A public process for changing task demands [ftip-00NL]

✍️sourceAGENTDRAFTED

Extend the public rewrite setting of § [ftip-00NG] by a sequence of demand states \(X_t\), with a declared initial distribution. A fixed transition law \(K_\theta \) governs how the demand state changes. Conditional on \(X_t\), a fixed generator \(G_\theta \) samples a certified task. The parameter \(\theta \), both laws and the rewrite rules are available to both campaigns. A demand state may favor particular compositions, expression sizes or interfaces, so an abstraction useful in one period need not remain useful in the next. The future random seeds are unrevealed, and the laws are fixed independently of either learner's decisions. The laws are given as computable programs; their execution and any derived approximation are charged.

For example, demand may move between tasks dominated by local cancellation, tasks requiring repeated composition, and tasks coupling several components through a shared boundary. This describes possible structure in the generator, not established difficulty of those tasks. The change law could make a local regularity predictive of later coupling, so acquiring a compositional representation has value before that coupling becomes common. An actual construction must specify the expressions, rules and transition probabilities, and show that its proposed investment really reduces later work.

A state \(X_t\) can be observed directly or inferred from the common history of revealed tasks and responses. Fix which case applies. If the state is latent, both campaigns receive the same observations; the source has no private reading of the current state or future seed. In the computational version, their problem is to process the available history and public laws cheaply enough. Uncertainty remaining even for an unlimited observer is common to both. Giving only the contributor an informative sensor or an undisclosed generator defines a separate information-access comparison.

Development uses earlier independently seeded episodes from the declared process family. It may teach a learner to recognize which histories predict useful future structure, but cannot supply the final episode's hidden state. Selection of the source and its retained state precedes final seeds. During evaluation, tasks arrive in order; any feedback and adaptation available after an answer follow the same specified schedule on both sides. The final correctness predicate, proof rules and certificate cap stay fixed throughout the changing demand distribution.