Stop retrieving, start traversing

A single mortgage has ~10^140 possible states - 200 activities, five-plus states each. The observable universe holds 10^80 atoms. You cannot embed your way out of that.

That was Keith Soura (CTO at Arch) at Ai4 this week, in one of the best sessions I attended: "Stop Retrieving. Start Traversing." One line stuck with me: embedding similarity is the encyclopedia; graph theory is the map.

What his team built: the workflow graph was already in the code, as data. Two concepts carry it. Facts are what the system knows or computes about a loan: income, credit score, etc. Activities are units of work that fire when fact conditions are met and write new facts back. Extracted from the codebase: 1,871 workflow activities, 25,856 declared fact references, 5,389 derived dependency edges across 12 business domains. Then they handed graph algorithms to the LLM as tools. Transitive reduction showed 77.5% of those edges were already implied - ~1,200 carry the real structure. The agent plans its route on the dependency graph, then verifies each step against live data before acting. Facts are cited by ID, never recomputed. Actions come only from declared edges - the agent cannot take a step the graph doesn't contain.

Building deterministic state machines: It's the conclusion I keep arriving at as well while building agentic systems: the model returns a response; code verifies it against the source and fails closed when invalid. Control flow follows schema-validated outputs through declared conditional edges. Approvals are database rows, re-verified inside every executor, and a forged proof triggers an error.

One difference in direction. Keith extracts rails from a brownfield system - eight years of hand-coding the Fannie Mae Selling Guide produced the graph as a byproduct. Most organizations don't have that asset. Yet we must declare the rails on day one: typed state machines, gate proofs, evals as shipping gates. Same destination, opposite direction.

Graph Tools: I learned useful new graph techniques during the session. Union-find for entity resolution to unify borrowers, and properties across all documents. Tarjan and transitive reduction as merge-time CI guards to prevent tangles and remove extra edges. Dominator trees as a runtime tool to track missing facts blocking closing date. And that was one session.

Mortgage Lending Selling Guide is public and the rails pattern is proven.

Probabilistic reasoning. Deterministic rails. That's the whole thesis.