Belief-Space Replica Scaling: The Price of Mean-Blind Autoscaling

A cluster serving a reasoning model cannot see how much work it has already taken on. A request that has emitted $200$ thinking tokens may stop at $210$ or run to $20,000$, and until it stops it holds KV-cache blocks and a share of decode bandwidth. Utilisation, queue depth and token rate all describe the present, while the quantity that fixes when capacity frees is the residual decode length of everything in flight. We show that this quantity is not measurable with respect to the filtration a serving stack generates, although its conditional law is, which makes capacity control for reasoning traffic a problem in belief space rather than one of regulation. Three consequences follow. Mean residual life obeys $m^{\prime }=mh-1$, so a heavy tail alone does not imply a growing residual. Policies measurable in the arrival-count filtration cannot separate two class mixes with different offered token load. And a controller that sees the belief only through its mean pays minimax regret $(1-\rho {)}^2/(4\rho )$ against mean-optimal capacity cost, which places reasoning serving in the uncertainty-dominated staffing regime where quantile prescriptions displace square-root rules. We then measure the premises on a four-replica vLLM cluster (Qwen3-1.7B, one NVIDIA L40S, $742$ decoded prompts). The two classes a deployment mixes differ by $28.3\times$ in median output length, the served mixture reaches $\mathrm{CV}=1.375$ ($95\%$ CI $[1.300,1.444]$, a lower bound under censoring), and cold start is a median $31.90$ s dominated by process bring-up rather than by the accelerator, so the actuation lag is structural. A sweep run before any length was measured put the belief-versus-point-estimate gap at exactly zero for $\mathrm{CV}\le 0.53$ and material only above $\mathrm{CV}\approx 0.87$, and the measured mixture clears that threshold with $P(\mathrm{CV}>0.87)=1.00$. We release the harness with every constant it needs already measured, and report no controller comparison on hardware: the GPU host became unreachable before that phase.