ENGINEERING BLOG
Technical research and engineering insights from the team building the operating system for responsible AI operations.
121 articles · Published by MARIA OS
Governance density as organizational self-awareness, a spectral stability condition, and the mathematical foundations of enterprise metacognition
We formalize an agentic company as a graph-augmented constrained Markov decision process G_t = (A_t, E_t, S_t, Pi_t, R_t, D_t) and define operational governance density over router-generated Top-K candidate actions, making D_t directly measurable from logs at each step. We derive a practical stability condition on the damped influence matrix W_eff,t = (1 - kappa(D_t)) W_t, yielding (1 - kappa(D_t)) lambda_max(W_t) < 1. We then show that governance constraints act as organizational metacognition: each constraint is a point where the system observes its own behavior. This frames metacognition not as overhead, but as the control parameter that determines whether an agentic company self-organizes stably or diverges. Planet-100 simulations validate that stable role specialization emerges in the intermediate governance regime.
Mathematical formalization of governance density across organizational scales, with phase-boundary analysis, civilization-scale extension, and convergence proofs
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), derive analytical phase boundaries between stagnation, stable specialization, and chaos, and extend the framework to civilization scale through D_eff = 1 - (1 - D_company)(1 - D_civ). We prove convergence conditions via contraction-mapping arguments 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.
From Enterprise Governance to AI Constitutions: How Institutional Economics and Meta-Governance Theory Stabilize Multi-Agent Societies
Multi-agent AI societies require more than individual metacognition: they also require institutional design. This article formalizes agentic-company governance, derives social objective functions for AI-human ecosystems, establishes the Speed Alignment Principle as a stability condition, and presents an AI-constitution model with revision rules. In simulations across 600 runs, adaptive institutional frameworks reduced spectral radius from 1.14 to 0.82 while maintaining audit scores above 0.85.
A mathematical framework for calibrating governance in self-organizing enterprises
We derive a stability condition linking the spectral radius of the influence-propagation matrix to governance constraint density. The law λ_max(A) < 1 - D separates stable role specialization from oscillatory or chaotic regimes.
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Complete list of all 121 published articles. EN / JA bilingual index.
121 articles
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