Identifying a persistent shared state in a synthetic intervention benchmark

A persistent shared state can be defined operationally by writing a randomized input, reading its delayed influence at several receivers, and testing erasure, address specificity and retention. This paper reports a finite synthetic benchmark that separates this operational signature from five specified alternatives. Each of two historical protocols used 240 development datasets and 600 confirmation datasets, with 384 operations per dataset. The initial protocol classified all 600 confirmation datasets correctly but recovered the planted retention time within a factor of two in only 69 of 100 persistent-state datasets, failing its fixed 80-of-100 joint gate. An outcome-informed amendment replaced an equally weighted binned retention fit with a trial-level fit, constrained a nondecaying message-aligned term to zero, and used fresh seeds without changing sample sizes or success thresholds. It correctly classified all 600 datasets and recovered all 100 retention times within the declared tolerance. Full retrospective replay reproduced both historical result files exactly; a separate CSV scorer reproduced their gate decisions. These results calibrate a detector within its specified generator family. They do not establish general identifiability, a physical shared field, or an advantage over standard system-identification methods. This is an author preprint and has not been peer reviewed. The supplement preserves the failed initial gate, outcome-informed amendment and reproducibility limits.