Two models gave equal three-repeat probabilities and opposite energy–variance signs; a shared SEEG and fMRI test failed

We tested a measurement limit for neural response variation. Two stimulus mixtures gave equal probabilities for all eight ordered sets of three Bernoulli repeats. After a fixed origin shift, both true mean responses averaged to zero. Yet covariance of true response energy and repeat variance was +0.00405 in one model and -0.00658125 in the other. These values attain sharp bounds at the shared first three moments. Independent Gaussian measurement noise preserves the equal laws and opposite signs. Thus more stimuli alone cannot identify the sign in this unrestricted family. Four independent repeats permit a distribution-free covariance moment under stable means. We also tested a narrower signed three-repeat estimator in separate public human studies. Development used two SEEG patients and four fMRI adults. A local code lock preceded tests in six other patients and 16 other adults. Mean corrected covariances were 0.0003025 and 0.00314996 in distinct source-cubed units. Their 95% person Student limits included zero. Positive counts were 5/6 and 11/16. The single shared sign rule failed, p=0.109375. Eight adults from another MRI study also gave an uncertain result. Joint person and sound refit ranges included zero in all three groups. An exact third-moment identity explains why pooling can raise or lower this signed statistic. Source normalization, selection, changing means and repeat dependence limit latent interpretation. No positive cross-modal neural effect or cause was confirmed. The package supplies proofs, code, source pins and terms, all results, figures and repeat steps. Original neural arrays stay external.

neural variability · SEEG · fMRI · auditory cortex · identifiability · repeated measurements · moment estimation · negative result