Z-U-V Triple Space Dynamics and Riemann Zeros: A Unified f-Shrink Operator Approach for Brain-Machine Interfaces and Blockchain Consensus

This paper proposes a unified control framework based on Z-U-V triple space dynamics and Riemann zero coding, with applications in both brain-machine interfaces and blockchain consensus. The framework originates from the balance equation ln f + (π/2)f = 0 and its unique positive real solution f ≈ 0.47454 [1]. Building upon the previously established duality between Z-space (path/revolution) and U-space (state/rotation), we introduce V-space (anomaly/escape) to form a complete triple duality structure [3]. By assigning each agent (neuron or blockchain node) a unique Riemann zeta zero γ as its "genetic code," and combining it with the f-Shrink operator [2] for smooth, non-zero-converging adaptive control, the framework achieves remarkable results in both domains: (1) In a brain-machine interface simulation with 50 neurons, a robotic arm reaches its target (5.0, 3.0) with a final error of 0.001 within 600 steps, while V-space successfully detects and inhibits 2 anomalous neurons; (2) In a blockchain consensus simulation with 100 nodes, the system produces 201 stable blocks, while V-space identifies 20 fake nodes through γ distribution analysis. This work demonstrates that the Z-U-V triple space dynamics and Riemann zero coding constitute a cross-disciplinary mathematical framework, providing new theoretical foundations for the design of distributed intelligent systems.