Unified Epistemic Architecture (UEA v6.0):
Description
This paper presents the Unified Epistemic Architecture (UEA) v6.0, integrating the final theoretical upgrade layers into a complete covariant information-field geometry. The core theoretical stack comprises a Riemannian runtime manifold with constrained geodesic dynamics driven by an information viability field; Noether conservation of information-energy, spectral stability theory, and an information curvature tensor; a coupled scalar field theory with stress-energy conservation; an emergent causal structure via viability-deformed metric and information light-cones; and dynamical curvature evolution governing cascade stability. The discrete proximal execution layer from v5.0 is preserved as the operational realization of the continuous field theory.
This synthesis is supported by contemporary literature spanning Riemannian inference, variational field theory, ISS stability, Noether conservation in neural dynamics, and viability theory. All claims remain theoretical, and outstanding empirical validation requirements are explicitly itemized.
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References
- 1. Davidson, C. K. S. (2026). Toward a Unified Epistemic Architecture: Runtime Geometry, Operator Closure, and Geodesically Consistent Constraint Dynamics (Consolidated Synthesis Paper with Full Verification Suite — v5.0). Synthesis Working Paper. ORCID: 0009-0007-2990-8716. 2. Aubin, J.-P. (1991). Viability Theory. Birkhäuser. 3. Amari, S. (2016). Information Geometry and Its Applications. Springer. 4. Banach, S. (1922). "Sur les opérations dans les ensembles abstraits." Fundamenta Mathematicae. 5. Bartels, R. H., & Stewart, G. W. (1972). "Solution of the Matrix Equation AX + XB = C." Communications of the ACM. 6. Bhatia, R. (2007). Positive Definite Matrices. Princeton University Press. 7. Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press. 8. Friston, K. (2010). "The free-energy principle." Nature Reviews Neuroscience. 9. Hairer, E., Lubich, C., & Wanner, G. (2006). Geometric Numerical Integration. Springer. 10. Mahalanobis, P. C. (1936). "On the generalised distance in statistics." Proceedings of the National Institute of Sciences of India. 11. Nesterov, Y. (2004). Introductory Lectures on Convex Optimization. Springer. 12. Rockafellar, R. T., & Wets, R. J.-B. (1998). Variational Analysis. Springer. 13. Villani, C. (2009). Optimal Transport. Springer. 14. Absil, P.-A., Mahony, R., & Sepulchre, R. (2008). Optimization Algorithms on Matrix Manifolds. Princeton University Press.
- Mao, R., Zhang, Z., Yang, M., et al. (2026). "RiemannInfer: Improving transformer inference through Riemannian geometry." Scientific Reports 16, 6636. DOI: 10.1038/s41598-026-37328-x | Diepeveen, W. & Needell, D. (2026). "Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry." arXiv:2505.08087v3 | Chae, B.G. (2026). "A Unified Dynamical Field Theory of Learning, Inference, and Emergence." arXiv:2601.10221v2 | Tanaka, H. & Kunin, D. (2021/2025). "Noether's Learning Dynamics: Role of Symmetry Breaking in Neural Networks." ICLR 2021. | Grothus, M. & Vilasini, V. (2024). "Characterizing Signalling: Connections between Causal Inference and Space-time Geometry." arXiv:2403.00916 | Vanchurin, V. (2025). "Emergent Field Theories from Neural Networks." arXiv:2411.08138