Evaluating epistemic admission in shared agent memory is difficult because repeated occurrences of the same claim can be mistaken for independent evidence. An agent may copy a retrieved belief verbatim or paraphrase it before writing; admitting a false claim exposes later agents to misinformation. To address this, we introduce the Correlated Promotion Benchmark (CPB), which assesses whether candidate claims should be admitted to shared memory.\ \ CPB has two configurations. CPB-Static freezes a test split from publicly annotated sources and provides fixed gold‑standard actions. CPB-Live runs multi‑agent teams over a common store, logs all writes and retrievals, and tracks source lineage for each scenario. A separate consumer reads only from the store to evaluate answer quality derived solely from memory.\ \ We evaluate eight admission policies across four agent families. Results show that policies that deduplicate sources reject many true claims together with false ones, while coverage‑focused policies admit nearly as many false claims as unrestricted sharing. Gating on declared source type reduces false adoption to $0.06$--$0.09$, compared with $0.22$--$0.47$ for other answering policies.\ \ Once an uncontested false belief enters memory, the consumer asserts it in $0.97$--$0.99$ of probes across all families. No non‑oracle policy consistently rejects false claims across verbatim copies, paraphrases, and paraphrases declared authoritative. These findings reveal the fundamental limitation of admission policies that lack access to source lineage.\ \ Review