the thin properties are *correct*, *sufficient* and *value* (P4)

Agent-decided, reversible, provisional names (the thin-legitimacy round). Correct: on the actual process's support her later credence is the actual conditional given her later record. Sufficient: the reference — her earlier record beside the baseline's later record — is a garbling of her later record. Value: for every finite decision problem, best-responding to her credence under the actual process pays at least as much as every rule on the reference (ThinLegitimacy.Correct, Sufficient, Value). Rejected alternative: calibrated, informed, dominant — which read as properties of her rather than of the process.