A signal change rule bounded correlation error by 0.01 in 12 AOMIC runs with fixed unweighted OLS and centered outputs

We tested a rule for correlation error after separate repeated removal of drift and motion. The rule uses the last signal change and the angle between two nuisance spaces. It requires fixed columns and time rows, unweighted OLS, and centered outputs. A valid error fraction below one proves that a joint residual is nonzero. We derived a sharp algebraic bound and a sign rule. For a common error fraction limit q, correlation error is at most 2q squared. We tested 100 cortical regions in 12 fixed AOMIC working-memory runs from ds002785 and ds002790, version 2.0.0. At ten cycles, 11 runs had pair errors above 0.01. Signs changed for 136 of 59,400 pairs. The stop rule gave error limits of 0.01 for all pairs after 13 to 234 cycles, with a median of 53. The largest measured error at these stops was 0.004941. The global signal limit of 0.000001 required 67 to 1986 cycles. These accuracy targets differ. No speed benefit is claimed. A constructed signal pair had a correlation error near two despite a global signal error below 0.000001. The audit passed 144 separate QR and direct-cycle checks, constructed cases, a source extraction replay, and an exact numerical repeat. The proof uses exact arithmetic. The implementation uses float64 and does not use interval arithmetic. The fixed sample does not support a population or clinical claim. The package preserves code, regional data, source versions and hashes, proof, full results, and reproduction instructions.

correlation error · ordinary least squares · alternating projections · error bounds · functional MRI · AOMIC