Zeta Cognitive Architecture

Zeta Cognitive Architecture ZCA (Zeta Cognitive Architecture) is an algebraic cognitive architecture that performs sequence prediction entirely within the quotient ring Z₁₃[η]/(η²+1), replacing all floating-point arithmetic, gradient descent, and heuristic methods with exact integer-algebraic computation. The architecture decomposes Z₁₃[η] via Chinese Remainder Theorem into Z₁₃ × F₁₆₉ using idempotent projectors e₁ and e₂₃, enabling three spectral attention heads [P₁, P₂₃, P₂₃] with a 13-adic positional kernel — no softmax, no floats. Reasoning follows an S₃ Galois symmetry cascade (REFLECT → CONTRADICT → CORRECT), and error correction is achieved through Bézout correction: one-shot, exact, and unique. Additional algebraic structures include Hensel lifting for p-adic root recovery, Witt vectors for precision preservation, and Gröbner bases for ideal classification. The architecture enforces the No-FIAT principle (No Floats, No Intuition, No Assumption, No Tuning) with zero violations across all 31 validation tests on CUDA. ZCA addresses four AGI gap closures — Grounding, Composition, Autonomy, and Alignment — through ten cognitive faculties grounded entirely in ring-theoretic operations. Citation: Navrátil, D. (2026). Zeta: A Sequence Prediction Architecture over the p-Adelic Integer Ring Z_13[eta].Zenodo. https://doi.org/10.5281/zenodo.20057473