From Pressure to Priority: Correctable Particle Transport for Dynamic Partitions

Distributed systems expose two views of contention that age at different rates: an occasional membership snapshot records which workloads shared a resource, while fresher local telemetry reports only how crowded each workload's own group appears. The latter behaves like a noisy observation of latent block cardinality, not like an identity-bearing edge measurement. A bootstrap partition filter ignores that distinction and spends its particles on split-merge transitions that fresh telemetry has already contradicted; replacing the belief by the most plausible single partition discards the ambiguity that same-cardinality groups necessarily carry. We introduce Pressure-Residual Partition Transport (\prpt), a full-support proposal for sequential inference over dynamic set partitions. factorizes a pressure-conditioned move into an event, a target cardinality, and a product-weighted fixed-cardinality subset. An elementary-symmetric-polynomial recursion samples splits and evaluates their proposal probabilities without enumerating exponentially many subsets, so exact importance correction remains available. The resulting kernel is permutation equivariant and costs $O(k|V|+k^2+{\sum }_{C\in \text{partn}}|C{|}^2)$ for $k$ blocks. With 32 particles under contaminated observations, lowers posterior total variation from $0.206$ to $0.065$ on an exactly enumerable benchmark, and removing correction raises it to $0.378$. In delayed, lossy multi-step experiments, it improves a prespecified decision objective in all six test conditions. On 600 held-out Alibaba trace-derived episodes with mostly exact pressure, it reduces total variation by $0.042$ and raises the effective-sample-size ratio by $0.211$ relative to an equal-budget bootstrap filter; a separate 397-episode non-exact slice retains the ESS gain but exposes day-dependent posterior accuracy. These results delimit when cardinality telemetry improves finite-particle inference without pretending that it identifies membership.