Deriving Physical Constants from Discrete Dynamics and Emergent Structure

We investigate whether several physical constants can be understood as derived consequences of discrete update dynamics rather than independent empirical inputs. Physical evolution is modeled as a sequential algorithm operating in discrete system cycles: elementary constituents are updated one after another, and all sub-cycle behavior is inherently granular, requiring a transport description rather than continuous microscopic fields. From the resulting emergent background organization, we derive structural relations that express the speed of light, Planck’s constant, the fine-structure constant, and the vacuum permittivity in terms of a small set of internal system parameters (cycle time, elementary update action, a microscopic spacing scale, and a geometric transport factor). Physical units enter only through a minimal scale anchoring to established reference quantities; no multi-observable fitting is introduced. When rewritten in these structural variables, the standard QED definition of the fine-structure constant becomes algebraically identical to the effective oscillator-response relation of the emergent background, suggesting that quantum-electrodynamic vacuum relations can be interpreted as macroscopic parametrizations of a single underlying discrete transport-and-response structure.