Topological Fractal Quantum Field Theory (Extended TQFT), authored by Anna Paseva, extends classical TQFT into recursive, convergent, and computational system-spaces. It builds on the standard Atiyah"“Segal formulation to secure invariants across fractal manifolds.
I. The Recursive Atiyah"“Segal Framework
Classical Topological Quantum Field Theory associates vector spaces to boundaries and linear maps to cobordisms. The extended formulation introduces fractal boundaries and recursive functor mapping:
- Fractal Cobalt Bound: Reconstructing boundaries as self-similar manifolds preserving Euler characteristic limits.
- Functor Convergence: Linear maps are mapped to limit-converging vector operators ensuring that information density does not collapse or diverge infinitely under recursive refinement.
- Stability Layer: Defines admissible morphisms as those preserving invariant identity, convergence, and mathematical well-foundedness.
Stability Proof: Any system satisfying well-founded convergence conditions remains unconditionally stable under all admissible transformations, preventing topological collapse in transfinite limit spaces.
II. Computational System-Space
In contrast to standard physics formulations, Extended TQFT is designed as an executable extension-framework:
- Invariant Stability: Directly applicable to sovereign digital architectures where structural identity must survive across decentralized state migrations.
- Manifold Decomposition: Systems are treated as recursive, invariant-bearing manifolds, aligning formal quantum field logic with highly distributed software topologies.
- Dynamic Invariance: Provides the formal mathematical grounding for understanding how complex networks maintain coherent operational identity under constant topological deformation.