The TOPO-COMPLETE framework, developed by the Sovereign Machine Laboratory (SOMALA), aims to overcome the "stochastic illusion" in AI by providing deterministic guarantees for stability and equity. Core Thesis and Foundation Fundamental Principle: The framework is built on the rule "Fix a sparse reference. Let the rest adapt," a principle applied across domains, including neuroimaging, number theory, AI memory, and AI governance. Arithmetic Spectral Theory (AST): This theory uses a "pure kernel" of the first six prime numbers—$R=\{2,3,5,7,11,13\}$—to derive mathematical relationships between prime numbers and stable representations. The Prime 7: Positioned as the center prime of the first six, 7 acts as both the geometric anchor and the completion of the framework, maintaining structural symmetry. Universal Constants: The framework utilizes a safety constant $\Lambda = 0.9785142874$, derived from the pure kernel, and a seed value of 123 for all computations. The Four-Tier Architecture The TOPO-COMPLETE framework incorporates four specific tiers to eliminate bias and resistance against catastrophic forgetting: Tier 0: Data-Spectral Integrity: Ensures only "pure" samples enter the training pipeline by rejecting biased samples with 100% certainty. Tier 1: L-EFM Operator: The Laplace-Euler-Fourier-Mellin operator preserves values at the equitable frequency ($\sigma=0.5$) while annihilating all other spectral components. Tier 2: H2E-Sheriff-BIAS: Uses hyperbolic geometry to render biased associations geometrically impossible. Tier 3: Prime-Anchored Equity: Grounds all representations in prime coordinates, mapping each of the six primes to a fundamental equity principle. Empirical Certification and Resources The framework was validated on the GPT-OSS-20B model across five independent runs, achieving: Task Accuracy: A mean Task C accuracy of $92.3\% \pm 1.9\%$. Forgetting: A mean combined catastrophic forgetting rate of $1.6\% \pm 1.3\%$. Bias Elimination: A 100% bias rejection rate. Implementation: The full code for the framework is available at https://github.com/frank-morales2020/AST/blob/main/TOPO_COMPLETE.ipynb. Model Availability: The new TOPO-COMPLETE model is available at https://huggingface.co/frankmorales2020/topo-complete-2026. The Seven Consequences of Deterministic-AGI Mirroring the validation criteria for the Riemann Hypothesis, this validation framework includes seven consequences, each linked to a prime anchor and verified via cryptographic hash (e.g., Stability, Equity, Determinism, Geometry, Auditability, Scalability, and Sovereignty).