From Indefinite Causal Order to Definite Process Order: A Topological Reconstruction of the Quantum Switch via Discrete P-Tacts (П-такт)

Description This work develops a process-based reconstruction of the quantum switch and the notion of indefinite causal order by introducing P-tacts (П-tacts) as the primitive units of quantum dynamics. Within this framework, quantum evolution is not described as a sequence of time-ordered operations but as a composition of discrete process units connected through explicit topological relations. The present article builds directly on the foundational introduction of the P-tact as the primitive unit of quantum theory, where process is taken as ontologically prior to state and time is not assumed as a fundamental parameter(Pavlov, P-Tact (П-такт) as the Primitive Unit of Quantum Theory, Zenodo, 2026, DOI: 10.5281/zenodo.18516711). In earlier work, this process ontology was applied to the quantum switch, demonstrating that its behavior emerges naturally from discrete process connectivity rather than from fundamentally indefinite causal relations(Pavlov, Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт), Zenodo, 2026, DOI: 10.5281/zenodo.18498181). The connection between quantum switch behavior and quantum teleportation was subsequently clarified, showing that teleportation can be interpreted as a reindexing of process relations within a shared process topology(Pavlov, Quantum Switch and Teleportation, Zenodo, 2026, DOI: 10.5281/zenodo.18509173). Furthermore, the same P-tact framework was shown to give rise to emergent causality, time, gravity, and three-dimensional space as derived properties of discrete process graph dynamics rather than as fundamental background structures(Pavlov, Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact Dynamics, Zenodo, 2026, DOI: 10.5281/zenodo.18504244). In the present work, these results are unified and extended through the explicit introduction of superposition of process graphs as a formal object. Using pentagonal and pentagram (pentacle) structures constructed from P-tacts, the quantum switch is reconstructed as a definite process topology. The appearance of indefinite causal order is shown to arise solely from projecting this topology onto a time-indexed formalism. No global temporal parameter is required at the fundamental level. All process relations are explicitly defined through connectivity, and control operations occupy superpositions of topological positions, not temporal slots. As a result, indefinite causal order is reclassified as a methodological placeholder, signaling the breakdown of time-based descriptive language rather than a fundamental indeterminacy of nature. The framework preserves all experimentally verified predictions while restoring conceptual coherence. It aligns naturally with the Everett interpretation of quantum mechanics, maintaining universal unitarity and eliminating collapse or exceptional measurement postulates. Quantum branching is interpreted as divergence in process graphs rather than as stochastic temporal events. This work prepares the conceptual and formal ground for subsequent studies on process-based quantum computation and programming, where local, dynamically entangled process modules replace long, phase-accumulating quantum circuits, offering a new architectural approach to decoherence and scalability.