SOMALA: The Path to Deterministic-AGI

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).