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Two release designs at a MATCHED delay budget, so they differ only in how they delay: clock (batch at free-running ticks, the existing model) and jitter (each message waits its own exponential draw, mean set equal to the clock residual). Plus min_blend_delay, which forbids intervals shorter than it. Minimum interval -- a negative result, and provably so. A zero-length gap is instantaneous, so it never covers an arrival and is never sampled by the residual or by the size-biased interval. Excluding it therefore leaves the mean hold exactly unchanged, and with it blending and linkability; what it does change is E[S], the gap between release opportunities. Confirmed analytically and in simulation: 1.168s vs 1.167s at M=3. Timing attack -- the effective anonymity set of a release (perplexity of the observer posterior over which arrival produced it), plus MAP success, the chance its single best guess is right. The second matters because perplexity flatters a heavy tail: an exponential never fully excludes an old arrival, so it can look unlinkable while still being guessed correctly. At the baseline rate BOTH designs fail almost completely -- MAP success 0.98-0.99, effective set ~1. A relay handles so little traffic that in->out matching is trivial, which follows directly from the mixing~0 result. Traffic, not delay, is what buys timing protection. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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