Zero-Sum Ontological Model: Scientific and Philosophical Formalism of the Source Code.

This preprint formalizes the axiomatic framework of the Zero-Sum Ontological Model, establishing the fundamental identity $0 = \Sigma\infty$ and the Null Charge Ground State ($\vert{}0\rangle_{\text{vac}}$, $Q_{\text{net}} = 0$) as the governing ordering principle of the Omniverse. To eliminate the circularity inherent in continuous differential manifolds a priori, space-time is structured as a Discrete Causal Network via a graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$, where space emerges as topological graph distance $e(v_i, v_j) = d_{\mathcal{G}}(v_i, v_j)$ and time as a discrete processing latency $t = \tau \cdot \tau_0$. Vacuum excitation dynamics are driven by an unstable scalar potential $V(\Phi) = -\mu^2 \vert{}\Phi\vert{}^2 + \lambda \vert{}\Phi\vert{}^4$ ($\mu^2, \lambda > 0$) that induces Spontaneous Symmetry Breaking (SSB), generating conjugate perturbation pairs ($+R, -R$). To reconcile active local dynamics with a strictly null global norm, the state space is defined in an indefinite metric Krein Space $\mathcal{K} = (\mathcal{H}, \eta)$ under the Dirac/Wheeler-DeWitt type constraint $\hat{\mathcal{H}}_{\text{tot}} \vert{}\Psi_{\text{Omniverse}}\rangle = 0$. Using Kolmogorov Complexity and the Minimum Description Length (MDL) principle, it is demonstrated that the zero-net-charge architecture represents the sole self-contained system requiring zero arbitrary free parameters. Lastly, strict empirical, algorithmic, and computational Popperian falsification criteria are established. This document constitutes the first logical and axiomatic unit of the Treatise of the Zero-Sum Ontological Model.