fno_findings.md

TL-Ego FNO Toy Analysis — Findings

Fourier Structure Scan (50 ticks, tick 310-359)

1. Dominant Oscillation: 5-tick Period

Both concentration and competition oscillate with a clear 5-tick (15-second) period. This is the system's fundamental attractor rhythm.

2. Spectral Slope: Near Zero (-0.12)

• Fitted slope: −0.12 (95% CI would cross 0)
• Interpretation: near-white noise (slope=0), not pink noise (slope=−1) seen in biological brains
• Meaning: The system's noise is too unstructured. A biological attractor network has 1/f noise — more power at low frequencies, giving longer coherent epochs. TL-Ego's white noise means it oscillates too fast and lacks "momentum."

3. Phase Stability: 42% Phase Transition Rate

• 21 phase transitions in 50 ticks
• Phase changes almost every 2-3 ticks
• A healthy attractor should stay in a basin for 5-10x its oscillation period

4. Cross-correlation: conc and comp Move Together

• Zero-lag coupling, no detectable time delay
• Means concentration and competition are the same dynamical variable, not independent attractor dimensions

What This Means

Good News

• Fourier structure exists — a learned operator can work
• 5-tick rhythm is stable and predictable
• The dynamics are not chaotic (ordered spectrum)

Bad News

• System is "too oscillatory" — changes phase too often
• Noise is white, not pink — lacks the long-memory structure of biological neural noise
• conc and comp are not independent coordinates — the state space is effectively 1D right now

Actionable Changes

1. Shift noise from white to pink — inject more low-frequency power
2. Increase phase dwell time — tune concentration_lock threshold higher
3. Add more attractor dimensions — introduce a third state variable (e.g., "synthesis_degree") to give conc and comp independent dynamics
4. Collect more data — trajectory logger running at 2min intervals