Why it is a question
THEORY-244 now states two expectation bridges as re-derived: entropy and mutual information are the expectations of their Kolmogorov counterparts to within K(f). Grünwald and Vitányi (LIT-224, read in NOTE-776) also state a third. For a recursive distortion d, a total recursive source f and m i.i.d. repetitions, the expected structure function brackets the distortion-rate function, (1/m) E h_x(mR + K(f, d, m, R) + O(log n)) ≤ D_m(R) ≤ (1/m) E h_x(mR), and the per-symbol limit equals D(R) (Theorem 6.27, Corollary 6.29). The reading found the right-hand step asserted: it identifies h_x(mR) with the radius of x’s sphere in a canonical cover, with complexity conditioned on mR where h_x is unconditional. The arXiv record carries the authors’ own warning about errors in the draft.
What would answer it
A published version of Theorem 6.27, or of the Vereshchagin–Vitányi individual rate–distortion paper it follows, that fills in the right-hand inequality, or a derivation the record can follow step by step. It is answered no by a computable source f for which expected Kolmogorov complexity exceeds entropy by more than K(f) plus a constant (which would also break THEORY-244’s first bridge), or by a recursive source and distortion for which (1/m) E h_x(mR) fails to converge to D*(R). Empirical compression ratios cannot settle it, since a real compressor gives only upper bounds on K.