• Computer Science > Distributed, Parallel, and Cluster Computing [Submitted on 15 Sep 2025 (v1), last revised 25 Feb 2026 (this version, v2)] Title:A Uniqueness Theorem for Distributed Computation under Physical Constraint View PDF HTML (experimental)Abstract:Foundational models of computation often abstract away physical hardware limitations • However, in extreme environments like In-Network Computing (INC), these limitations become inviolable laws, creating an acute trilemma among communication efficiency, bounded memory, and robust scalability • Prevailing distributed paradigms, while powerful in their intended domains, were not designed for this stringent regime and thus face fundamental challenges • This paper demonstrates that resolving this trilemma requires a shift in perspective - from seeking engineering trade-offs to deriving solutions from logical necessity • We establish a rigorous axiomatic system that formalizes these physical constraints and prove that for the broad class of computations admitting an idempotent merge operator, there exists a unique, optimal paradigm • Any system satisfying these axioms must converge to a single normal form: Self-Describing Parallel Flows

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  • Computer Science > Distributed, Parallel, and Cluster Computing [Submitted on 15 Sep 2025 (v1), last revised 25 Feb 2026 (this version, v2)] Title:A Uniqueness Theorem for Distributed Computation under Physical Constraint View PDF HTML (experimental)Abstract:Foundational models of computation often abstract away physical hardware limitations. However, in extreme environments like In-Network Computing (INC), these limitations become inviolable laws, creating an acute trilemma among communication efficiency, bounded memory, and robust scalability. Prevailing distributed paradigms, while powerful

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