Eupnea Period from the Shared Oscillator

With one time anchor — the heart's intrinsic rhythm set to the cited resting rate 1.17 Hz — the lung's breathing rate falls out of the recovery-time ratio at 16.86 breaths/min, inside the cited 12–18 band. The breath-to-beat ratio 0.240 is structural, not fitted; rate grade [L], ratio [V].

A single anchor κ = 0.016327 s/arb (heart intrinsic := resting HR 1.17 Hz) fixes the clock; the τ_s ratio then gives 16.86 breaths/min (band 12–18), ratio 0.240. [V]/[L].

One time anchor fixes the clock

A single conversion κ from model time to seconds is fixed by declaring the heart's intrinsic relaxation rhythm equal to the cited resting heart rate, 1.17 Hz (70 bpm). That gives κ = 0.016327 s/arb. Nothing else about timing is tuned: every physical rate is the model rate divided by κ.

Breathing rate falls out of the τ_s ratio

Under that one anchor the lung's relaxation rhythm is fixed by the ratio of recovery times, not by a second fit. The result is 16.86 breaths/min, squarely inside the cited eupnea band of 12–18 breaths/min.

The breath-to-beat ratio 0.240 is therefore structural: it is the τ_s ratio, not a parameter. The absolute rate carries the cited anchor's grade [L]; the ratio is verified [V].

Robust across drive

Sweeping the excitatory drive keeps the breathing rate inside or adjacent to the eupnea band and never stops the oscillation, so the result is not a fragile operating point.