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 set by the chosen recovery times τ_s 18 and 95, not by γ; rate grade [L], ratio [code output].

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. [code output]/[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 a [code output] of the chosen τ_s values, which are constants in repro/cardioresp/repro/_engine/vp_car_engine.py, not outputs of γ. With the same anchor, a lung τ_s of 60 / 80 / 110 / 130 gives 25.47 / 19.70 / 14.76 / 12.65 breaths/min (review run, 2026-09-29), so the in-band result depends on the choice τ_s = 95.

[observation] Resting adult heart rate is normally 60–100 bpm and resting breathing rate about 12–20 breaths/min; the measured pulse–respiration quotient is typically about 4:1 (Scholkmann & Wolf 2019, Front. Physiol. 10:371). The model's 1/0.240 ≈ 4.2 lies in that range as an output of the chosen τ_s.

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.