The first directional experiment sometimes favored parabolic packets—but its fixed-angle control had an arbitrary width. This independent validation first gives that conventional control its best single shared width on the original ellipse, locks the choice, and then tests entirely different reflecting boundaries.
Read the locked protocol. Both probes have wave numbers 0.65 and 1.30 rad/cell, aimed straight ahead. Exactly two pings per wall word, 100 receiver samples per ping; the eight wall bits and their material stiffness are unchanged.
Candidate fixed angular widths: 0.45, 0.65, 0.90, 1.30 and 1.80. All are compared only on the original ellipse using the locked noisy recognition score; ties choose the smallest width. Unlike the parabolic packet, one fixed beam width must serve both frequencies.
These source-ellipse tuning scores are *not independent test results*.
| Unseen cavity | Parabolic | Optimized fixed | Difference |
|---|---|---|---|
| Awaiting tested receipt | |||
Exact eight-bit recognition under the same absolute Gaussian noise and source energy; a larger percentage is better. The decoder was trained only on the 37 allowed material states *within each new cavity*.
For any one frequency k, the supposedly conventional fixed-width packet can be set to q = k. It then has exactly the same angular weights, launch state and receiver echo as the parabolic packet.
The mathematical difference matters only when the source must act across multiple frequencies and is constrained to share one angular width. We test precisely that condition here, rather than claim a free-wave theorem proves memory reconstruction.
For this locked protocol, the parabolic design must outperform the optimized fixed-width control on both unfamiliar shapes to support the narrowly stated transfer hypothesis. A win on one and a loss on another means the claimed generalization fails.
This is a numerical simulation of a damped Robin/Neumann cavity, not a formal consequence of OpenAI's free Euclidean local-smoothing result. Geometry-dependent hardware emission costs and independent physical verification remain open.