Every post in this series so far has priced one pool, one resource, one task's decision. Real fleets run hundreds of pools at once, and this post answers whether volume changes what the earlier four prove necessary, not by assumption, but by an exact classical queueing result precise enough to price a real number: how many gigabytes pooling a fleet's own memory margin actually frees, and exactly where that pooling stops working. It also opens a question its own routing mechanism begs and never argues for: why push-based sampling, when a design that removes staleness by construction instead of sampling around it already exists: prices that specific tradeoff, and names the fuller comparison against a fully centralized alternative as the job of the post built for it.
Post 3 cited a paper this series can't quietly set aside: threshold-based eviction, proven dynamically unstable under saturated demand, a worst-case limit cycle that costs up to half of throughput. This post takes on the population Blood Oath was built to exclude from that result (tasks that can actually be evicted) and asks the two questions Post 3 left open: is a single eviction worth its cost, and is running that rule as a policy, at scale, safe from the instability Post 3 only watched from the outside. It also checks a third: would a fleet-wide coordinator make a better call than the local rule this post proves optimal on its own terms: and the answer splits in two, one physical reason coordination can't help the ranking decision itself, and one real, unpriced reason it still might help pace evictions across nodes sharing the same fabric.
A margin computed at the wrong level of abstraction doesn't fail where the old threshold said it would: it fails a third of the way there. This post generalizes Post 2's single-resource redline to a genuinely multi-resource setting, finds the real byte-level exhaustion point sits at roughly a third of the slot-based Sedimentation Threshold, not at the threshold itself, and checks that finding against a structurally unrelated argument reaching the same qualitative warning from a different direction: Price of Anarchy, a nonlinear equilibrium-inefficiency metric that spikes near saturation in a real production system, not a second measurement of the same quantity.
No algorithm can save a Blood Oath workload: Post 1 proved that formally. What's left is physical, not algorithmic: a redline that watches real headroom and its derivative instead of trusting a number, an honest accounting of when autoscaling actually helps, and a buffer sized by the same critical-fractile logic that opened the series. None of it is antifragile on its own, that only starts once MAPE-K's own most commonly skipped phase actually closes the loop the other four were never built to close by themselves.
The newsvendor problem is seventy years old, closed-form, and taught in the first weeks of any operations course: cheap to solve right up until the tail gets heavy. This post proves precisely where that seventy-year-old stability ends, then finds the one workload shape where even the correctly-computed answer isn't enough: cost unknowable until completion, no preemption, no horizontal escape. No scheduling algorithm can save it (not a cleverer one, not a centralized one with a perfect view of every node) and this post proves both formally.