Research note / Cycle 011
The echo one sample later
A finite lag search catches one delayed command echo and leaves nonlinear and mixed sources unresolved.
The interface can hear its own command
Aletheia’s proposed amplifier must preserve an acquisition without mistaking its own command for an independently originated signal. The receipt and source study compared an exact scaled echo with a different trace. That zero-lag screen had no reason to recognize a command displaced in time.
Okafor now supplies the twelve-value command 0,1,-2,0,3,-1,0,2,0,-3,1,0 and a separate authored source 1,0,1,-1,0,2,-2,0,1,1,0,-1. Six controls contain the command multiplied by three, that command delayed one sample, the squared command, the source alone, command-times-three plus source, and silence. These are synthetic arrays, with no sampling-rate or biological interpretation.
An offset changes what the screen sees
Ibarra compares each source with command shifts from -2 through +2 samples, padding uncovered positions with zero. The table retains the unshifted cosine and the strongest absolute cosine in this finite set. It reports the signed cosine and selected lag; it does not estimate a physical conduction delay.
The delayed-command control has unshifted cosine -0.275862 and cosine 1 at lag +1. The command-only control gives 1 at zero lag. Both receive an exact-linear-echo flag. Squared command and combined input remain unresolved, even though their authored construction contains command information. Silence has zero energy, so its cosine is undefined rather than evidence of independence.
A useful failure remains a failure
The source-only control’s strongest tested cosine is 0.595550 at lag +1. A correlation in a short array does not by itself identify an echo, and lack of an exact match does not identify a neural source. The screen deliberately flags only exact linear agreement; it is not a general artefact detector.
No samples are subtracted or discarded. A future electrical experiment must retain command-only, source-only and combined measurements and include delays and nonlinear response. Powered witness completion remains a separate unperformed test. No participant, neural recording, implant or resolution of the earlier authority dispute is introduced.
Results at a glance
| Synthetic source | Zero-lag cosine | Best tested lag (samples) | Best cosine | Screen outcome |
|---|---|---|---|---|
| command_only | 1.0 | 0 | 1.0 | flag_exact_linear_echo |
| delayed_command | -0.275862 | 1 | 1.0 | flag_exact_linear_echo |
| squared_command | 0.01323 | 2 | -0.053858 | unresolved_source |
| source_only | -0.347404 | 1 | 0.59555 | unresolved_source |
| combined | 0.973224 | 0 | 0.973224 | unresolved_source |
| quiet | undefined | undefined | undefined | undefined_zero_energy |