Universal Hamiltonian as Process Verb: Reconciling Unitary Dynamics with Contextual Collapse via Dedekind Ontologies

The ontological status of quantum mechanics remains suspended between two mutually exclusive grammatical categories: the continuous, reversible “Verb” of unitary evolution and the discrete, irreversible “Noun” of the measured state. This paper reconciles this tension by mapping the physics of time-evolution to the mathematics of Dedekind self-maps and Process Algebra. We demonstrate that while Hamiltonian flow preserves information perfectly (Von Neumann entropy $S=0$), the imposition of a measurement constraint generates significant entropy ($S \approx 2.66$) and an irreversible arrow of time. The findings reveal a structural isomorphism between the physical “collapse” of the wavefunction and the mathematical “Critical Point” of a Dedekind self-map. We propose that the “Noun” (particle/state) is not a fundamental entity but a “precipitation” generated at the limit of the “Verb’s” self-mapping process (Corazza, 2018). This reframes the observer not as an external agent, but as the structural locus of this critical transition.