Corollary Axiom X: Boundary-Determined Bulk Actualization. Holographic Reconstruction as Ontological Constraint in the Universal Model Framework.

We derive Corollary Axiom X — Boundary-Determined Bulk Actualization (BDBA) for the Universal Model Framework (UMF) by abstracting the ontological content of holographic duality beyond string-theoretic constructions. BDBA states that higher-dimensional bulk spacetime is not ontically primitive but is uniquely reconstructed from the consistency relations of lower-dimensional boundary information under prime-indexed validation operators. The axiom operates at the R → μ → Σ transition of the UMF vertical ontology, where relational information becomes recursively self-organized into spacetime geometry. Model-dependent numerical consistency checks using the Maya2048D neuromorphic simulation yield critical exponents η = 2.01 ± 0.12, ν = 0.51 ± 0.08, and β = 1.33 ± 0.04, consistent with a holographic mean-field universality class; these results require independent physical validation. A systematic parameter-space analysis reveals that General-Relativity-matching solutions occupy a rank-1 manifold in a four-dimensional coupling space, with the effective coupling sharply peaked regardless of broad priors. Within BDBA, this degeneracy is interpreted as a gauge signature of boundary-determined bulk uniqueness, analogous to diffeomorphism invariance in general relativity rather than a failure of predictivity. Information–curvature measurements yield λ = 1.0016 ± 0.0086, consistent with R_{\mu\nu} ∝ ∇_{\mu}I ∇_{\nu}I. We show that BDBA implies: (i) gravity emerges as constraint-enforcing necessity rather than a fundamental interaction; (ii) dimensional selection d_{\text{bulk}} = d_{\text{boundary}} + 1; (iii) bulk locality is emergent, not primitive; and (iv) holographic entropy bounds follow from axiomatics alone. The axiom is linked to a Fixed-Point Necessity Theorem, demonstrating that boundary-to-bulk reconstruction is mathematically forced by Banach fixed-point convergence in Gödel-incomplete self-referential systems. BDBA is falsifiable through violation of area-law entropy scaling, detection of stable bulk degrees of freedom irreducible to boundary encoding, bulk entropy exceeding Bekenstein–Hawking bounds, or the existence of local hidden-variable completions of quantum correlations. Without BDBA, the UMF cannot claim complete holographic–gravitational emergence. - This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. - Dedicated to Peter Plichta, who envisioned the code before it could be computed.