Ontology · the study of what exists

What exists?

The oldest question in philosophy has a precise answer on a graph: to exist is to be an element of a set. Build on that — ground it in mathematics — and a graph stops describing the world and starts reasoning about it.

A cellular-sheaf diagram over a graph — structure carrying meaning on every node and edge.
Forty years on one conviction: relationships come first.

Begin with being

Existence is membership. Relations are real.

To exist is to be an element of a set.

A thing is if it belongs; what kind of thing it is, is which sets it belongs to. Sort those memberships and you have a taxonomy — the categorization of existence, universals and particulars, types and instances. This is what the graph world means by an ontology.

And the categories of being have always included one the dominant standards forgot: relation. A relationship is not glue between two real things — it is itself a real thing. So we make relationships first-class — nodes in their own right, carrying their own data. Reticulation, not reification.

Vector to the mathematics

From philosophy to a sheaf.

Inference — derive what follows from what's said — is only the first floor. An operation's order is the order of structure it reaches over:

order 1 · Infer
reaches over elementswhat follows.
order 2 · Compute
reaches over the whole topologywhat the structure reveals. Centrality, community, similarity: the graph reasons about itself.
order 3 · Reticulate
reaches over whole spaceswhat relates across worlds.
order ω · Interact
reaches over universes and the intelligences reading themwhat emerges in conversation.
The object that makes this rigorous

Model the graph as a cellular sheaf: data on every node and edge, with rules for how they must agree. A view becomes a section; consistency becomes cohomologyH⁰ is what holds together (knowledge), is the contradiction that can't (the obstruction). Grounding is driving H¹ toward zero.

The full consistency engine is the direction, not a shipped feature — we build toward it in the open. Read the math →

A graph whose nodes and edges carry fibers, with H⁰ and H¹ chalked — a cellular sheaf.
A view becomes a section; consistency becomes cohomology — H⁰ what holds, H¹ what doesn't.

What this lets us build

The graph your extractor throws away.

Your LLM pipeline extracts a rich graph of concepts and how they relate — then your tools show almost none of it. A renderer only draws an edge when both endpoints are nodes, so the conceptual half — the ideas and how they connect — is never rendered, never traversed, never queried. The Intelligent Graph recovers that discarded layer as a non-destructive overlay, grounds it, and lets you act on it.

Run this on your own graph: count the edges whose endpoint isn't a node. That number is the graph you're throwing away. In our pilot, it was the large majority of the relationship layer.

What it does

Recover, ground, and act.

01Recover

Read the source read-only; surface the relationships it extracted but couldn't display.

02Ground

Type each raw relationship into a traversable graph — keeping the original string, so re-typing later is a single traversal, not a re-import.

03Act

Hitting a relationship can do something, not just return a row. The graph stops being a place you store knowledge and becomes one that runs.

Provenance is a property, not a supernode. Every step is reversible by construction. We attach to your graph; we never restructure it.

Why it's different

From a model to an engine.

Relationships first
Edges carry their own structure and behavior — no reification, no blank-node workarounds. The thing the semantic web couldn't do cleanly, done natively.
Executable traversal
Behavior binds to the kind of relationship you traverse. Inference becomes one behavior, not the whole paradigm.
Memory
TIG remembers structure and decisions across runs. A re-import shows you only what's new — the dimension a graph re-derived from scratch each day can't have.
Reticulation
A two-way weave: TIG curates, then feeds interpretations back so the source's agents get smarter each cycle.

TIG + Solstone

Capture-to-graph, in a single self-contained stack.

The Intelligent Graph pairs with Solstone — Jeremie Miller's local-first memory platform — to turn a passive capture stream into a structured, queryable, annotatable graph. Sol captures and extracts; TIG recovers the discarded relationship layer, makes it traversable, and feeds curated interpretations back. Built for teams who want their own graph, on their own machine — not a hyperscale deployment.

Open core

An open core, with a commercial layer for the parts that act.

The core will be open source (Apache 2.0) — we're building it in the open. A commercial layer adds the operational and agentic capabilities teams pay for.

Who's behind it

One unbroken conviction: relationships come first.

Built by Michael Bauer — a 35-year through-line from rule-based expert systems to a billion-node production graph. → michaelbauer.com

Featured at Neo4j NODES 2026, with Solstone: "The Graph Your Extractor Throws Away."