Predictable integrable signals give zero expected future-stop scores with rates from other independent Bernoulli runs, a common probability, fixed denominators, and retained runs

We studied a score that links a current signal to the next stop label. We prove that its expectation is zero when rates come from other independent runs. The proof requires one common Bernoulli stop probability, signals known before the next label, fixed trial denominators, and all runs, including runs with zero signals. The probability can be unknown. Exact enumeration passed 60 cases. Simulation used 40,000 cohorts in 20 settings. In the primary count simulation, normal tests rejected zero in 94.0 percent of cohorts with rates from the same run and 5.65 percent with rates from other runs. A benchmark used all 226 AOMIC PIOP2 event files. The count score changed from -0.0614 to -0.00490 when it used other-run rates. A post-plan conditional check found that the common independent Bernoulli model did not fit the run stop counts. Thus the public scores remain descriptive. The method does not establish the cause of the earlier human response association. The package preserves source files, provenance, proofs, code, all score draws, and a verified rerun.

future-stop score · independent runs · Bernoulli assignment · sample covariance · predictable signal · stop-signal task · AOMIC PIOP2