Feynman’s path integral treats quantum evolution as a sum over all possible histories, yet mainstream physics cannot explain the ontological origin of path distribution, weight generation, or the emergence of optimal trajectories. Based on the PFUSRC axiom system, this paper addresses three core assertions: (1) The “all-paths” concept is reinterpreted as a global topological spread determined by primordial geometry, not a literal traversal. (2) The observed optimal path is a low-dimensional projection illusion, not the real evolutionary mechanism. (3) The action and path weights are not fundamental; they arise from primordial topology and the Noetic Primordium operator Ω. This paper formalizes the Noetic Primordium as a mathematical operator on path space, defines the β₁ field as the background geometry for nonlocal coherence, and links the Noeton to the valuation axiom. Unifying PFUSRC 18, PFUSRC 22, and PFUSRC 23, this work provides a complete origin-level interpretation of the path integral and an axiomatic foundation for quantum ontology.
Feynman’s path integral treats quantum evolution as a sum over all possible histories, yet mainstream physics cannot explain the ontological origin of path distribution, weight generation, or the emergence of optimal trajectories. Based on the PFUSRC axiom system, this paper addresses three core assertions: (1) The “all-paths” concept is reinterpreted as a global topological spread determined by primordial geometry, not a literal traversal. (2) The observed optimal path is a low-dimensional projection illusion, not the real evolutionary mechanism. (3) The action and path weights are not fundamental; they arise from primordial topology and the Noetic Primordium operator Ω. This paper formalizes the Noetic Primordium as a mathematical operator on path space, defines the β₁ field as the background geometry for nonlocal coherence, and links the Noeton to the valuation axiom. Unifying PFUSRC 18, PFUSRC 22, and PFUSRC 23, this work provides a complete origin-level interpretation of the path integral and an axiomatic foundation for quantum ontology.
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.
This expository companion paper provides an intuitive, non-technical introduction to the core concepts of the PFUSRC theoretical system. Using the natural growth of apples and pears as accessible metaphors, it explains the invisible primordial expansion of Taiyi space, the dual nature of dynamic growth and static steady-state formation, the role of topological anchor points, the function of the β₁ field, and the topological reinterpretation of quantum path phenomena. The paper does not present new mathematical proofs or experimental results; its sole purpose is to build a conceptual bridge to the formal PFUSRC series. It clarifies common misunderstandings of mainstream quantum interpretations and illustrates how the system coherently addresses puzzles such as nonlocal entanglement, cosmic expansion, and quantum coherence in biological systems. All rigorous definitions and derivations are referenced to the corresponding formal papers in the PFUSRC series.
This paper establishes a complete, ontological interpretation of quantum tunneling within the PFUSRC framework, based on the 11-dimensional triple coaxial bicone as the universal primordial structure. Quantum tunneling is not a stochastic effect in 4D spacetime, but a deterministic topological motion occurring in the cone–prism interlayer domain. The mechanism is governed by golden-ratio fractal recursion, gap-driving axiom, inherent symmetry breaking, and the Noetic–Affective dual-terminal drive. This work unifies normal and anomalous tunneling phenomena with a self-consistent, falsifiable, geometrically grounded theory.
This paper starts from the three century-old core puzzles of quantum mechanics, namely double-slit interference, wave function collapse, and the uncertainty principle. Adopting the PFUSRC transcendental topological framework, this study unveils their essential nature: these quantum phenomena do not prove that the universe is fundamentally random, but merely represent inevitable manifestations of the ontology-projection hierarchical structure within low-dimensional observational systems. Measurement constitutes a first-center anchoring request toward the ontological structure. Wave function collapse is defined as deterministic topological ownership locking of projection paths. Quantum uncertainty originates from the active risk-avoidance mechanism of the β₁ topological field under excessive observational perturbation. Furthermore, this paper establishes a rigorous structural definition of reality manifestation. It topological interprets the inherent logical principles behind the propositions that inherent destiny is fixed within an innate baseline boundary while acquired fortune trajectory allows continuous optimization, and that human transcendence is essentially topological alignment with universal ontological order. As a phased culmination of the PFUSRC theoretical system, this research constructs a complete logical chain that unifies quantum mechanical interpretation, individual existential path optimization, and macroscopic civilizational structural evolution.
The path integral is a foundational formalism of quantum mechanics, yet mainstream physics cannot answer: where does the distribution of paths come from? Who determines the weights? How does the system maintain global coherence? Based on the PFUSRC framework, this paper establishes the theory of Cosmic Traffic Rules. Core claims: 1. A path is not a curve in space. A path is the spatiotemporal projection of Ψ-Ξ anchoring relationships (PFUSRC-009). It is the historical trace of anchoring, not a spatial curve.2. The orbital network is determined by bicone topological ontology (PFUSRC-00). All path distributions are predetermined by topological rigidity, not “explored” by particles.3. Coupling Interface 0 is where anchoring occurs. Its projection in the mother universe ontology is the bicone waist ring; its projection in the 4D universe projection layer is the minimal spatial gap.4. The vertex is absolutely impenetrable (PFUSRC-38). Any particle reaching the vertex is reflected — this is a topological prohibition, not a mechanical collision.5. Path conflict triggers exclusion (PFUSRC-004). When ΔA exceeds the tolerance limit, the system triggers deterministic rejection. The excluded structures become dark matter/dark energy.6. Conduction failure can lead to mother universe topological rupture (corollary). When the scale exceeds the synchronization limit of information conduction, breathing desynchronization may trigger structural disintegration. In this paper, π₁ = 12/11 is a presupposed axiom of the PFUSRC system; the complete derivation is found in PFUSRC-001. The containment relationship with general relativity is a physical mapping, not a mathematical equivalence proof.
The photon acts as the core connecting node of relativity, quantum mechanics, electrodynamics and cosmology, yet mainstream physics only treats its masslessness, light-speed propagation, energy quantization and wave-particle duality as empirical input axioms without topological derivation of their necessity. Within the axiomatic PFUSRC biconical topological system, this paper defines photons as instantaneous slicing projection events of global four-dimensional flow state variables on three-dimensional spacetime, which simultaneously serve as the standardized coupling interface for inter-structural energy exchange. All core quantum optical phenomena including wave-particle duality, double-slit interference, delayed choice, EPR nonlocality and vacuum virtual fluctuations are self-consistently deduced from four-to-three dimensional projection constraints without extra ad-hoc hypotheses. This paper proposes the Estimation-Avoidance-Selection anchoring mechanism to replace the stochastic superposition interpretation of Feynman path integrals, reconstructs the topological origin and dynamic stabilization mechanism of Planck’s constant, and strictly proves that Lagrangian mechanics is merely a degenerate projection limit of PFUSRC’s bicone expansion-convergence dynamics under four idealized boundary conditions, rather than a fundamental first principle. Testable experimental corollaries for high-precision quantum optical measurement are put forward at the end.