Why it is a question
THEORY-377 holds what Olston, Loo and Widom (2001) simulated. Their rule widens a cached interval on a value-initiated refresh and narrows it on a query-initiated one, with probabilities set by ρ = 2C_vr/C_qr. It settled within 1% of the best fixed width on one random walk and within 5% over eight walk settings. On one 50-host trace it almost matched a tuned adaptive exact-caching rule. The claim that it converges to the best width is argued from the balance condition ρ·P_vr = P_qr (THEORY-386), not proved, and every result is the authors’ own simulation. Until 2026-10-20 this was THEORY-377’s promote_when.
What would answer it
- A proof that, under stated processes for value changes and query precision demands, the width the rule sets converges, in distribution or in time-average cost, to within a stated factor of the best fixed width.
- A trace study on data other than the authors’, measuring the rule’s cost against the best fixed width and against an adaptive cache-or-not rule.
What would not answer it: more simulations on random walks, or further results on the authors’ own traces.