Classic control theory has failed. New approach: injection locking. This is a technique where an external signal forces an oscillator to synchronise to its frequency. Famous example: two pendulum clocks on the same wall — they synchronise through vibration. Applied here: if you can inject a signal at the Flamelock's thermal oscillation frequency, the Flamelock will lock to you and you can then steer it to a safe passage temperature.
Injection locking was formalised by Adler (1946). The lock range is: Δω_lock = ω₀/(2Q) × (V_inj/V_osc). For the Flamelock, Q (quality factor) ≈ 10¹⁵ (extremely high Q resonator). Your injection signal amplitude vs Flamelock: V_inj/V_osc ≈ 10⁻²⁰. Lock range: absurdly small.
| System | Lock Range | Frequency Drift | Lock Possible? |
|---|---|---|---|
| Two pendulum clocks | ~0.001 Hz | ~0.0001 Hz/s | YES (famous case) |
| Radio injection lock | ~10 kHz | ~100 Hz/s | YES (common) |
| Laser mode locking | ~100 GHz | ~1 MHz/s | YES (with effort) |
| YOU vs Flamelock | 4×10⁻²⁷ Hz | ~10⁶ Hz/s | NO (33 orders of magnitude off) |
Your injection signal is so far below the Flamelock's threshold that it doesn't even register as noise. The Flamelock's thermal oscillations would need to spontaneously drift to within 4×10⁻²⁷ Hz of your frequency. The probability: effectively zero over any meaningful timescale.