Your old Slider2 drew a three-dimensional orbit from recorded audio blocks. This successor compares one traveling tone, two phase-locked crossing waves, the same two directions with scrambled phases, and six phase-scrambled waves—all with matched physical mean-square amplitude. Its new microscope preserves interference before squaring, then solves a screened auxiliary-disk potential.
Target spatial mean-square displacement of every signal; equality verified numerically, not a matched acoustic loudness at a single listening point.
Each polarization channel adds complex wave amplitudes before measuring energy; diagonal-only power is the phase-blind control.
A positive Green-potential surrogate on a nine-by-nine polarization grid. Not the exact OpenAI conserved tensor.
One spatial direction, one phase. A perfectly predictable orbit with no between-mode interference.
Two different directions keep a reproducible interference pattern. A fixed relationship despite the same total power.
Same two directions, frequencies, amplitudes and power as B. Only relative phase stability changes between samples.
Six directions change their relative phases across trials. Instantaneous interference remains, but its spatial pattern wanders.
| Physical condition | Power | Raw-lift contrast | Potential contrast | Phase cross-terms | Repeat correlation |
|---|---|---|---|---|---|
| Measurements will appear when the simulations finish. | |||||
Power is the spatial mean of the squared real field. Raw-lift contrast is the peak-to-mean of coherent directional density summed over disk. Potential contrast uses the disk Green solve. “Phase cross-terms” means the relative absolute difference between coherent and diagonal-only densities; it is not a learned classification score. Repetition measures spatial-map correlation between two independent phase samples.
The OpenAI manuscript constructs a positive, conserved lifted wave-current tensor in additional coordinates, then uses a planar auxiliary Dirichlet potential to obtain bounds. Slider3 borrows the coherent summation, a polarization disk, and a positive screened inverse. Our finite-difference surrogate uses an isotropic spatial Laplacian, not the paper's directional, variable-coefficient geometry. Its channels are approximate, and no conservation theorem is claimed.
The three fields are synthetic periodic 2D spatial waves—not quantum dynamics or microphone recordings. Slider2's actual cable-and-speaker loop remains an earlier, distinct hardware experiment.
Not merely prettier interference images. The auxiliary potential would have to improve a predeclared task—say predicting which source produced an unknown noisy field, or tracking stable coherent relationships—over raw signal energy, standard phase coherence, a coherent density without the potential, and simpler spatial smoothing, at comparable observation and computation costs. This first page tests mathematical feasibility and exposes those controls; it does not yet demonstrate a neural learning rule.
OpenAI wave manuscript (October 25, 2026) · Derivation, guardrails and next experiment