Nine states of one scalar reproduced eight-site sound means in separate human SEEG and fMRI studies

Time averaging can hide a scalar with fixed monotone readouts. We give an exact construction for any finite real mean map with free readout offsets, ranges and condition-specific dwell times. P coordinates need at most P+1 fixed scalar states. The universal finite-state bound is sharp. A range formula is exact within a one-jump threshold family. Separate public studies supplied SEEG from eight patients and fMRI from 28 adults. Fixed eight-site panels had 165 sound means per person. Nine states reproduced all maps within 9.42e-16 of each coordinate mean range. Reserved applications used six patients, 16 B2021 adults and eight NH2015 adults. Mean required range factors were 4.3515, 4.3490 and 3.9520. Independent time integrals and integer programs checked all 36 fits. An exact positive-output example had crossed mean orders, nonzero area and zero repeat variance. A stricter check froze readers from repeat 0. It failed on at least one later sound in 29 of 30 reserved people. Later weights used later outcomes, so this was not prediction. The result is a measurement limit and a checked tool. It does not establish one-dimensional brain activity, a shared neural code or causality. Condition-driven dwell times retain model complexity. Different cohorts, clinical sampling, source screens, filters, time scales and vascular effects limit biological interpretation. The package supplies code, proof, source pins and terms, all scalar results, figures and repeat instructions. Neural arrays remain external.

human neuroscience · SEEG · fMRI · time averaging · monotone readout · neural dimensionality · scalar mixture · measurement limits · reproducibility