Indeterminate Cognitive Automata: Provably Fast Topological Memory Retrieval and Correlation Bounds for Autonomous Reasoning

Existing deep learning architectures face severe computational constraints due to the O(L^2) quadratic bottleneck of transformer self-attention and von Neumann memory-bus latency. In this work, we present Indeterminate Cognitive Automata (ICA), a non-symbolic framework for autonomous self-learning via internal topological field relaxation. ICA projects continuous sensory streams directly onto high-dimensional memory manifolds using structured two-dimensional arrays termed Perceptlets and Conceptlets. By replacing exhaustive global vector scans with localized graph traversals across an Exalted Data Stage (EDS), the architecture establishes a provably fast two-stage retrieval pipeline: first, achieving constant-time O(1) memory search and context pruning relative to repository size N; second, guaranteeing tight error bounds epsilon for dynamic correlation indexing over candidate spaces. We provide rigorous mathematical proofs for these search and correlation complexity limits, supported by an asymptotic spatial bound of O(ND + M). Furthermore, we specify a Processing-in-Memory (PIM) hardware substrate equipped with SRAM-based Topological Edge Routing Engines (TERE). Theoretical analysis confirms that ICA eliminates primary algorithmic and hardware bottlenecks, offering a scalable foundation for lifelong, non-von Neumann autonomous cognitive architectures.