Why it is a question
THEORY-155 is a theorem about an idealized chain: learners who share one prior, whose likelihood matches the production distribution, and who each sample a hypothesis from their posterior. Griffiths and Kalish (LIT-769, read in NOTE-599) prove it, and the record checked the proof. Until 2026-10-19 the THEORY’s promotion condition also asked for the theorem’s application to people. At the owner’s direction, from the owner’s promotion audit of that date, the two are separated: the THEORY holds the theorem and is Active, and this question holds the application.
It is open because nothing the record holds meets the condition below.
The nearest test is Kalish, Griffiths and Lewandowsky (LIT-820, read in
NOTE-616): 28 of 32 human chains settled on a positive linear function,
whatever the first learner was trained on, which is the bias the authors
took from earlier function-learning studies. The prior was neither measured
on these learners nor set by manipulation, stationarity is unconfirmed, and
a strong mode would be reached by sampling and MAP learners alike.
NOTE-616’s references to THEORY-155’s promote_when are to this
condition. Kirby, Cornish and Smith’s laboratory chains (LIT-771, skimmed
in NOTE-596) become more structured, but no participant’s prior was
measured, and their Experiment 2 filters what is transmitted, which the
theorem does not cover. NOTE-628 shows community size changing the outcome
among interacting learners, which a single chain does not model.
What would answer it
The condition formerly on THEORY-155, unchanged: a transmission-chain experiment in which the learners’ prior over the hypotheses is measured or set independently of the chain (for example by manipulation or a separate elicitation), and the chains’ long-run distribution of hypotheses is compared against it, matching it where the learners’ responses behave as posterior samples and departing from it in the direction the MAP analysis predicts where they behave as maximizers. Chains that merely become more structured, with no independent measure of the prior, cannot settle it either way.