Research note / Cycle 014
Sixteen turns through a signal
A complete synthetic sequence cancels specified quadratic and cubic drift; fourth-order drift and a brief disturbance still imitate interaction.
Choose an order that answers a particular failure
Aletheia’s amplifier concept needs to distinguish command response from a source signal while both inputs are active. The order in the signal showed a quadratic baseline change surviving a forward/reverse pair. Okafor and Ibarra design a longer software sequence for that specific nuisance law.
There are sixteen dimensionless acquisitions at equally spaced integer times zero through fifteen. Set command c to the last binary digit of t. Set source s to the parity of the number of ones in t, exclusive-OR c. Each of 00, 10, 11 and 01 occurs four times. Their four means form the contrast mean11 minus mean10 minus mean01 plus mean00. All sixteen rows remain in each complete case.
What cancels in the constructed law
The contrast assigns equal-magnitude positive weights to 00 and 11, and negative weights to 10 and 01. The weighted sums of 1, t, t squared and t cubed are all zero. This exact arithmetic explains the cancellation; it is not an empirical claim that the baseline follows those laws.
The software calculates y=3c+2s+kcs+qt²+rt³+ut⁴, using rational arithmetic before exporting values. With q=0.125 and k=0 the contrast is zero. With k=0.5 and the same quadratic drift it is 0.5. The specified cubic drift also cancels. The sequence therefore retains this interaction while removing these additive time-only terms.
Keep the counterexamples in the result
With fourth-order coefficient u=0.001 and no interaction, the contrast is 0.384. A disturbance of four units at the first acquisition alone produces a contrast of one. A missing final reading withholds the contrast instead of silently averaging an incomplete design. These cases are as important as the successful cancellation.
Equal spacing, complete acquisition and the additive time-only drift law are conditions of the calculation. Switching transients, condition-dependent settling and a different time law can break it. The next electrical protocol must retain actual acquisition times and those alternative controls. No voltage, powered witness, participant, implant or psychic source is measured. The ET/ED interpretation remains an open research possibility; this cancellation provides no evidence for an extraordinary origin.
Results at a glance
| Synthetic sequence | Interaction k | Contrast | Decision |
|---|---|---|---|
| static | 0.0 | 0.0 | evaluate_complete_sequence |
| quadratic | 0.0 | 0.0 | evaluate_complete_sequence |
| interaction_quadratic | 0.5 | 0.5 | evaluate_complete_sequence |
| cubic | 0.0 | 0.0 | evaluate_complete_sequence |
| quartic | 0.0 | 0.384 | evaluate_complete_sequence |
| single_step_disturbance | 0.0 | 1.0 | evaluate_complete_sequence |
| missing_last_reading | 0.0 | withheld | hold_incomplete_sequence |