Emergent Spacetime via Discrete Information Updates: A Framework for Reinterpreting Systematic Errors in Continuous Approximations

This paper proposes a novel conceptual framework where spacetime is treated as a secondary construct emerging from discrete information updates at the Planck scale. By employing a "rendering" analogy, we reinterpret the macroscopic universe as a stable projection derived from finite informational processes. Key highlights of this framework include: • Time as Information Differential: We propose an operational definition of time (Δt) as a function of informational entropy states, introduced through the following scaling ansatz: Δt ≈ t_P · ln(Ω_eff) • This reinterprets relativistic time dilation as a modulation of informational sampling rates. • Dark Matter as a Rendering Artifact: We hypothesize that gravitational anomalies are not physical particles but systematic "rendering artifacts" arising from the discrete-to-continuous approximation of spacetime geometry. This is represented by the modified Einstein field equation: G_μν + Λg_μν = 8πG(T_μν + δT_μν^error) • The Non-Coordinate Observer: The functional observer is redefined as a "transducer" that acts as a non-coordinate information-processing origin (sink/source), providing a bridge between informational discreteness and macroscopic continuity. • Operational Singularity: The observer is treated as a reference structure exterior to the rendered coordinates. • Conceptual Scope: Issues regarding multi-observer synchronization are reserved for future frameworks. Conclusion: Treating Dark Matter as a computational artifact and time as an entropic differential offers a path to unify discrete information theory with macroscopic physics. This model establishes a foundational "question" regarding the informational origins of spacetime.