The October 25 wave manuscript uses an angular multiplier whose width decreases as frequency increases. Here that same law shapes a physically launched wave packet. Both source designs inject equal energy into the eight-wall ellipse, and a single receiver measures signed echoes. The crucial question: which packet better distinguishes wall memories never used for calibration?
The complete 256-state simulation is a scoring oracle only. The trained reader sees 37 or 93 calibration states, identically chosen for both source arms. The oracle stays inside a worker.
Both use Gaussian angular weights. Parabolic: exp[−ρ k(1−cos Δθ)]. Fixed: replace k with reference k₀=0.9. They are identical at k=k₀, but not at these two test frequencies.
Snapshot at step 45 through a blank cavity, with the selected physical packet. This is for visualization only. The memory decoder receives no field snapshots or FFT features.
Both injected wave energies are normalized to E = 1.
Correct 8-bit memories at common noise, never included in calibration.
Same injected energy, frequency, steering, number of pings, receiver and decoder.
Each held-out record will be scored at matched noise. This compares source shaping, not a new local-smoothing theorem.
Median nearest distinct wall-response distance divided by detector noise RMS, calculated from the entire independent oracle. This is an ideal upper-bound diagnostic, not an affordable memory decoder.
In the October 25 OpenAI Euclidean-wave manuscript, imaginary translation of a free positive half-wave supplies a directional multiplier exp[−ρk(1−cos θ)]. Our source synthesizes a coherent angular superposition using those weights, then propagates a real, approximately forward-moving Gaussian packet through a bounded, damped Neumann/Robin cavity. This is an engineering analogy, **not** the actual complex-time evolution or a theorem inherited by the cavity.
Both arms use 48 angular components, equal spatial packet width, the same wave numbers (0.65 and 1.30 rad/cell), three directions (−60°, 0°, +60°), equal discrete kinetic-plus-gradient source energy E = 1, same 96×96 cavity and one receiver, same 100-sample windows, one ping per selected packet, the same sparse calibration states and common Gaussian detector noise. A narrower lobe by itself is not a discovery.
Success requires reproducible gains in separating the 219 (pair calibration) or 163 (triple calibration) unseen wall records relative to the fixed-angle control, not just larger echo amplitude. A tie or loss is a genuine rejection for these parameters. The full dictionary diagnostic is explicitly separated from the restricted-calibration score. Independent cavities, calibrated noisy training, matched elapsed waiting time and hardware validation remain outside this experiment.