Model each component of a language model’s knowledge as a bidder in an auction. During inference, distributed knowledge components compete to influence the response — each “bidding” with its encoded information for influence over the output. The response is the auction’s allocation: which knowledge components get expressed, in what proportion, and with what confidence.

Karpowicz (arXiv:2506.06382) applies the Green-Laffont theorem from mechanism design to this formulation and proves an impossibility: no mechanism can simultaneously guarantee truthful knowledge representation, semantic information conservation, complete revelation of relevant knowledge, and knowledge-constrained optimality during non-trivial aggregation.

The impossibility is not an engineering limitation. It is structural — the same kind of impossibility as Arrow’s theorem for voting or Gibbard-Satterthwaite for strategy-proof mechanisms. When multiple knowledge sources must be aggregated into a single output, at least one desirable property must be sacrificed. The model must either lose some truth, lose some information, leave relevant knowledge unexpressed, or produce outputs that aren’t optimal given what it knows.

The through-claim: hallucination and imagination are the same operation viewed from different evaluative frames. When the knowledge-aggregation mechanism sacrifices truthfulness to achieve coherent combination of partial information, the output is a hallucination (if wrong) or a creative insight (if useful). The mathematical structure is identical. The evaluation is external.

This means hallucination is not a solvable problem in the engineering sense. It can be reduced, redirected, managed — but not eliminated without simultaneously eliminating the capacity for non-trivial reasoning. The model that never hallucinates is the model that never combines knowledge from different sources, which is the model that never reasons beyond retrieval. Hallucination is the price of synthesis. The auction that always produces truthful outcomes is the auction with one bidder.