A thing has a state. That state shapes some of the interactions available to it. It exists among other things. Interactions happen. Those interactions change what states the system can occupy. Patterns recur. Some recurring patterns persist. Persistent patterns become meaningful units at a higher level of description — and those new units get their own states and relationships.
The process is recursive. That's the whole idea, and everything else is an attempt to make it precise.
state ↓ possible relations ↓ interaction ↓ changed state ↓ recurrence ↓ persistent pattern ↓ emergent object ↓ new state space
Most useful models start by defining objects and then connecting them. For a huge range of problems, that works beautifully.
RFT is interested in the cases where it doesn't — where the relationships themselves change what the objects effectively are. Where context changes meaning. Where the observer changes the useful boundary. Where different scales expose different entities. Where history changes the current interpretation. Where an emergent pattern should itself become something you can address directly.
The claim is not that graphs, probabilities, embeddings or state machines are wrong. They obviously aren't. The question is whether some systems need a representational layer that can hold several of those perspectives at once.
The current formulation keeps apart five quantities that are usually collapsed together.
q — semantic state.
What state is being represented — the orientation or categorical state of the entity within the current frame.
o — context.
Where, when, and from what frame is it being observed? Spatial, temporal, observer-relative, scale-relative, boundary-relative. The same apparent object can occupy different meaningful states under different contextual coordinates.
r — relationship.
How can states influence one another? Not a label attached after the objects exist — in some systems, a constraint on what states, transformations and future relationships are even possible.
p — path / confidence weight.
How strongly does current evidence support a particular path or transition? Probability is not the same thing as semantic state, and we don't let them blur.
u — uncertainty.
What's unresolved? Kept separate because low confidence, high ambiguity and missing information are genuinely different problems.
One experimental RFT representation uses three ternary axes. Each takes −1, 0, or +1.
3³ = 27 semantic coordinates.
The cube isn't meant to represent every property of reality. It's a compact coordinate system — a fixed scaffold across which richer contextual detail is organised. Which is exactly why the axes have to be explicit, and why context, probability, uncertainty and relationship each stay in their own lane. That separation is the point, not a detail.
In most systems, zero means absence, neutrality, null. RFT asks whether the centre can instead hold a branching or unresolved state — if, else, or, while, neither, both-possible, not-yet-determined.
The vocabulary doesn't matter. What matters is that indeterminacy itself can have structure.
The interesting part of zero is everything that could still happen.
Possibly the most important question in RFT.
Take a collection of components. Individually they have properties. Together they interact. Their interactions produce recurring organisation. Eventually another part of the system starts responding to that organisation as a unit. At that point, treating it as a list of lower-level parts becomes less useful than treating it as a new object.
A company. A traffic jam. A memory. A market. A storm. A behavioural pattern. A software service. An organism.
None of these are independent of their parts. But none of them are usefully described by enumerating those parts forever.
RFT tries to formalise promotion — the move from recurring relational pattern to higher-order object — and, where needed, demotion — the reversible decomposition back into the relations it emerged from.
It is not a proven physical theory. It is not a replacement for probability. It is not an argument that graphs are obsolete. It is not a claim that all complex systems are the same one. It is not evidence for a theory of consciousness. It is not an excuse to rename established mathematics. And it is not finished.
RFT is an attempt to build a coherent representational framework around a recurring problem. Its value will come down to whether it earns its keep against the alternatives. That burden is ours.
Read the Current Formalisation See RFT Benchmarks View Open Questions Inspect the Changelog