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Prices two ways of delaying at a matched latency budget: the free-running clock (batch at the tick) against an independent per-message draw. Measured by the effective anonymity set of a release, and by MAP success -- how often the observer single best guess is right -- because perplexity flatters a heavy tail. The dominant result is that at the specified cover rate timing linkage is essentially total under BOTH designs: the best guess is right 98-99% of the time. That follows directly from the mixing~0 result of 3.10 -- a relay holds about one message, and delay cannot manufacture ambiguity out of one message. Traffic buys timing protection; delay does not. Between designs the independent draw wins at equal cost, against the intuition that batching should be safer: a tick is a hard boundary the observer can exclude behind, whereas an exponential never excludes anything outright. But the margin is a third of what the set size suggests (68% larger set, 19% better against the best guess), so perplexity alone would have overstated the case for Poisson-style mixing threefold. A minimum release interval changes nothing, structurally: a zero-length gap is instantaneous, so it never covers an arrival and is never sampled. Section 5 updated -- the timing caveat is discharged, and the structural results are now flagged as an upper bound on the anonymity a deployment actually gets. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>