The CCEGA Programme: One Geometry, Four Open Problems, Four Falsifiable Predictions — A Synthesis of the Ten-Paper Series

The Curvature-Controlled Extra-Dimensional Gravity and Emergent Unification (CCEGA) framework proposes that spacetime singularities are resolved by a modulus field φ that saturates the effective gravitational coupling Gₑff = G (1−φ) → 0 before any curvature divergence. This paper synthesises the results of a ten-paper series establishing the theoretical foundations, internal consistency, and observational predictions of the programme. The framework addresses four long-standing open problems — singularity resolution, black hole information, the cosmological bounce, and the hierarchy problem — through a single geometric mechanism governed by one free parameter: the critical density ρc ≳ 10 ρₙuc, constrained independently by neutron-star observations. The programme produces four independent falsifiable predictions: gravitational-wave echoes with radion sidebands in Δf ∈ 240, 2400 Hz detectable by the Einstein Telescope (~2035) ; CMB quadrupole suppression at ℓ = 2, 3 conditionally on Nᵢnf ∈ 50. 9, 54. 2 testable by LiteBIRD (~2028) ; neutron-star radii ~10% larger than GR testable by NICER (ongoing) ; and tidal deformability ΛCCEGA/ΛGR ∈ 1. 38, 1. 63 testable by LIGO O5 and the Einstein Telescope. All predictions are fixed by the same ρc that satisfies neutron-star maximum-mass constraints. We identify what has been rigorously derived, what remains conjectural, and what observations will decide.