TAG ARCHIVE
mathematics
4 MARIA OS blog articles tagged mathematics. Formal models for convergence, stability, game theory, graph dynamics, and multi-agent evaluation. This canonical topic archive supports 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.
Agentic R&D as Governed Decision Science: Six Research Frontiers for Speed, Quality, and Responsibility in Judgment Operating Systems
How to build a self-improving governance OS through six mathematical research programs, four agent teams, and a Research Universe architecture
Judgment is harder to scale than execution, especially in high-stakes decision environments. This paper presents six research frontiers — from hierarchical speculative pipelines to constrained reinforcement learning — for extending MARIA OS from product operations into governed decision science. We formalize each frontier with mathematical models, design four agent-human hybrid research teams, and introduce the Research Universe: a governance structure where each experiment is evaluated through the same fail-closed gates it studies.
Evidence Coherence Spectral Analysis: Detecting Fraud Through Eigendecomposition of Audit Evidence
Using spectral methods on evidence correlation matrices to identify inconsistencies, fabrication patterns, and systemic fraud signals
Traditional audit systems often rely on rule-based checks and statistical sampling, which can under-detect coordinated fabrication patterns. This paper introduces Evidence Coherence Spectral Analysis, a framework that treats evidence sets as vector spaces, builds correlation matrices from evidence attributes, and applies eigendecomposition to identify anomalous spectral gaps associated with inconsistency or fabrication risk. We define a coherence score, relate it to false-discovery behavior, and describe integration with MARIA OS Evidence Bundles. In controlled financial-statement audit experiments, spectral analysis detected 94.7% of fabricated evidence sets while maintaining a false-positive rate below 2.3%, with streaming support for near-real-time analysis.
Decision Intelligence Theory: A Unified Framework for Responsible AI Governance
Five axioms, four pillar equations, and five theorems that transform organizational judgment into executable decision systems
Decision Intelligence Theory formalizes decision-making as a control system, integrating evidence, conflict, responsibility, execution, and learning. This capstone article presents a unified mathematical framework — five axioms, four pillar equations, and five theorems — together with implementation mappings and internal cohort analyses across finance, healthcare, legal, and manufacturing.
Audit Stopping Criteria: Mathematical Foundations for Knowing When Enough Is Enough
Defining audit termination conditions through MAX constraints and probability thresholds to minimize False Allow Rate
Every audit faces the same question: when is evidence sufficient to stop? Stopping too early can allow defects to escape into production, while stopping too late consumes budget and attention with diminishing returns. This paper formalizes audit stopping criteria as a constrained optimization problem, derives solutions under MAX constraints and sequential probability ratio testing, and describes integration with the MARIA OS Fail-Closed Gate Engine. In evaluated SOX workloads, the approach reported a False Allow Rate below 0.3%.