Fourier-Tumble Oscillatory Memory MVP

experiment.py implements the first-Fourier recurrent channel: [ \Pi_1=\sum_j q_j e^{i\theta_j},\quad \gamma=\alpha(1-\Re\Pi_1),\quad \Omega=\alpha\Im\Pi_1, ] followed by the exact transition exp(-gamma*dt) R(Omega*dt).

Run:

/home/maxwelhelp/main/bin/python3 experiment.py

The script writes results.json and checks three mechanism predictions:

1. Discretized circular probability distributions have |Pi_1| <= 1; their recurrent Jacobian norm is no larger than one.
2. A homogeneous trajectory follows exp(-gamma*t) cos(Omega*t); fitted damping and frequency are compared to the values induced by Pi_1.
3. The envelope 1/e memory time scales as 1/gamma while the phase is fixed, with a sweep toward |Pi_1|=1.

Observed results from the fixed-seed run are in results.json: maximum sampled |Pi_1|=0.9352, maximum Jacobian norm 0.9373, and zero numerical fit error for the generated exact transition. The memory sweep increases from 1.0 steps at gamma=1 to 25.29 steps at gamma=0.0395.

The delayed-recall numbers are only a secondary, untrained sanity comparison between a fixed Fourier channel and a fixed-radius scalar retention baseline; they are not evidence of a trained task-level accuracy win. No sequential-MNIST, GRU, or optimized parameter-count-matched training experiment was run.