, addressing energy dissipation, entropy increase, irreconcilable phase and spin topologies, and time delay. The 720^\circ spin recovery property serves as a key empirical anchor, revealing the topologically entangled nature of microscopic particles. From a dimensional-geometric perspective, this paper further demonstrates that fundamental physical equations — the Lagrangian, the Feynman path integral, the Dirac equation, and the Einstein field equations — are all three-dimensional cross-sectional approximations of the four-dimensional biconic ontological topology, inherently discarding the degrees of freedom of the Gap Field, the \Psi/\Xi dual-field screening mechanism, and four-dimensional topological temporal ordering. Accordingly, this paper proposes the Global Path Formula as a unified ontological meta-framework. This framework is not a single computational equation; its core function is to delineate the domains of applicability, the missing degrees of freedom, and the hierarchical positioning of all classical, quantum, and gravitational physical equations. It also subsumes the scattered phenomenological corrections in contemporary frontier physics under a unified global correction logic grounded in four-dimensional ontological topology. This paper accomplishes an ontological reinterpretation of the quantum path problem and provides a unified foundational classificatory paradigm for all fundamental physical equations.