Emergent 3D Spacetime Geometry and the Computational Origin of Inertia from Non-Markovian Causal Graphs

The persistent irreconcilability between General Relativity and Quantum Field Theory is deeplyrooted in the axiomatic assumption of a differentiable pseudo-Riemannian continuum, which inevitably yields unrenormalizable ultraviolet (UV) divergences at the Planck scale. To resolve thesefoundational pathologies, we introduce the Z-Canvas framework: an open, non-Markovian causalgraph governed by an asynchronous, thermodynamically driven network flow. We demonstrate thatmacroscopic spacetime emerges via stochastic topological percolation, strictly avoiding small-worlddimensional collapse to stabilize at a spectral dimension of Ds ≈ 3. By enforcing a finite localnodal capacity mapped via the Max-Flow Min-Cut theorem, the graph’s algorithmic dynamics intrinsically derive the Bekenstein holographic bound (S ∝ |∂V|) as a topological edge-cut constraintnatively satisfying Strong Subadditivity. Crucially, we establish that classical Newtonian inertia(F = ma) is not an intrinsic scalar property of matter, but an emergent computational latency.The spatial translation of highly entangled topological subgraphs is physically resisted by the network’s continuous rewiring, a process formally governed by a Nakajima-Zwanzig memory kernelmapping abstract Hilbert space latency to classical kinematics via the high-frequency reactive limitof topological dynamic susceptibility. Finally, to ensure strict empirical demarcation, we providea falsifiable prediction regarding transverse holographic noise (∆L ∝ L1/2) and parameterize thehigh-frequency cut-off (ωc ∼ 1011 Hz) via the Maldacena-Shenker-Stanford quantum scramblingbound anchored to the intrinsic Dark Energy vacuum scale, exposing the underlying fundamentaljitter to next-generation interferometers while naturally satisfying current null constraints.