Emergent Dark Energy from an Entropic G₂ Lattice: EGESB-G₂ Version 7 (Final)

We present the cosmological sector of the EGESB-G₂ framework, in which dark energy emerges from an entropic condensation mechanism associated with a seven-dimensional lattice with G₂ symmetry. The model derives FRW dynamics without introducing a cosmological constant and predicts a positive wa parameter, providing a falsifiable observational signature distinguishable from ΛCDM. This Version 7 (Final) represents the stabilized cosmological formulation. Version 7.5 update: Appendix A upgraded from assumption to theorem (Z₂³ invariance).Logical dependency chain revised.SPARC validation unchanged.No free parameters. This version (v7.5) introduces the conditional derivation of the C3 relation,reducing OP-26a to a single geometric assumption. Key updates: Conditional derivation of compact volume factor (T⁷/Z₂³) Strengthened OP-26a status Updated closure propagation chain No additional free parameters introduced Audit-compliant document Open problems remaining:OP-1 (continuum limit), OP-2 (Λ_eff), OP-25d (QCD geometric origin),full nonlinear Einstein resummation. This version (v7.4) introduces the conditional derivation of the C3 relation, reducing OP-26a to a single geometric assumption. Key updates:- Conditional derivation of compact volume factor (T⁷/Z₂³)- Strengthened OP-26a status- Updated closure propagation chain- No additional free parameters introduced- Audit-compliant document Open problems remaining:OP-1 (continuum limit), OP-2 (Λ_eff), OP-25d (QCD geometric origin), full nonlinear Einstein resummation. Previous version:EGESB-G₂ Core v7.0 — DOI: 10.5281/zenodo.19200583