L6 — a self-supervised world model: prediction is forward settling, error is the learning wave
The substrate predicts itself. Prediction is forward settling — the learned asymmetric transition field acts on the present, the L0 attractor cleans up the next state — and learning is the difference wave (an error-gated update). Held-out next-step error falls monotonically 0.978 → 0.126, generative rollout stays faithful to a 12-step horizon, and a forward model beats a reactive store by directionality.
Predict-next is the universal self-supervised training signal, and a large error wave is a novelty / surprise signal. All four milestones pass: the model learns an unlabeled stream from its own error (W1), rolls out plausible continuations to horizon 12 then drifts honestly (W2), grades novelty by error magnitude (W3), and — the headline — a forward model anticipates where a reactive store that saw every transition only returns the present (W4). The honest [O]: error-gating halts at prediction-sufficiency (the operator is directionally, not magnitude-identically, the L2 coupling, cosine ≈ 0.81).
L6 makes the substrate a self-supervised learner: it predicts its own next state and turns its own error into the learning signal, with no external labels (session v0.7, digest 41e81a7f…). This is the free-energy-like core — a generative world model built from the frozen L0 and the L2 trajectory.
Prediction is forward settling; learning is the difference wave
The forward step is the learned asymmetric coupling acting on the present (thresholded), followed by L0 clean-up onto the next attractor. The error — prediction minus outcome — is a difference wave that drives an error-gated delta update. Held-out next-step error falls monotonically from 0.978 to 0.126, sign-stable across stream length (m ∈ {4,6,8}) and learning rate (η ∈ {0.25,0.5,1.0}).
Four milestones, all verified
| milestone | result | grade |
|---|---|---|
| W1 learn an unlabeled stream | held-out error 0.978 → 0.126, monotone | [V] |
| W2 generative rollout | faithful to horizon 12, honest drift at step 13 | [V] |
| W3 novelty / surprise | graded: familiar ≈ 0, full violation ≈ 0.97, boundary 0.1 | [V] |
| W4 forward > reactive (headline) | forward anticipates; reactive only returns the present | [V] |
Why the forward model wins
W4 is the key result and it honours the L5 break. A reactive store that has seen every transition can only return the present state; a forward model anticipates the next. The advantage is therefore directionality / structure, not a missing abstraction — confirmed by controls: on a fixed-point stream the gap vanishes, and an untrained model has no real advantage.