We present the Information-Geometric Structural Debt Framework (IGSDF), a unified geometric theory that connects nuclear structure, quantum coherence limits, and cosmological expansion through a single variational principle. The framework introduces a debt-weighted Lagrangian and derives the vacuum energy density from first principles. It predicts a critical quantum coherence threshold of 78.53 bits and a Baryon Acoustic Oscillation scale of 143.13 Mpc — a prediction that can be tested at >5σ by the DESI survey. The theory also reveals that structural health scales quadratically with complexity and that cosmic expansion imposes a redshift-dependent stability tax.