Computational Reconstruction and Localized Deformation of Spacetime from a Pre-Geometric Ontological Substrate

This work presents a computationally verified pre-geometric framework in which spacetime and stress-energy emerge from a relational ontological substrate. Starting from the variational principle δ𝒟[Ω] = 0, two independent reconstruction mechanisms—chain-volume geometry (𝔽_chain) and spectral geometry (𝔽_spec)—are implemented and shown to converge toward an effective Lorentzian metric. Experiment 1 demonstrates that flat spacetime (Minkowski 1+1) is recovered from a finite ontological substrate, with convergence scaling Δ_g ∼ N-0.83 and exact spectral dimension d_spec = 2.0000, confirming that geometric structure emerges directly from causal order. Experiment 2 introduces non-trivial configurations of the defect field φ = Ω_max − Ω and shows that spacetime deformation is governed by relational gradients rather than amplitude. A strong correlation (r = −0.942) is found between max|∇_O Ω|² and localized metric deformation Δ_g^int − Δ_g^ext. The emergent stress-energy tensor satisfies ‖Tμν(Ω)‖ ∝ max|∇_O Ω|², establishing that matter arises from gradient structure rather than scalar defect magnitude. Across all configurations, the spectral dimension remains invariant, demonstrating that dimensionality is encoded in the causal order and is independent of ontological perturbations. All results are fully reproducible through an explicit computational pipeline provided in the appendix. This work is part of the research program “Law of Continuity of Being (LCS)”.