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 δ𝒟Ω = 0, two independent reconstruction mechanisms—chain-volume geometry (𝔽chain) and spectral geometry (𝔽ₛpec) —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 Δg ∼ N^-0. 83 and exact spectral dimension dₛpec = 2. 0000, confirming that geometric structure emerges directly from causal order. Experiment 2 introduces non-trivial configurations of the defect field φ = Ωₘax − 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 Δgⁱnt − Δgᵉxt. The emergent stress-energy tensor satisfies ‖T⏛⏜^ (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) ”.