---
id: test-jj-phase1-coupled-cavity
type: test
title: Test JJ Phase 1 — Coupled-Cavity Joint 7-Vector Search
date_published: 2026-05-09
date_updated: 2026-05-12
project: gwc_test_jj
status: open
log_subtype: experiment
tags: [test-jj, coupled-cavity, fdtd, joint-operator, decoh, fingerprint]
author: Jonathan Shelton
data_supporting: []
data_refuting: []
predicts:
  - joint-7-vector-emerges-under-coupling
see_also:
  - aperture-coupling-falsified
attachments: []
---

## Author notes

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/<scope>_<timestamp>/` 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](/research/notes/aperture-coupling-falsified.html)
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

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.