Definition
A100: min_T D_obs(T) + λ D_decision(T) + γ D_structure(T) subject to I(U;V) ≤ R, “where U and V are source and target realizations, R is the information-rate budget, and the three distortion terms measure complementary aspects of fidelity. This is the mathematical centerpiece. The translation, diffusion, and telephone-game cases become different ways of instantiating the same construction.”
Manuscript §6: L = L_obs + λL_str + γL_dec, “a flexible directed fidelity functional; there is no universal choice of weights or observational tasks.”
What changed silently
Three things, none argued for in the exchange, on the chunk-6 reader’s reading (the manuscript’s form is later than U37):
- the rate budget left the objective and went to §5’s rate–distortion function;
- the weights swapped, so that λ now weighs structure and γ decision;
- “centerpiece” became “flexible”.
Its terms are TERM-021 (observational) and TERM-028 (decision); the structural term is the restriction defect of C6 Appendix B.
Why it is still Active
TERM-043 replaced the weighted scalar as the foundation of fidelity on 2026-10-10. Under it, transports are compared component by component, and a scalar exists only once a task fixes the weights. The weighted sum survives in that role, as the scalar a task-fixed weighting gives. It is also what the manuscript §6 states, as “a flexible directed fidelity functional”, and no draft has yet changed that.