S-AI-Recursive: Convergent Recursive Reasoning

This article introduces S-AI-Recursive, a bio-inspired Sparse Artificial Intelligence architecture in which reasoning is implemented as a hormonally regulated closed-loop iteration rather than a single feed-forward pass. The Recursive Reasoning Cycle (RRC) is governed by two recursive hormones: Clarifine, a convergence signal, and Confusionin, a residual-uncertainty signal. Their antagonistic interaction regulates state refinement, stopping, resource allocation, and recursive-engram retrieval. The revised framework distinguishes hormonal-subsystem stability from joint cognitive state-hormone convergence and gives explicit sufficient conditions for coupled contraction on fixed-point-structured tasks. It also includes Lyapunov analysis, conditional entropic contraction, multi-signal stopping, Euler-Maruyama discretization with projection, constrained agent selection, and warm-start memory. Experimental evaluation combines controlled SAI-UT+ simulations with exactly verifiable task-level tests. On convergent Maze instances, adaptive stopping reduces mean depth from 20.00 to 11.31 iterations at unchanged resolution, a 43.4 percent reduction. On compatible recurring Sudoku instances, warm-start reduces mean depth from 18.39 to 2.00 cycles, saving 16.39 cycles at unchanged resolution. ARC-style tasks are used to assess operator portability rather than full benchmark performance. Robustness tests show an advantage over residual-only stopping on deceptive plateaus, but not under homogeneous Gaussian noise. These results support adaptive temporal parsimony, memory-assisted acceleration, and selected robustness under stated conditions, without establishing superiority over independently trained external architectures.