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 (Λₑff), 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 (Λₑff), OP-25d (QCD geometric origin), full nonlinear Einstein resummation. Previous version: EGESB-G₂ Core v7. 0 — DOI: 10. 5281/zenodo. 19200583