TAG ARCHIVE
lyapunov
2 MARIA OS blog articles tagged lyapunov, organized as a Bonginkan topic archive for search engines and LLM retrieval.
Judgment OS / Decision Intelligence OS
Core MARIA OS research on turning organizational judgment into executable decision systems.
Agentic Company Architecture
Research on human-agent organizations, delegation boundaries, role topology, and governed autonomy.
Responsibility Gates and AI Governance
Safety, accountability, fail-closed gates, auditability, and human-in-the-loop control for AI agents.
Multi-Agent Mathematics
Formal models for convergence, stability, game theory, graph dynamics, and multi-agent evaluation.
Agentic R&D and Judgment Science
Research operations, simulation labs, judgment science, recursive improvement, and experimental AI governance.
Industrial Loop Stability: Mathematical Foundations for Self-Monitoring Capital-Physical-Ethical Control Systems
Lyapunov analysis, contraction mappings, and spectral methods for proving convergence of the autonomous Capital-Operation-Physical-External governance loop
The Autonomous Industrial Loop — Capital, Operation, Physical, External — is the highest-level feedback cycle in MARIA OS, governing the continuous interaction between financial allocation, operational execution, physical-world robotics, and external market signals across an entire holding structure. This paper provides rigorous mathematical foundations for proving that the loop converges rather than oscillates, that drift accumulates within bounded envelopes, and that fail-closed gates preserve stability under stochastic external shocks. We develop five interlocking stability frameworks: Lyapunov energy functions that guarantee asymptotic stability of the four-phase loop, contraction mapping theorems that bound convergence rates, spectral analysis of the loop Jacobian that identifies instability modes before they manifest, cross-universe conflict propagation bounds that prevent local failures from cascading across the holding graph, and stochastic stability results via Ito calculus that accommodate market volatility, sensor noise, and adversarial perturbations. The Industrial Loop Stability Analysis produces three operational instruments: a Drift Index that aggregates ethical-operational-financial deviation into a single monotone metric, a Spectral Early Warning system that detects eigenvalue migration toward the unit circle boundary, and a Fail-Closed Holding Gate that enforces max_i scoring at the holding level with mathematically guaranteed bounded recovery time. Simulation across 4,800 synthetic subsidiary configurations demonstrates loop convergence in 94.7% of configurations, mean drift index below 0.12, and zero undetected instability events when spectral monitoring is active.
Decision Stability Scoring for Energy Grids: Lyapunov Functions for Power Supply-Demand Governance
Evaluating power grid decision stability through Lyapunov energy functions and responsibility-gated load balancing
Power grids can operate near stability limits, where dispatch errors or delayed interventions may trigger cascading disruptions. This paper introduces a Lyapunov-based decision-stability score for energy-grid AI agents, providing formal criteria for when autonomous grid-management actions remain within stable operating regions.