Why it is a question
A18: “We have discussed statistical distinguishability, information retention, availability, reconstructibility, access cost, and action feasibility. These shouldn’t all be compressed into ‘usable information.’” Its schematic definition: C_ε(D | M) = inf over procedures δ of the cost C(δ) such that P[δ(M) ≠ D] ≤ ε. It said what is missing: “a distribution over tasks or inputs, a computational-cost model, and a specification of the target variable.”
CLAIM-199’s usable information fixes a rule class and asks what it can extract. This asks for the cost of extraction as a quantity, so that CLAIM-304’s infeasible case and CLAIM-199’s helpful garbling sit on one scale.
An answer is a definition with those three parameters fixed, shown to recover CLAIM-199’s rule-class case and CLAIM-304’s computational case as special cases. Time-bounded Kolmogorov complexity and computational learning theory are the nearest existing tools.
Note of 2026-10-21: V-information fixes two of the three parameters
Xu, Zhao, Song, Stewart and Ermon 2020 (LIT-1309, NOTE-1048), read in full on 2026-10-21. Their V-information fixes the class of procedures (a predictive family V) and the success criterion (log loss), and with V the one-coordinate rules it recovers CLAIM-199’s rule-class case (THEORY-846). It has no cost of recovery: a procedure is in V or not. CLAIM-304’s computational case would be V the efficient predictors, which the paper names (its §3.3) and proves nothing about. Its PAC bound (THEORY-840) makes the quantity estimable for a family of bounded complexity, which is a cost of measuring it, not of recovering the distinction. So it is one of the “nearest existing tools”, not an answer. The question stays Open.