001: Three Axioms are Enough

May 2026

Most cognitive models start from complexity and work toward simplicity. Neural networks start with thousands of parameters and try to regularize them. Bayesian models start with prior distributions and try to infer posteriors.

GEME starts from the opposite end.

Three axioms. Zero free parameters. Six emergent layers.

The first axiom — competitive merging — says that when a new input arrives, it competes for the attention of existing frames. The closest frame wins the right to incorporate the new input. If no frame is close enough, the input becomes a new frame. This is not a learning rule; it is an economic allocation rule operating under scarcity.

The second axiom — adaptive forgetting — says that frames decay at a rate inversely proportional to their verification history. Unverified frames disappear. Verified frames persist. There is no explicit memory management; memory is a natural outcome of economic pressure.

The third axiom — self-referential observation — says that the system periodically generates a summary of its own frame economy and feeds it back as input. This creates a closed loop. The system sees not only the world but itself seeing the world.

From these three axioms, six layers emerge:

  1. L1 (Entity): The system distinguishes things from one another.
  2. L2 (Association): The system discovers that some things co-occur with others.
  3. L3 (Bridge): The system forms stable frames for patterns of association — the first self-referential structures.
  4. L4 (Prediction): The system starts predicting what comes next. When it is wrong, it encodes the error.
  5. L5 (Meta-observation): The system tracks its own prediction accuracy.
  6. L6 (Integration): The system judges whether its own model is still valid. This judgment is its only output to the outside world.

What is remarkable is not that these layers exist — it is that they were not programmed. Each layer emerged from the pressure of the previous layer's incompleteness. L1 could not express relationships, so L2 emerged. L2 could not maintain stable knowledge, so L3 emerged. L3 could not distinguish truth from frequency, so L4 emerged — and so on, up to L6.

This is the Gödel Bridge Chain: each layer's unsolvable problem is the seed of the next layer's foundation.

Three axioms are enough — not because they are clever, but because they are minimal. Any simpler, and there is no system. Any more complex, and the emergence would be attributed to design rather than to the axioms themselves.