The Coordination Calculus: Cosmological and Subatomic Limits of the Execution–Interaction–Memory Framework

Abstract This paper develops the cosmological and subatomic implications of the Execution–Interaction–Memory (EIM) framework, demonstrating that fundamental physical phenomena—from neutrino masses to black hole horizons—are asymptotic limits of an underlying algebraic coordination graph. By replacing the traditional continuous spacetime manifold with a discrete pre-geometric ontology, we show that physical laws emerge as phase-specific regimes of graph connectivity. We define the Null Limit of the photon as a state of free coordination current that bypasses Interaction–Memory irreversibility, and a Threshold Limit for the neutrino representing the minimum spectral weight for stable existence in d = 3 spatial dimensions. At the cosmological scale, gravitational and cosmological horizons are reinterpreted as Asymptotic Saturation Limits : black hole singularities are replaced by a Saturation Ceiling where the coordination graph reaches maximal rigidity, while the Big Bang is modeled as a Condensation Transition from a pre-geometric operator space to a percolated manifold. Dark Matter is identified as the Uncoordinated Residue —disconnected graph components that lack topological bridges for gauge interaction but contribute to gravitational curvature. We present a simulation methodology for the coordination phase transition and prove that the strictly monotonic growth of coordination cost establishes Forbidden Cyclicity : a structural barrier to cosmological recollapse mandating an irreversible arrow of time. The cosmological constant problem is resolved by identifying the effective Λ as a derivative of memory debt rather than a vacuum energy density. Five falsifiable predictions are presented, testable at current and next-generation facilities. PACS: 04.60.-m; 04.70.-s; 95.35.+d; 98.80.-k; 98.80.Es; 14.60.Pq