The Law of Continuity of Being: A Pre-Geometric Variational Framework for the Emergence of Spacetime and Gravity

This paper develops the Law of Continuity of Being (LCS) as a pre-geometric framework from which spacetime and gravity emerge as effective structures. Starting from the apodeictic proposition “Sum”, the work derives a relational ontological substrate (O, ⪯, Ω), constructs a pre-geometric variational principle δD[Ω] = 0, and shows that an effective Lorentzian metric gμν and the Einstein–Hilbert action arise in the continuum limit. A dual reconstruction mechanism is introduced: (1) chain-volume geometry (F_chain) and (2) spectral geometry (F_spec). A computational experiment (Appendix A) verifies the convergence theorem, showing Δ_g → 0 as N → ∞ and an exact spectral dimension d_spec = 2.0000. Matter is identified as a configuration of the defect field φ = Ω_max − Ω, and the corresponding stress-energy tensor emerges without additional postulates. The framework is fully falsifiable through predictions in galactic rotation curves, cosmology, gravitational waves, and black hole structure. Spacetime is not fundamental: it is the visible equilibrium of continuity. This work includes a computational appendix with executable pseudocode and numerical validation of metric convergence and is part of the research program “Law of Continuity of Being (LCS)”.