Author notes — full detail, auditor-facing
Test JJ Phase 1 is the empirical search for a *joint* 7-vector operator — whether two coupled cavities, driven with mismatched per-cell drive, produce a spectral fingerprint that cannot be decomposed into the sum of two independent cavity fingerprints. If such a joint emergence exists, it would be the empirical handle on the framework's prediction that the seven foundational expressions (CONCENTRATE / DISTRIBUTE / RADIATE / POLARIZE / TRIANGULATE / CUBIFY / FRUSTRATE) compose when geometries couple.
Three coupling topologies under test:
| Topology | Physical picture | Expected if joint exists |
|---|---|---|
aperture |
Two cavities sharing a small opening | Joint mode appears when aperture < λ/2 of shared resonance |
shared_wall |
Cavities adjacent across a thin wall | Joint mode appears when wall thickness < skin depth at shared resonance |
near_field |
Cavities adjacent but uncoupled, control | If joint mode appears here, the "joint" signal is an artifact |
Decoh teeter-totter protocol. Each topology is driven with mismatched per-cell decoh: (0.10/0.50) → (0.30/0.30) → (0.50/0.10). The teeter-totter sweeps drive imbalance through neutral and out the other side. If the joint fingerprint is real, it should show a *non-monotonic* response to drive balance — appearing at the boundaries but vanishing at symmetric drive, or vice-versa. A monotonic response is consistent with linear mixing only.
Per-config artifacts. Each (topology, decoh_A, decoh_B) tuple produces: 1. pair.npy — full waveform of the coupled run (saved atomically: write to .tmp with explicit file handle to avoid numpy's .npy auto-append, then os.rename to final). 2. baseline_A.npy, baseline_B.npy — single-cavity controls run at the same step count (STEPS = steps_for_decoh(max(decoh_A, decoh_B))) so FFT bins align across all three sims in the config. 3. summary.json — top-30 peaks, spectrum_summary (centroid, bandwidth, entropy, band_energy_fraction), cos-distance(pair, A+B) — the fingerprint comparison. 4. Source snapshot at results_test_jj/_scripts/ with SHA256 manifest so every result is traceable to the exact code that produced it.
The previous Phase 1 attempt (aperture-only) was falsified — see the aperture-coupling-falsified log. That null result is what motivated extending Phase 1 to three topologies plus the teeter-totter. If all three topologies null out across the full decoh sweep, the joint-7-vector hypothesis is empirically dead in coupled FDTD and the framework needs to either (a) propose a different test rig (higher-dimensional simulation, non-EM substrate) or (b) accept that the seven expressions don't compose under classical EM coupling at this scale.
Pre-registration. Null result on all three topologies = joint-7-vector hypothesis falsified at FDTD scale. Joint mode appearing only in aperture + shared_wall (and not near_field) = positive evidence with the right selectivity. Joint mode appearing in near_field = artifact, halt and debug.
Summary — reader-facing
Test JJ Phase 1 looks for *emergent* spectral behavior when two FDTD cavities are coupled and driven slightly out of balance. The theory predicts that the seven foundational geometric expressions should *compose* when geometries couple — producing a joint fingerprint distinct from the sum of two single-cavity fingerprints. Phase 1 puts that prediction in front of three different coupling topologies and a sweep of drive imbalance.
Each test config produces a top-30 peak list, a four-number spectrum summary, and a cos-distance comparison between the coupled run and the two single-cavity baselines. Every artifact is archived with a SHA256 manifest of the exact script that produced it, so any result is reproducible from this page alone.
The previous aperture-only attempt was falsified — see the linked research note. Phase 1 expands to three topologies so the falsification has to hold across all of them, not just one. Pre-registered outcomes: null on all three = hypothesis dead at this scale; positive on aperture + shared_wall only = the right kind of evidence; positive on the near_field control = artifact.
Status: in progress on Hetzner. Results post here as configs complete.