Research note / Cycle 012
When the inputs stop adding
An authored interaction term defeats prediction from isolated command and source responses, constraining the next electrical test.
The combined acquisition is a separate condition
Aletheia’s intended amplifier must record a signal while its own commands are active. The delayed-echo study retained mixed and nonlinear sources without classifying them. Okafor and Ibarra now ask a prior question: would the command-only and source-only acquisitions predict what happens when both inputs are present?
The inputs are dimensionless authored amplitudes c and s. Twelve deterministic cases use six input pairs under two specified laws: y = 3c + 2s and y = 3c + 2s + 0.5cs. The latter term is deliberately introduced interaction. These are equations evaluated in software, with no sample rate, electrical transfer measurement or biological source.
The isolated responses can look perfectly ordinary
For each pair the command-only response uses s=0, and the source-only response uses c=0. The interaction term vanishes in both isolated conditions. Their sum therefore predicts the linear combined response exactly, with zero residual in all six additive controls.
In the interaction cases the combined output differs by 0.5, -0.5, -0.5, 0.5, 1 and 0 across pairs (1,1), (1,-1), (-1,1), (-1,-1), (2,1) and (0,2). Reversing one input changes the sign; increasing the command changes the difference. The zero-command control gives zero despite the interaction law remaining present.
Subtraction does not name the remaining source
Removing a separately measured command-only trace would leave 2s + 0.5cs under the specified interaction law. That remainder still depends on the command. Its existence cannot identify a neural contribution, let alone support the amplifier’s extraordinary ambitions.
The next electrical protocol must retain isolated and combined conditions, input reversals, amplitudes and raw output. No subtraction is authorized for acquired samples. Powered witness completion remains a separate unresolved experiment; this calculation supplies neither a storage result nor evidence from a participant or implant.
Results at a glance
| Command | Source | Solo sum | Combined | Difference |
|---|---|---|---|---|
| 1 | 1 | 5.0 | 5.5 | 0.5 |
| 1 | -1 | 1.0 | 0.5 | -0.5 |
| -1 | 1 | -1.0 | -1.5 | -0.5 |
| -1 | -1 | -5.0 | -4.5 | 0.5 |
| 2 | 1 | 8.0 | 9.0 | 1.0 |
| 0 | 2 | 4.0 | 4.0 | 0.0 |