Black Holes as Closure Engines - Dimensional Demotion, Fold Energy, and the Dual Source Structure of Dark Energy

Abstract A companion paper to Resolution Geometry v5.5 providing a structural mechanism for the cosmologically coupled black hole (CCBH) hypothesis. Structural analysis conducted via Resolution Engine diagnostic pipeline. The cosmologically coupled black hole (CCBH) hypothesis proposes that black holes convert infalling matter into dark energy, potentially resolving three observational anomalies: the source of dark energy, the Hubble tension, and the neutrino mass problem. This paper provides a structural mechanism for that conversion using the Resolution Geometry (RG) framework, which derives spacetime from constraint satisfaction on a two-dimensional substrate. The central claim: extreme gravitational compression forces three-dimensional structure past a geometric stability threshold (the Layer 14 fold point), triggering dimensional demotion from 3D to 2D. This process produces two separable outputs: - structural residue (a candidate contribution to the non-baryonic gravitational sector) - liberated fold energy (cosmologically coupled dark energy). Three quantitative results anchor the framework. First, the total fold energy for a Schwarzschild black hole of mass M equals Mc² exactly, demonstrated via the Gibbons-Hawking-York boundary term with bending modulus κ = c⁴/G derived from the framework (Appendix A). Second, the integrated black hole mass density (~10⁻⁶ to 10⁻⁵ of critical density) is insufficient to account for observed dark energy (ΩDE = 0.68), motivating a dual-source model: a constant component from the scaffold’s global efficiency threshold (Layer 19), and a time-varying component from black hole closure costs that tracks star formation history. Third, the CCBH cosmological coupling constant k ≈ 3 is derived as the volumetric scaling exponent of exchange-path routing around closure regions in three spatial dimensions, with a predicted sub-integer correction k = 3 − ε from foam packing frustration (ε ~ 0.01–0.05). The framework makes falsifiable predictions distinguishable from both standard ΛCDM and the CCBH hypothesis, including the k = 3 derivation, redshift-dependent coupling (k approaching 3 from below as z decreases), and a directional falsification criterion: if k > 3 at any measurement precision, the routing mechanism is wrong.