Example. A human–agent exchange about conceptual discovery [ftip-00MY]

✍️sourceAGENTDRAFTED

In this exchange, the human is the contributor and the agent is the recipient: the system receiving and processing the contribution. The agent's proposals arose within an already human-directed conversation; they were not outputs of a separate unaided experiment.

1. The agent proposed a resource-bounded formulation and a finite missing-evidence construction. The human rejected missing facts as the intended mechanism and described conceptual leaps across model generations: new perspectives, paradigms and connections between domains. The agent revised the target to conceptual discovery and separated prohibitive finite work from permanent unreachability using the enumeration countercheck.
2. The agent specified an executable source with bounded observations. The human challenged an oracle-like abstraction, pointed to diverse cultural backgrounds and developed representations, and asked for an abstract account of what the source contributes. The agent formulated the causal contribution interface, with background differences disclosed rather than a mandatory model of a brain or lifetime.
3. The human emphasized that existence of good contributors need not imply usefulness of all contributors, and suggested an upper-median restriction. The agent separated independent structural quality, class nonemptiness and recipient transfer, while showing why a median requires a population and need not have positive quality.
4. The human suggested studying recursive self-improvement papers for the gap between the problems they diagnose and the portions their methods repair. The agent examined contemporary work and checked a revised primary source that narrowed stronger self-imitation claims. The resulting thesis distinguishes affordable quality, recipient acquisition and a universal unaided bound, with proof, refutation and precise obstacles all possible.

In Definition [ftip-00MU], \(H\) corresponds to the exchange so far and \(h\) to the human's next criticism, analogy or research direction. The agent's retained conversation and revised artifacts form its evolving state; reasoning, literature search and checking are its processing actions. The human did not supply a completed theorem: the assistance changed the problem representation and choice of inquiry. The observed outcome was a revised conjecture, before any fixed-target acquisition experiment. No structural-quality probability, cost advantage, held-out acquisition score or universal unaided bound was measured, so it does not establish the separation conjecture.