TAG ARCHIVE
contraction-mapping
2 MARIA OS blog articles tagged contraction-mapping, 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.
Evidence, RAG, and Knowledge Governance
Evidence bundles, retrieval architecture, Graph RAG, knowledge trust, and auditable reasoning pipelines.
Agentic R&D and Judgment Science
Research operations, simulation labs, judgment science, recursive improvement, and experimental AI governance.
From Agent to Civilization: Multi-Scale Metacognition and the Governance Density Law
Exact contraction, buffered operating envelopes, and civilization-scale governance across organizational layers
This paper presents a mathematical theory of governance density as a stability parameter across organizational scales, from individual agents to enterprises and civilizations. We formalize agentic-company dynamics as G_t = (A_t, E_t, S_t, Pi_t, R_t, D_t), distinguish exact local contraction (1 - D_t) lambda_max(A_t) < 1 from the buffered operating envelope lambda_max(A_t) < 1 - D_t, and derive analytical phase boundaries between stagnation, buffered specialization, fragile specialization, and cascade. We extend the framework to civilization scale through D_eff = 1 - (1 - D_company)(1 - D_civ) and analyze a market revaluation model P_{t+1} = P_t + kappa(V_t - P_t) + zeta_t to show how periodic shocks interact with governance density. The result is a unified control view of phase transitions in self-organizing multi-agent systems.
Recursive Self-Improvement Under Governance Constraints: Governed Recursion via Contraction Mapping and Lyapunov Stability
How MARIA OS's Meta-Insight turns unbounded recursive self-improvement into convergent self-correction while preserving governance constraints
Recursive self-improvement (RSI) — an AI system improving its own capabilities — is both promising and risky. Unbounded RSI raises intelligence-explosion concerns: a system improving faster than human operators can evaluate or constrain. This paper presents governed recursion, a Meta-Insight framework in MARIA OS for bounded RSI with explicit convergence guarantees. We show that the composition operator M_{t+1} = R_sys ∘ R_team ∘ R_self(M_t, E_t) implements recursive improvement in meta-cognitive quality, while a contraction condition (gamma < 1) yields convergence to a fixed point instead of divergence. We also provide a Lyapunov-style stability analysis where Human-in-the-Loop gates define safe boundaries in state space. The multiplicative SRI form, SRI = product_{l=1..3} (1 - BS_l) * (1 - CCE_l), adds damping: degradation in any one layer lowers overall autonomy readiness. Across simulation and governance scenarios, governed recursion retained 89% of the unconstrained improvement rate while preserving measured alignment stability.