Hypergraphs , metagraph for aware AI

Metagraph, hypergraphs, fractal and holonic structures for AI agents and memory

From Property Graph to RDF: A Hands-On Translation Guide for LadybugDB

You built your agent memory in LadybugDB. Typed node tables, polymorphic relationships, bipartite edge nodes — the whole Semantic Spacetime apparatus running on LadybugDB embedded engine. It works. It’s fast. It fits on your laptop.

March 24, 2026

Why Your AI Agent Needs a Graph Database on the Device

Most AI agent architectures treat memory as an afterthought — a flat list of conversation turns, a vector store bolted on the side, or a remote database that the agent calls over a network. These approaches all share the same fundamental flaw: they model memory as retrieval, not as structure.

March 15, 2026

The Power of Properties in LadybugDB: Structs, Lists, Unions, and the View from Semantic Spacetime

How LadybugDB’s rich type system transforms property graphs from flat key-value stores into expressive, queryable knowledge structures — and why this matters for AI memory, sovereign agents, and graph

March 14, 2026

Beyond the Context Window: How Memory and Promise Graphs Make Powerful Agents

Your AI agent forgets everything the moment the session ends. Here is why — and how to fix it.

March 09, 2026

LLM Friendly Graphs for AI Memory — From Triples to Facts

So, you know that I’m working on the book about the memory, about the temporal context of the memory.

March 07, 2026

Semantic Spacetime in LadybugDB: Hypergraphs, Metagraphs, and Memory — Without Leaving Cypher

Building expressive AI memory structures on a graph database you can actually run today

February 21, 2026

From Triples to Metagraphs: Modeling Humanlike Agentic Memory with Complex Graph Structures

My graph journey began as an AI agent memory guy. Like most people in this space, I started with what seemed like the obvious choice: directed graphs and triples — the classic subject-predicate-object model borrowed from RDF and the semantic web tradition. It’s clean, it’s mathematically well-understood, and it has decades of tooling behind it.

February 20, 2026

Why Properties Matter for Agentic Memory

The cognitive architecture of AI agents demands a fundamental rethinking of how we represent knowledge. While the database community has spent decades optimizing properties away — hiding them inside nodes for compactness and query performance — neuroscience and practical agent systems tell a different story: properties aren’t just metadata to be tucked away. They’re primary perceptual primitives that deserve first-class citizenship in our knowledge graphs.

February 08, 2026

Beyond the Graph: Why AI Agent Networks Need Higher-Order Thinking

The foundation of modern AI systems rests on networks — neural networks that learn patterns, knowledge graphs that store relationships, and increasingly, networks of AI agents that collaborate to solve complex problems. But there’s a fundamental limitation in how we typically model these networks: we assume all relationships are pairwise, connecting exactly two entities at a time. This assumption, borrowed from traditional graph theory, may be holding back the next generation of agentic AI systems.

February 07, 2026

Why LLMs Don’t Need Ontologies (But Knowledge Graphs Do)

The tech discourse is awash with articles claiming that large language models desperately need ontologies. LinkedIn overflows with such proclamations, each one more emphatic than the last. Thought leaders proclaim that without formal ontological frameworks, LLMs are fundamentally incomplete. But here’s the reality that cuts through the noise: LLMs don’t need ontologies at all.

February 04, 2026

The Context Graph Hype: When Engineering Expertise Gets Lost in the Noise

The recent explosion of interest in "context graphs" reveals a troubling pattern in our industry: the rush to rebrand existing concepts without understanding the foundational knowledge beneath them. This isn't about context graphs themselves—which you can read about in my series of articles—but about what their meteoric rise tells us about the state of technical expertise in AI and data engineering.

January 25, 2026

Vectors vs Graphs: How Topology and Geometry Are Transforming Machine Learning

The debate between vector embeddings and graph representations has become increasingly prominent in AI and machine learning circles. We see constant arguments about which is superior, or proposals for hybrid approaches combining both. But I’ve come to an intriguing realization: perhaps we don’t need to choose between them at all. What we actually need are different kinds of embeddings for different purposes, and the key to understanding this lies in topology and geometry.

January 15, 2026

The Shape of Knowledge: Topology Theory for Knowledge Graphs

Moving Beyond Embeddings to Understand Graph Structure

December 21, 2025

Lex: A Formal Ontology Language for Property Graphs

Property graphs have become the dominant paradigm for modeling connected data, yet they lack the formal semantic rigor that RDF/OWL brought to knowledge representation. While RDF graphs are constrained by their triple-based structure, property graphs offer richer modeling capabilities through typed edges with properties. However, this expressiveness comes at a cost: the absence of standardized formal semantics and constraint languages that can reason about graph structure and properties simultaneously.

December 20, 2025

Axioms in Ontology: Beyond Schema to Reasoning Systems

When most developers first encounter ontologies, they see them as elaborate schemas—formalized ways to define classes, properties, and relationships. But ontologies built on Description Logic (DL) are fundamentally different from schemas, and the difference hinges on one crucial element: axioms.

December 12, 2025

Beyond Binary Relations: The HyperGraph-Graph (HG²)

The Resource Description Framework (RDF) has long served as the foundation of the Semantic Web, yet its binary triple structure inherently limits the representation of complex, multi-dimensional relationships. The HyperGraph-Graph (HG²) data structure emerges as a sophisticated solution that transcends these limitations by combining the expressive power of hypergraphs with the structured clarity of traditional graphs. This article provides a comprehensive technical analysis of HG² architecture, examining its formal definition, mapping mechanisms for RDF integration, and implications for next-generation knowledge representation systems. We demonstrate how HG² addresses fundamental challenges in semantic computing while maintaining backward compatibility with existing RDF infrastructure.

November 30, 2025

The Geometry of Knowledge: How Cubic Types Reveal the Hidden Architecture of Metagraphs

A journey into the mathematical foundations that unite topology, type theory, and hierarchical networks

November 29, 2025

Metagraphs and Hypergraphs for complex AI agent memory and RAG

We have many papers about Knowledge graphs and how they help LLM fight hallucinations and give more accurate answers. Graphs are everywhere.

November 28, 2025

Metagraphs as Homoiconic Structures: Revolutionizing Knowledge Representation

In the rapidly evolving landscape of knowledge representation systems, metagraphs have emerged as a powerful framework for modeling complex, multi-dimensional relationships. When implemented as homoiconic structures, metagraphs unlock unprecedented capabilities for self-representation, introspection, and dynamic adaptation. This article explores the theoretical foundations, practical implementations, and future directions of metagraphs as homoiconic structures, delving into the transformative potential of this synthesis for artificial intelligence, knowledge engineering, and complex systems modeling.

November 28, 2025

Open World vs Closed World: Modeling OWL and SHACL Semantics in Agda

The tension between the Open World Assumption (OWA) and Closed World Assumption (CWA) represents one of the fundamental philosophical and practical divides in knowledge representation. OWL (Web Ontology Language) embraces OWA, treating absence of information as unknown rather than false. SHACL (Shapes Constraint Language), conversely, validates data under CWA, where what is not explicitly stated is considered false. This article explores how dependent type theory, specifically Agda, can model both approaches and potentially bridge this conceptual gap.

November 28, 2025

Holons and Metagraphs: Universal Interfaces from Atoms to Organisms

A deep exploration of how holonic principles unify agent systems, knowledge representation, temporal structures, and system design

November 28, 2025