Beyond Learnable Novelty

Abstract

Learnable novelty formalizes the reusable structure that a computationally bounded observer can extract from data and supplies a differentiable estimator that can be optimized across dynamical systems, representations, and agents. Fractalish treats this as an important but incomplete stage of intelligence: extraction without persistent, governed integration.

A persistent observer must retain not only what was learnable, but the evidence and conditions under which an interpretation was formed; the observer, target, scale, and protocol; uncertainty and representational residue; contradiction and correction history; downstream consequence; counterfactual uncertainty; and the way the encounter should alter future accessibility.

The bounded observer is necessary but not sufficient

Let an observer receive data conditioned on prior context. Learnable novelty identifies reusable structure that the bounded observer can acquire and reuse. That is a useful measure of observer-relative extractable structure.

It does not, by itself, specify what should happen to the observer after the structure is extracted.

Fractalish therefore treats learnability as a candidate input to weighting, not as a complete governance system.

Persistent understanding as changed accessibility

A persistent observer is a history-bearing system in which an encounter can produce inspectable, versioned changes to future accessibility, retrieval, caution, association, correction, and action posture.

B_(t+1) = Pi_G(B_t, E_t, W_t)

The update rule above is an architectural contract, not a universal law. The point of the public note is the separation of evidence, weights, governance, replay, and action boundary.

The WeightReceipt

For an encounter, observer, target, context, and time, UFWK specifies a structured field with structural, contextual, affective-significance, prospective, consequential, mnemonic, residual, and counterfactual dimensions. An uncertainty envelope travels beside it.

A task-specific routing projection may be derived from the field, but it must never replace the underlying field.

Why learnability is one signal, not the governor

Learnable novelty may contribute to structural significance, observer-relative novelty, prospective learning value, and mnemonic priority. It must remain distinct from evidentiary support, truth, authority, causal responsibility, moral value, rights, and action permission.

The Acrobot result matters precisely because it shows that intrinsic learnability can conflict with a declared task objective. That is evidence for separation of candidate signal and governance, not an indictment of the measure.

Deterministic integrity, Cognitive Basin, and host-independent continuity

Natural Math contributes exact local transitions, deterministic receipts, replay, lineage, and fail-closed integrity. Cognitive Basin is the routing layer that turns approved receipts into changed accessibility. Bolt-On separates continuity from the current host so portable semantics survive host replacement while execution remains host-owned.

Experimental design and falsification

The main comparison is between stateless, summary-based, vector-based, novelty-only, and history-bearing observers under contradiction, correction, delay, and host substitution. The stronger claim should be narrowed or rejected if simpler memory baselines perform as well, weights prove unstable, receipt overhead dominates benefit, or substitution cannot preserve protected evidence.